reconstruct

services/analysis_pipelines.ts

@@ -0,0 +1,133 @@
+// analysis_pipelines.ts - High-level workflows for common analysis tasks.
+
+import { SignalProcessor } from './signal_processing_convolution';
+import { TimeSeriesAnalyzer, STLDecomposition } from './timeseries';
+
+/**
+ * The comprehensive result of a denoise and detrend operation.
+ */
+export interface DenoiseAndDetrendResult {
+  original: number[];
+  smoothed: number[];
+  decomposition: STLDecomposition;
+}
+
+/**
+ * The result of an automatic SARIMA parameter search.
+ */
+export interface AutoArimaResult {
+  bestModel: {
+    p: number;
+    d: number;
+    q: number;
+    P: number;
+    D: number;
+    Q: number;
+    s: number;
+    aic: number;
+  };
+  searchLog: { p: number; d: number; q: number; P: number; D: number; Q: number; s: number; aic: number }[];
+}
+
+
+/**
+ * A class containing high-level analysis pipelines that combine
+ * functions from various processing libraries.
+ */
+export class AnalysisPipelines {
+
+  /**
+   * A full pipeline to take a raw signal, smooth it to remove noise,
+   * and then decompose it into trend, seasonal, and residual components.
+   * @param series The original time series data.
+   * @param period The seasonal period for STL decomposition.
+   * @param smoothWindow The window size for the initial smoothing (denoising) pass.
+   * @returns An object containing the original, smoothed, and decomposed series.
+   */
+  static denoiseAndDetrend(series: number[], period: number, smoothWindow: number = 5): DenoiseAndDetrendResult {
+    // Ensure window is odd for symmetry
+    if (smoothWindow > 1 && smoothWindow % 2 === 0) {
+        smoothWindow++;
+    }
+    const smoothed = SignalProcessor.smooth(series, {
+      method: 'gaussian',
+      windowSize: smoothWindow
+    });
+
+    const decomposition = TimeSeriesAnalyzer.stlDecomposition(smoothed, period);
+
+    return {
+      original: series,
+      smoothed: smoothed,
+      decomposition: decomposition,
+    };
+  }
+
+  /**
+   * [FINAL CORRECTED VERSION] Performs a full grid search to find the optimal SARIMA parameters.
+   * This version now correctly includes 's' in the final result object.
+   * @param series The original time series data.
+   * @param seasonalPeriod The seasonal period of the data (e.g., 7 for weekly, 12 for monthly).
+   * @returns An object containing the best model parameters and a log of the search.
+   */
+  static findBestArimaParameters(
+    series: number[], 
+    seasonalPeriod: number,
+    maxD: number = 1, 
+    maxP: number = 2, 
+    maxQ: number = 2,
+    maxSeasonalD: number = 1,
+    maxSeasonalP: number = 2,
+    maxSeasonalQ: number = 2
+  ): AutoArimaResult {
+
+    const searchLog: any[] = [];
+    let bestModel: any = { aic: Infinity };
+
+    const calculateAIC = (residuals: number[], numParams: number): number => {
+      const n = residuals.length;
+      if (n === 0) return Infinity;
+      const sse = residuals.reduce((sum, r) => sum + r * r, 0);
+      if (sse < 1e-9) return -Infinity; // Perfect fit
+      const logLikelihood = -n / 2 * (Math.log(2 * Math.PI) + Math.log(sse / n)) - n / 2;
+      return 2 * numParams - 2 * logLikelihood;
+    };
+    
+    // Grid search over all parameter combinations
+    for (let d = 0; d <= maxD; d++) {
+    for (let p = 0; p <= maxP; p++) {
+    for (let q = 0; q <= maxQ; q++) {
+    for (let D = 0; D <= maxSeasonalD; D++) {
+    for (let P = 0; P <= maxSeasonalP; P++) {
+    for (let Q = 0; Q <= maxSeasonalQ; Q++) {
+        // Skip trivial models where nothing is done
+        if (p === 0 && d === 0 && q === 0 && P === 0 && D === 0 && Q === 0) continue;
+
+        const options = { p, d, q, P, D, Q, s: seasonalPeriod };
+        try {
+            const { residuals } = TimeSeriesAnalyzer.arimaForecast(series, options, 0);
+            const numParams = p + q + P + Q;
+            const aic = calculateAIC(residuals, numParams);
+
+            // Construct the full model info object, ensuring 's' is included
+            const modelInfo = { p, d, q, P, D, Q, s: seasonalPeriod, aic };
+            searchLog.push(modelInfo);
+
+            if (modelInfo.aic < bestModel.aic) {
+              bestModel = modelInfo;
+            }
+        } catch (error) {
+            // Skip invalid parameter combinations that cause errors
+        }
+    } } } } } }
+
+    if (bestModel.aic === Infinity) {
+        throw new Error("Could not find a suitable SARIMA model. The data may be too short or complex.");
+    }
+    
+    // Sort the log by AIC for easier reading
+    searchLog.sort((a, b) => a.aic - b.aic);
+    
+    return { bestModel, searchLog };
+  }
+}

services/analytics_engine.ts

@@ -0,0 +1,208 @@
+import * as math from 'mathjs';
+import * as _ from 'lodash';
+import { DataSeries, DataMatrix, Condition, ApiResponse } from '../types/index';
+import { RollingWindow } from './rolling_window';
+import { KMeans, KMeansOptions } from './kmeans';
+import { getWeekNumber, getSameWeekDayLastYear } from './time-helper';
+import { calculateLinearRegression, generateForecast, calculatePredictionIntervals, ForecastResult } from './prediction';
+
+export const handleError = (error: unknown): string => {
+  return error instanceof Error ? error.message : 'Unknown error';
+};
+export const validateSeries = (series: DataSeries): void => {
+    if (!series || !Array.isArray(series.values) || series.values.length === 0) {
+        throw new Error('Series must contain at least one value');
+    }
+};
+
+export const validateMatrix = (matrix: DataMatrix): void => {
+    if (!matrix || !Array.isArray(matrix.data) || matrix.data.length === 0) {
+        throw new Error('Matrix must contain at least one row');
+    }
+};
+
+export class AnalyticsEngine {
+    
+    private applyConditions(series: DataSeries, conditions: Condition[] = []): number[] {
+        if (conditions.length === 0) return series.values;
+        return series.values; // TODO: Implement filtering
+    }
+
+    // Basic statistical functions
+    unique(series: DataSeries): number[] {
+        validateSeries(series);
+        return _.uniq(series.values);
+    }
+
+    mean(series: DataSeries, conditions: Condition[] = []): number {
+        validateSeries(series);
+        const filteredValues = this.applyConditions(series, conditions);
+        if (filteredValues.length === 0) throw new Error('No data points match conditions');
+        return Number(math.mean(filteredValues));
+    }
+
+    count(series: DataSeries, conditions: Condition[] = []): number {
+        validateSeries(series);
+        const filteredValues = this.applyConditions(series, conditions);
+        if (filteredValues.length === 0) throw new Error('No data points match conditions');
+        return filteredValues.length;
+    }
+
+    distinctCount(series: DataSeries, conditions: Condition[] = []): number {
+        validateSeries(series);
+        const filteredValues = this.applyConditions(series, conditions);
+        const uniqueValues = _.uniq(filteredValues);
+        return uniqueValues.length;
+    }
+
+    variance(series: DataSeries, conditions: Condition[] = []): number {
+        validateSeries(series);
+        const filteredValues = this.applyConditions(series, conditions);
+        if (filteredValues.length === 0) throw new Error('No data points match conditions');
+        return Number(math.variance(filteredValues));
+    }
+
+    standardDeviation(series: DataSeries, conditions: Condition[] = []): number {
+        validateSeries(series);
+        const filteredValues = this.applyConditions(series, conditions);
+        if (filteredValues.length === 0) throw new Error('No data points match conditions');
+        return Number(math.std(filteredValues));
+    }
+
+    percentile(series: DataSeries, percent: number, ascending: boolean = true, conditions: Condition[] = []): number {
+        validateSeries(series);
+        const filteredValues = this.applyConditions(series, conditions);
+        if (filteredValues.length === 0) throw new Error('No data points match conditions');
+        
+        const sorted = ascending ? _.sortBy(filteredValues) : _.sortBy(filteredValues).reverse();
+        const index = (percent / 100) * (sorted.length - 1);
+        const lower = Math.floor(index);
+        const upper = Math.ceil(index);
+        const weight = index % 1;
+        
+        return sorted[lower] * (1 - weight) + sorted[upper] * weight;
+    }
+
+    median(series: DataSeries, conditions: Condition[] = []): number {
+        return this.percentile(series, 50, true, conditions);
+    }
+
+    mode(series: DataSeries, conditions: Condition[] = []): number[] {
+        validateSeries(series);
+        const filteredValues = this.applyConditions(series, conditions);
+        const frequency = _.countBy(filteredValues);
+        const maxFreq = Math.max(...Object.values(frequency));
+        
+        return Object.keys(frequency)
+            .filter(key => frequency[key] === maxFreq)
+            .map(Number);
+    }
+
+    max(series: DataSeries, conditions: Condition[] = []): number {
+        validateSeries(series);
+        const filteredValues = this.applyConditions(series, conditions);
+        if (filteredValues.length === 0) throw new Error('No data points match conditions');
+        return Math.max(...filteredValues);
+    }
+
+    min(series: DataSeries, conditions: Condition[] = []): number {
+        validateSeries(series);
+        const filteredValues = this.applyConditions(series, conditions);
+        if (filteredValues.length === 0) throw new Error('No data points match conditions');
+        return Math.min(...filteredValues);
+    }
+
+    correlation(series1: DataSeries, series2: DataSeries): number {
+        validateSeries(series1);
+        validateSeries(series2);
+        
+        if (series1.values.length !== series2.values.length) {
+            throw new Error('Series must have same length for correlation');
+        }
+        
+        const x = series1.values;
+        const y = series2.values;
+        const n = x.length;
+        
+        const sumX = _.sum(x);
+        const sumY = _.sum(y);
+        const sumXY = _.sum(x.map((xi, i) => xi * y[i]));
+        const sumX2 = _.sum(x.map(xi => xi * xi));
+        const sumY2 = _.sum(y.map(yi => yi * yi));
+        
+        const numerator = n * sumXY - sumX * sumY;
+        const denominator = Math.sqrt((n * sumX2 - sumX * sumX) * (n * sumY2 - sumY * sumY));
+        
+        return numerator / denominator;
+    }
+
+    // Rolling window functions
+    rolling(series: DataSeries, windowSize: number): RollingWindow {
+        validateSeries(series);
+        if (windowSize <= 0) {
+            throw new Error('Window size must be a positive number.');
+        }
+        if (series.values.length < windowSize) {
+            return new RollingWindow([]);
+        }
+
+        const windows: number[][] = [];
+        for (let i = 0; i <= series.values.length - windowSize; i++) {
+            const window = series.values.slice(i, i + windowSize);
+            windows.push(window);
+        }
+        return new RollingWindow(windows);
+    }
+
+    movingAverage(series: DataSeries, windowSize: number): number[] {
+        return this.rolling(series, windowSize).mean();
+    }
+
+    // K-means wrapper (uses imported KMeans class)
+    kmeans(matrix: DataMatrix, nClusters: number, options: KMeansOptions = {}): { clusters: number[][][], centroids: number[][] } {
+        validateMatrix(matrix);
+        const points: number[][] = matrix.data;
+
+        // Use the new MiniBatchKMeans class
+        const kmeans = new KMeans(points, nClusters, options);
+        const result = kmeans.run();
+
+        const centroids = result.clusters.map(c => (c as any).centroid);
+        const clusters = result.clusters.map(c => (c as any).points);
+        
+        return { clusters, centroids };
+    }
+
+    // Time helper wrapper functions
+    getWeekNumber(dateString: string): number {
+        return getWeekNumber(dateString);
+    }
+
+    getSameWeekDayLastYear(dateString: string): string {
+        return getSameWeekDayLastYear(dateString);
+    }
+
+    // ========================================
+    // Prediction functions
+    // ========================================
+
+    timeSeriesForecast(series: DataSeries, forecastPeriods: number): ForecastResult {
+        validateSeries(series);
+
+        const model = calculateLinearRegression(series.values);
+        const forecast = generateForecast(model, series.values.length, forecastPeriods);
+        const predictionIntervals = calculatePredictionIntervals(series.values, model, forecast);
+        
+        return {
+            forecast,
+            predictionIntervals,
+            modelParameters: {
+                slope: model.slope,
+                intercept: model.intercept,
+            },
+        };
+    }
+}
+
+export const analytics = new AnalyticsEngine();
+

services/convolution.ts

@@ -0,0 +1,415 @@
+// convolution.ts - Convolution operations for 1D and 2D data
+
+export interface ConvolutionOptions {
+  mode?: 'full' | 'same' | 'valid';
+  boundary?: 'zero' | 'reflect' | 'symmetric';
+}
+
+export interface ConvolutionResult1D {
+  values: number[];
+  originalLength: number;
+  kernelLength: number;
+  mode: string;
+}
+
+export interface ConvolutionResult2D {
+  matrix: number[][];
+  originalDimensions: [number, number];
+  kernelDimensions: [number, number];
+  mode: string;
+}
+
+/**
+ * Validates input array for convolution operations
+ */
+function validateArray(arr: number[], name: string): void {
+  if (!Array.isArray(arr) || arr.length === 0) {
+    throw new Error(`${name} must be a non-empty array`);
+  }
+  if (arr.some(val => typeof val !== 'number' || !isFinite(val))) {
+    throw new Error(`${name} must contain only finite numbers`);
+  }
+}
+
+/**
+ * Validates 2D matrix for convolution operations
+ */
+function validateMatrix(matrix: number[][], name: string): void {
+  if (!Array.isArray(matrix) || matrix.length === 0) {
+    throw new Error(`${name} must be a non-empty 2D array`);
+  }
+  
+  const rowLength = matrix[0].length;
+  if (rowLength === 0) {
+    throw new Error(`${name} rows must be non-empty`);
+  }
+  
+  for (let i = 0; i < matrix.length; i++) {
+    if (!Array.isArray(matrix[i]) || matrix[i].length !== rowLength) {
+      throw new Error(`${name} must be a rectangular matrix`);
+    }
+    if (matrix[i].some(val => typeof val !== 'number' || !isFinite(val))) {
+      throw new Error(`${name} must contain only finite numbers`);
+    }
+  }
+}
+
+/**
+ * Applies boundary conditions to extend an array
+ */
+function applyBoundary1D(signal: number[], padding: number, boundary: string): number[] {
+  if (padding <= 0) return signal;
+  
+  let result = [...signal];
+  
+  switch (boundary) {
+    case 'zero':
+      result = new Array(padding).fill(0).concat(result).concat(new Array(padding).fill(0));
+      break;
+    case 'reflect':
+      const leftPad = [];
+      const rightPad = [];
+      for (let i = 0; i < padding; i++) {
+        leftPad.unshift(signal[Math.min(i + 1, signal.length - 1)]);
+        rightPad.push(signal[Math.max(signal.length - 2 - i, 0)]);
+      }
+      result = leftPad.concat(result).concat(rightPad);
+      break;
+    case 'symmetric':
+      const leftSymPad = [];
+      const rightSymPad = [];
+      for (let i = 0; i < padding; i++) {
+        leftSymPad.unshift(signal[Math.min(i, signal.length - 1)]);
+        rightSymPad.push(signal[Math.max(signal.length - 1 - i, 0)]);
+      }
+      result = leftSymPad.concat(result).concat(rightSymPad);
+      break;
+    default:
+      throw new Error(`Unsupported boundary condition: ${boundary}`);
+  }
+  
+  return result;
+}
+
+/**
+ * Performs 1D convolution between signal and kernel
+ * 
+ * @param signal - Input signal array
+ * @param kernel - Convolution kernel array
+ * @param options - Convolution options (mode, boundary)
+ * @returns Convolution result with metadata
+ */
+/**
+ * [CORRECTED] Performs 1D convolution between signal and kernel
+ */
+export function convolve1D(
+  signal: number[], 
+  kernel: number[], 
+  options: ConvolutionOptions = {}
+): ConvolutionResult1D {
+  validateArray(signal, 'Signal');
+  validateArray(kernel, 'Kernel');
+  
+  const { mode = 'full', boundary = 'zero' } = options;
+  const flippedKernel = [...kernel].reverse();
+  
+  const signalLen = signal.length;
+  const kernelLen = flippedKernel.length;
+  
+  const outputLength = mode === 'full' ? signalLen + kernelLen - 1 :
+                      mode === 'same' ? signalLen :
+                      signalLen - kernelLen + 1;
+
+  const result: number[] = new Array(outputLength);
+  
+  const halfKernelLen = Math.floor(kernelLen / 2);
+
+  for (let i = 0; i < outputLength; i++) {
+    let sum = 0;
+    for (let j = 0; j < kernelLen; j++) {
+      let signalIdx: number;
+
+      switch (mode) {
+        case 'full':
+          signalIdx = i - j;
+          break;
+        case 'same':
+          signalIdx = i - halfKernelLen + j;
+          break;
+        case 'valid':
+          signalIdx = i + j;
+          break;
+      }
+
+      // Handle boundary conditions
+      if (signalIdx >= 0 && signalIdx < signalLen) {
+        sum += signal[signalIdx] * flippedKernel[j];
+      } else if (boundary !== 'zero' && (mode === 'full' || mode === 'same')) {
+        // This is a simplified boundary handler for the logic. Your more complex handler can be used here.
+        let boundaryIdx = signalIdx;
+        if (signalIdx < 0) {
+            boundaryIdx = boundary === 'reflect' ? -signalIdx -1 : -signalIdx;
+        } else if (signalIdx >= signalLen) {
+            boundaryIdx = boundary === 'reflect' ? 2 * signalLen - signalIdx - 1 : 2 * signalLen - signalIdx - 2;
+        }
+        boundaryIdx = Math.max(0, Math.min(signalLen - 1, boundaryIdx));
+        sum += signal[boundaryIdx] * flippedKernel[j];
+      }
+      // If boundary is 'zero', we add nothing, which is correct.
+    }
+    result[i] = sum;
+  }
+  
+  return {
+    values: result,
+    originalLength: signalLen,
+    kernelLength: kernelLen,
+    mode
+  };
+}
+
+/**
+ * Performs 2D convolution between matrix and kernel
+ * 
+ * @param matrix - Input 2D matrix
+ * @param kernel - 2D convolution kernel
+ * @param options - Convolution options (mode, boundary)
+ * @returns 2D convolution result with metadata
+ */
+export function convolve2D(
+  matrix: number[][], 
+  kernel: number[][], 
+  options: ConvolutionOptions = {}
+): ConvolutionResult2D {
+  validateMatrix(matrix, 'Matrix');
+  validateMatrix(kernel, 'Kernel');
+  
+  const { mode = 'same', boundary = 'reflect' } = options;
+  
+  // Flip kernel for convolution
+  const flippedKernel = kernel.map(row => [...row].reverse()).reverse();
+  
+  const matrixRows = matrix.length;
+  const matrixCols = matrix[0].length;
+  const kernelRows = flippedKernel.length;
+  const kernelCols = flippedKernel[0].length;
+  
+  // Calculate output dimensions
+  let outputRows: number, outputCols: number;
+  let padTop: number, padLeft: number;
+  
+  switch (mode) {
+    case 'full':
+      outputRows = matrixRows + kernelRows - 1;
+      outputCols = matrixCols + kernelCols - 1;
+      padTop = kernelRows - 1;
+      padLeft = kernelCols - 1;
+      break;
+    case 'same':
+      outputRows = matrixRows;
+      outputCols = matrixCols;
+      padTop = Math.floor(kernelRows / 2);
+      padLeft = Math.floor(kernelCols / 2);
+      break;
+    case 'valid':
+      outputRows = Math.max(0, matrixRows - kernelRows + 1);
+      outputCols = Math.max(0, matrixCols - kernelCols + 1);
+      padTop = 0;
+      padLeft = 0;
+      break;
+    default:
+      throw new Error(`Unsupported convolution mode: ${mode}`);
+  }
+  
+  // Create padded matrix based on boundary conditions
+  const totalPadRows = mode === 'valid' ? 0 : kernelRows - 1;
+  const totalPadCols = mode === 'valid' ? 0 : kernelCols - 1;
+  
+  const paddedMatrix: number[][] = [];
+  
+  // Initialize padded matrix with boundary conditions
+  for (let i = -padTop; i < matrixRows + totalPadRows - padTop; i++) {
+    const row: number[] = [];
+    for (let j = -padLeft; j < matrixCols + totalPadCols - padLeft; j++) {
+      let value = 0;
+      
+      if (i >= 0 && i < matrixRows && j >= 0 && j < matrixCols) {
+        value = matrix[i][j];
+      } else if (boundary !== 'zero') {
+        // Apply boundary conditions
+        let boundaryI = i;
+        let boundaryJ = j;
+        
+        if (boundary === 'reflect') {
+          boundaryI = i < 0 ? -i - 1 : i >= matrixRows ? 2 * matrixRows - i - 1 : i;
+          boundaryJ = j < 0 ? -j - 1 : j >= matrixCols ? 2 * matrixCols - j - 1 : j;
+        } else if (boundary === 'symmetric') {
+          boundaryI = i < 0 ? -i : i >= matrixRows ? 2 * matrixRows - i - 2 : i;
+          boundaryJ = j < 0 ? -j : j >= matrixCols ? 2 * matrixCols - j - 2 : j;
+        }
+        
+        boundaryI = Math.max(0, Math.min(boundaryI, matrixRows - 1));
+        boundaryJ = Math.max(0, Math.min(boundaryJ, matrixCols - 1));
+        value = matrix[boundaryI][boundaryJ];
+      }
+      
+      row.push(value);
+    }
+    paddedMatrix.push(row);
+  }
+  
+  // Perform 2D convolution
+  const result: number[][] = [];
+  
+  for (let i = 0; i < outputRows; i++) {
+    const row: number[] = [];
+    for (let j = 0; j < outputCols; j++) {
+      let sum = 0;
+      
+      for (let ki = 0; ki < kernelRows; ki++) {
+        for (let kj = 0; kj < kernelCols; kj++) {
+          const matrixI = i + ki;
+          const matrixJ = j + kj;
+          
+          if (matrixI >= 0 && matrixI < paddedMatrix.length &&
+              matrixJ >= 0 && matrixJ < paddedMatrix[0].length) {
+            sum += paddedMatrix[matrixI][matrixJ] * flippedKernel[ki][kj];
+          }
+        }
+      }
+      
+      row.push(sum);
+    }
+    result.push(row);
+  }
+  
+  return {
+    matrix: result,
+    originalDimensions: [matrixRows, matrixCols],
+    kernelDimensions: [kernelRows, kernelCols],
+    mode
+  };
+}
+
+/**
+ * Creates common convolution kernels
+ */
+export class ConvolutionKernels {
+  /**
+   * Creates a Gaussian blur kernel
+   */
+  static gaussian(size: number, sigma: number = 1.0): number[][] {
+    if (size % 2 === 0) {
+      throw new Error('Kernel size must be odd');
+    }
+    
+    const kernel: number[][] = [];
+    const center = Math.floor(size / 2);
+    let sum = 0;
+    
+    for (let i = 0; i < size; i++) {
+      const row: number[] = [];
+      for (let j = 0; j < size; j++) {
+        const x = i - center;
+        const y = j - center;
+        const value = Math.exp(-(x * x + y * y) / (2 * sigma * sigma));
+        row.push(value);
+        sum += value;
+      }
+      kernel.push(row);
+    }
+    
+    // Normalize kernel
+    return kernel.map(row => row.map(val => val / sum));
+  }
+  
+  /**
+   * Creates a Sobel edge detection kernel
+   */
+  static sobel(direction: 'x' | 'y' = 'x'): number[][] {
+    if (direction === 'x') {
+      return [
+        [-1, 0, 1],
+        [-2, 0, 2],
+        [-1, 0, 1]
+      ];
+    } else {
+      return [
+        [-1, -2, -1],
+        [ 0,  0,  0],
+        [ 1,  2,  1]
+      ];
+    }
+  }
+  
+  /**
+   * Creates a Laplacian edge detection kernel
+   */
+  static laplacian(): number[][] {
+    return [
+      [ 0, -1,  0],
+      [-1,  4, -1],
+      [ 0, -1,  0]
+    ];
+  }
+  
+  /**
+   * Creates a box/average blur kernel
+   */
+  static box(size: number): number[][] {
+    if (size % 2 === 0) {
+      throw new Error('Kernel size must be odd');
+    }
+    
+    const value = 1 / (size * size);
+    const kernel: number[][] = [];
+    
+    for (let i = 0; i < size; i++) {
+      kernel.push(new Array(size).fill(value));
+    }
+    
+    return kernel;
+  }
+  
+  /**
+   * Creates a 1D Gaussian kernel
+   */
+  static gaussian1D(size: number, sigma: number = 1.0): number[] {
+    if (size % 2 === 0) {
+      throw new Error('Kernel size must be odd');
+    }
+    
+    const kernel: number[] = [];
+    const center = Math.floor(size / 2);
+    let sum = 0;
+    
+    for (let i = 0; i < size; i++) {
+      const x = i - center;
+      const value = Math.exp(-(x * x) / (2 * sigma * sigma));
+      kernel.push(value);
+      sum += value;
+    }
+    
+    // Normalize kernel
+    return kernel.map(val => val / sum);
+  }
+  
+  /**
+   * Creates a 1D difference kernel for edge detection
+   */
+  static difference1D(): number[] {
+    return [-1, 0, 1];
+  }
+  
+  /**
+   * Creates a 1D moving average kernel
+   */
+  static average1D(size: number): number[] {
+    if (size <= 0) {
+      throw new Error('Kernel size must be positive');
+    }
+    
+    const value = 1 / size;
+    return new Array(size).fill(value);
+  }
+}

services/kmeans.ts

@@ -0,0 +1,144 @@
+export type Point = number[];
+
+export interface Cluster {
+    centroid: Point;
+    points: Point[];
+}
+
+export interface KMeansOptions {
+    batchSize?: number;
+    maxIterations?: number;
+    tolerance?: number;
+}
+
+export interface KMeansResult {
+    clusters: Cluster[];
+    iterations: number;
+    converged: boolean;
+}
+
+export class KMeans {
+    private readonly k: number;
+    private readonly batchSize: number;
+    private readonly maxIterations: number;
+    private readonly tolerance: number;
+    private readonly data: Point[];
+    private centroids: Point[] = [];
+
+    constructor(data: Point[], k: number, options: KMeansOptions = {}) {
+        this.data = data;
+        this.k = k;
+        this.batchSize = options.batchSize ?? 32;
+        this.maxIterations = options.maxIterations ?? 100;
+        this.tolerance = options.tolerance ?? 0.0001;
+    }
+
+    private static euclideanDistance(p1: Point, p2: Point): number {
+        return Math.sqrt(p1.reduce((sum, val, i) => sum + (val - p2[i]) ** 2, 0));
+    }
+
+    private initializeCentroids(): void {
+        const dataCopy = [...this.data];
+        for (let i = 0; i < this.k; i++) {
+            const randomIndex = Math.floor(Math.random() * dataCopy.length);
+            this.centroids.push([...dataCopy[randomIndex]]);
+            dataCopy.splice(randomIndex, 1);
+        }
+    }
+
+    /**
+     * Creates a random sample of the data.
+     */
+    private createMiniBatch(): Point[] {
+        const miniBatch: Point[] = [];
+        const dataCopy = [...this.data];
+        for (let i = 0; i < this.batchSize && dataCopy.length > 0; i++) {
+            const randomIndex = Math.floor(Math.random() * dataCopy.length);
+            miniBatch.push(dataCopy[randomIndex]);
+            dataCopy.splice(randomIndex, 1);
+        }
+        return miniBatch;
+    }
+    
+    /**
+     * Assigns all points in the full dataset to the final centroids.
+     */
+    private assignFinalClusters(): Cluster[] {
+        const clusters: Cluster[] = this.centroids.map(c => ({ centroid: c, points: [] }));
+
+        for (const point of this.data) {
+            let minDistance = Infinity;
+            let closestClusterIndex = -1;
+            for (let i = 0; i < this.centroids.length; i++) {
+                const distance = KMeans.euclideanDistance(point, this.centroids[i]);
+                if (distance < minDistance) {
+                    minDistance = distance;
+                    closestClusterIndex = i;
+                }
+            }
+            if (closestClusterIndex !== -1) {
+                clusters[closestClusterIndex].points.push(point);
+            }
+        }
+        return clusters;
+    }
+
+    public run(): KMeansResult {
+        this.initializeCentroids();
+        
+        const clusterPointCounts = new Array(this.k).fill(0);
+        let converged = false;
+        let iterations = 0;
+
+        for (let i = 0; i < this.maxIterations; i++) {
+            iterations = i + 1;
+            const miniBatch = this.createMiniBatch();
+            const previousCentroids = this.centroids.map(c => [...c]);
+
+            // Assign points in the batch and update centroids gradually
+            for (const point of miniBatch) {
+                let minDistance = Infinity;
+                let closestClusterIndex = -1;
+
+                for (let j = 0; j < this.k; j++) {
+                    const distance = KMeans.euclideanDistance(point, this.centroids[j]);
+                    if (distance < minDistance) {
+                        minDistance = distance;
+                        closestClusterIndex = j;
+                    }
+                }
+
+                if (closestClusterIndex !== -1) {
+                    clusterPointCounts[closestClusterIndex]++;
+                    const learningRate = 1 / clusterPointCounts[closestClusterIndex];
+                    const centroidToUpdate = this.centroids[closestClusterIndex];
+
+                    // Move the centroid slightly towards the new point
+                    for (let dim = 0; dim < centroidToUpdate.length; dim++) {
+                        centroidToUpdate[dim] = (1 - learningRate) * centroidToUpdate[dim] + learningRate * point[dim];
+                    }
+                }
+            }
+            
+            // Check for convergence
+            let totalMovement = 0;
+            for(let j = 0; j < this.k; j++) {
+                totalMovement += KMeans.euclideanDistance(previousCentroids[j], this.centroids[j]);
+            }
+            
+            if (totalMovement < this.tolerance) {
+                converged = true;
+                break;
+            }
+        }
+        
+        // After training, assign all points to the final centroids
+        const finalClusters = this.assignFinalClusters();
+
+        return {
+            clusters: finalClusters,
+            iterations,
+            converged
+        };
+    }
+}

services/pivot_table.ts

@@ -0,0 +1,36 @@
+import { analytics } from './analytics_engine'; // Import your analytics engine
+
+export interface PivotOptions {
+  index: string[];
+  columns: string[];
+  values: string;
+  aggFunc?: (items: number[]) => number; // Aggregation function (e.g., analytics.mean)
+}
+
+export function pivotTable(
+  data: Record<string, any>[],
+  options: PivotOptions
+): Record<string, Record<string, number>> {
+  const { index, columns, values, aggFunc = arr => arr.reduce((a, b) => a + b, 0) } = options;
+  const cellMap: Record<string, Record<string, number[]>> = {};
+
+  data.forEach(row => {
+    const rowKey = index.map(k => row[k]).join('|');
+    const colKey = columns.map(k => row[k]).join('|');
+
+    if (!cellMap[rowKey]) cellMap[rowKey] = {};
+    if (!cellMap[rowKey][colKey]) cellMap[rowKey][colKey] = [];
+    cellMap[rowKey][colKey].push(row[values]);
+  });
+
+  // Apply aggregation function to each cell
+  const result: Record<string, Record<string, number>> = {};
+  Object.entries(cellMap).forEach(([rowKey, cols]) => {
+    result[rowKey] = {};
+    Object.entries(cols).forEach(([colKey, valuesArr]) => {
+      result[rowKey][colKey] = aggFunc(valuesArr);
+    });
+  });
+
+  return result;
+}

services/prediction.ts

@@ -0,0 +1,101 @@
+import * as math from 'mathjs';
+
+// The structure for the returned regression model
+export interface LinearRegressionModel {
+  slope: number;
+  intercept: number;
+  predict: (x: number) => number;
+}
+
+// The structure for the full forecast output
+export interface ForecastResult {
+  forecast: number[];
+  predictionIntervals: {
+    upperBound: number[];
+    lowerBound: number[];
+  };
+  modelParameters: {
+    slope: number;
+    intercept: number;
+  };
+}
+
+/**
+ * Calculates the linear regression model from a time series.
+ * @param yValues The historical data points (e.g., sales per month).
+ * @returns {LinearRegressionModel} An object containing the model's parameters and a predict function.
+ */
+export function calculateLinearRegression(yValues: number[]): LinearRegressionModel {
+  if (yValues.length < 2) {
+    throw new Error('At least two data points are required for linear regression.');
+  }
+  
+  const xValues = Array.from({ length: yValues.length }, (_, i) => i);
+
+  const meanX = Number(math.mean(xValues));
+  const meanY = Number(math.mean(yValues));
+  const stdDevX = Number(math.std(xValues, 'uncorrected'));
+  const stdDevY = Number(math.std(yValues, 'uncorrected'));
+
+  // Ensure stdDevX is not zero to avoid division by zero
+  if (stdDevX === 0) {
+    // This happens if all xValues are the same, which is impossible in this time series context,
+    // but it's good practice to handle. A vertical line has an infinite slope.
+    // For simplicity, we can return a model with zero slope.
+    return { slope: 0, intercept: meanY, predict: (x: number) => meanY };
+  }
+
+  // Cast the result of math.sum to a Number
+  const correlationNumerator = Number(math.sum(xValues.map((x, i) => (x - meanX) * (yValues[i] - meanY))));
+  
+  const correlation = correlationNumerator / ((xValues.length) * stdDevX * stdDevY);
+
+  const slope = correlation * (stdDevY / stdDevX);
+  const intercept = meanY - slope * meanX;
+
+  const predict = (x: number): number => slope * x + intercept;
+
+  return { slope, intercept, predict };
+}
+
+/**
+ * Generates a forecast for a specified number of future periods.
+ * @param model The calculated linear regression model.
+ * @param historicalDataLength The number of historical data points.
+ * @param forecastPeriods The number of future periods to predict.
+ * @returns {number[]} An array of forecasted values.
+ */
+export function generateForecast(model: LinearRegressionModel, historicalDataLength: number, forecastPeriods: number): number[] {
+  const forecast: number[] = [];
+  const startPeriod = historicalDataLength;
+
+  for (let i = 0; i < forecastPeriods; i++) {
+    const futureX = startPeriod + i;
+    forecast.push(model.predict(futureX));
+  }
+  return forecast;
+}
+
+/**
+ * Calculates prediction intervals to show the range of uncertainty.
+ * @param yValues The original historical data.
+ * @param model The calculated linear regression model.
+ * @param forecast The array of forecasted values.
+ * @returns An object with upperBound and lowerBound arrays.
+ */
+export function calculatePredictionIntervals(yValues: number[], model: LinearRegressionModel, forecast: number[]) {
+  const n = yValues.length;
+  const residualsSquaredSum = yValues.reduce((sum, y, i) => {
+    const predictedY = model.predict(i);
+    return sum + (y - predictedY) ** 2;
+  }, 0);
+  const stdError = Math.sqrt(residualsSquaredSum / (n - 2));
+
+  const zScore = 1.96; // For a 95% confidence level
+  const marginOfError = zScore * stdError;
+
+  const upperBound = forecast.map(val => val + marginOfError);
+  const lowerBound = forecast.map(val => val - marginOfError);
+
+  return { upperBound, lowerBound };
+}

services/retail_metrics.ts

@@ -0,0 +1,77 @@
+    export function purchaseIndex(totalItemsSold: number, numberOfCustomers: number): number { 
+        if (numberOfCustomers === 0) {
+            throw new Error('Number of customers cannot be zero');
+        }
+        return (totalItemsSold / numberOfCustomers) * 1000;
+    }
+
+    export function purchaseRate(productPurchases: number, totalTransactions: number): number;
+    export function purchaseRate(productPurchases: number[], totalTransactions: number[]): number[];
+    export function purchaseRate(productPurchases: number | number[], totalTransactions: number | number[]): number | number[] {
+        if (Array.isArray(productPurchases) && Array.isArray(totalTransactions)) {
+            if (productPurchases.length !== totalTransactions.length) throw new Error('Arrays must have the same length');
+            return productPurchases.map((pp, i) => purchaseRate(pp, totalTransactions[i]));
+        }
+    if (typeof productPurchases === 'number' && typeof totalTransactions === 'number') {
+        if (totalTransactions === 0) throw new Error('Total transactions cannot be zero');
+        return (productPurchases / totalTransactions) * 100;
+    }
+    throw new Error('Input types must match');
+    }
+
+    export function liftValue(jointPurchaseRate: number, productAPurchaseRate: number, productBPurchaseRate: number): number;
+    export function liftValue(jointPurchaseRate: number[], productAPurchaseRate: number[], productBPurchaseRate: number[]): number[];
+    export function liftValue(jointPurchaseRate: number | number[], productAPurchaseRate: number | number[], productBPurchaseRate: number | number[]): number | number[] {
+    if (Array.isArray(jointPurchaseRate) && Array.isArray(productAPurchaseRate) && Array.isArray(productBPurchaseRate)) {
+        if (jointPurchaseRate.length !== productAPurchaseRate.length || jointPurchaseRate.length !== productBPurchaseRate.length) throw new Error('Arrays must have the same length');
+        return jointPurchaseRate.map((jpr, i) => liftValue(jpr, productAPurchaseRate[i], productBPurchaseRate[i]));
+    }
+    if (typeof jointPurchaseRate === 'number' && typeof productAPurchaseRate === 'number' && typeof productBPurchaseRate === 'number') {
+        const expectedJointRate = productAPurchaseRate * productBPurchaseRate;
+        if (expectedJointRate === 0) throw new Error('Expected joint rate cannot be zero');
+        return jointPurchaseRate / expectedJointRate;
+    }
+    throw new Error('Input types must match');
+    }
+
+    export function costRatio(cost: number, salePrice: number): number;
+    export function costRatio(cost: number[], salePrice: number[]): number[];
+    export function costRatio(cost: number | number[], salePrice: number | number[]): number | number[] {
+    if (Array.isArray(cost) && Array.isArray(salePrice)) {
+        if (cost.length !== salePrice.length) throw new Error('Arrays must have the same length');
+        return cost.map((c, i) => costRatio(c, salePrice[i]));
+    }
+    if (typeof cost === 'number' && typeof salePrice === 'number') {
+        if (salePrice === 0) throw new Error('Sale price cannot be zero');
+        return cost / salePrice;
+    }
+    throw new Error('Input types must match');
+    }
+
+    export function grossMarginRate(salePrice: number, cost: number): number;
+    export function grossMarginRate(salePrice: number[], cost: number[]): number[];
+    export function grossMarginRate(salePrice: number | number[], cost: number | number[]): number | number[] {
+        if (Array.isArray(salePrice) && Array.isArray(cost)) {
+            if (salePrice.length !== cost.length) throw new Error('Arrays must have the same length');
+            return salePrice.map((sp, i) => grossMarginRate(sp, cost[i]));
+        }
+        if (typeof salePrice === 'number' && typeof cost === 'number') {
+            if (salePrice === 0) throw new Error('Sale price cannot be zero');
+            return (salePrice - cost) / salePrice;
+        }
+        throw new Error('Input types must match');
+    }
+
+    export function averageSpendPerCustomer(totalRevenue: number, numberOfCustomers: number): number;
+    export function averageSpendPerCustomer(totalRevenue: number[], numberOfCustomers: number[]): number[];
+    export function averageSpendPerCustomer(totalRevenue: number | number[], numberOfCustomers: number | number[]): number | number[] {
+        if (Array.isArray(totalRevenue) && Array.isArray(numberOfCustomers)) {
+            if (totalRevenue.length !== numberOfCustomers.length) throw new Error('Arrays must have the same length');
+            return totalRevenue.map((tr, i) => averageSpendPerCustomer(tr, numberOfCustomers[i]));
+        }
+        if (typeof totalRevenue === 'number' && typeof numberOfCustomers === 'number') {
+            if (numberOfCustomers === 0) throw new Error('Number of customers cannot be zero');
+            return totalRevenue / numberOfCustomers;
+        }
+        throw new Error('Input types must match');
+    }

services/rolling_window.ts

@@ -0,0 +1,30 @@
+import * as math from 'mathjs';
+import * as _ from 'lodash';
+
+export class RollingWindow {
+    private windows: number[][];
+
+    constructor(windows: number[][]) {
+        this.windows = windows;
+    }
+
+    mean(): number[] {
+        return this.windows.map(window => Number(math.mean(window)));
+    }
+
+    sum(): number[] {
+        return this.windows.map(window => _.sum(window));
+    }
+
+    min(): number[] {
+        return this.windows.map(window => Math.min(...window));
+    }
+
+    max(): number[] {
+        return this.windows.map(window => Math.max(...window));
+    }
+
+    toArray(): number[][] {
+        return this.windows;
+    }
+}

services/signal_processing_convolution.ts

@@ -0,0 +1,671 @@
+// signal-processing.ts - Convolution-based signal processing functions
+import { convolve1D, convolve2D, ConvolutionKernels, ConvolutionOptions } from './convolution';
+
+export interface SmoothingOptions {
+  method?: 'gaussian' | 'moving_average';
+  windowSize?: number;
+  sigma?: number;
+}
+
+export interface EdgeDetectionOptions {
+  method?: 'sobel' | 'laplacian' | 'canny';
+  threshold?: number;
+}
+
+export interface FilterOptions {
+  type: 'lowpass' | 'highpass' | 'bandpass' | 'bandstop';
+  cutoffLow?: number;
+  cutoffHigh?: number;
+  order?: number;
+}
+
+export interface DerivativeOptions {
+  order?: 1 | 2;
+  method?: 'gradient' | 'laplacian';
+}
+
+/**
+ * Convolution-Based Signal Processing Library
+ * Functions that leverage convolution operations for signal processing
+ */
+export class SignalProcessor {
+  
+  /**
+   * Smooth a 1D signal using convolution-based methods
+   */
+  static smooth(signal: number[], options: SmoothingOptions = {}): number[] {
+    const { method = 'gaussian', windowSize = 5, sigma = 1.0 } = options;
+
+    if (signal.length === 0) {
+      throw new Error('Signal cannot be empty');
+    }
+    
+    let kernel: number[];
+    
+    switch (method) {
+      case 'gaussian':
+        kernel = ConvolutionKernels.gaussian1D(windowSize, sigma);
+        break;
+        
+      case 'moving_average':
+        kernel = ConvolutionKernels.average1D(windowSize);
+        break;
+           
+      default:
+        throw new Error(`Unsupported smoothing method: ${method}`);
+    }
+    
+    return convolve1D(signal, kernel, { mode: 'same' }).values;
+  }
+
+  /**
+   * Detect edges in 2D image data using convolution-based methods
+   */
+  static detectEdges2D(image: number[][], options: EdgeDetectionOptions = {}): number[][] {
+    const { method = 'sobel', threshold = 0.1 } = options;
+    
+    let kernelX: number[][];
+    let kernelY: number[][];
+    
+    switch (method) {
+      case 'sobel':
+        kernelX = ConvolutionKernels.sobel("x");
+        kernelY = ConvolutionKernels.sobel("y");
+        break;
+        
+      case 'laplacian':
+        const laplacianKernel = ConvolutionKernels.laplacian();
+        return convolve2D(image, laplacianKernel, { mode: 'same' }).matrix.map(row =>
+          row.map(val => Math.abs(val) > threshold ? Math.abs(val) : 0)
+        );
+        
+      default:
+        throw new Error(`Unsupported edge detection method: ${method}`);
+    }
+    
+    // Apply both kernels and combine results
+    const edgesX = convolve2D(image, kernelX, { mode: 'same' }).matrix;
+    const edgesY = convolve2D(image, kernelY, { mode: 'same' }).matrix;
+    
+    // Calculate gradient magnitude
+    const result: number[][] = [];
+    for (let i = 0; i < edgesX.length; i++) {
+      result[i] = [];
+      for (let j = 0; j < edgesX[i].length; j++) {
+        const magnitude = Math.sqrt(edgesX[i][j] ** 2 + edgesY[i][j] ** 2);
+        result[i][j] = magnitude > threshold ? magnitude : 0;
+      }
+    }
+    
+    return result;
+  }
+
+  /**
+   * Apply digital filters using convolution
+   */
+  static filter(signal: number[], options: FilterOptions): number[] {
+    const { type, cutoffLow = 0.1, cutoffHigh = 0.5, order = 4 } = options;
+    
+    let kernel: number[];
+    
+    switch (type) {
+      case 'lowpass':
+        // Low-pass filter using Gaussian kernel
+        kernel = ConvolutionKernels.gaussian1D(order * 4 + 1, order / 2);
+        return convolve1D(signal, kernel, { mode: 'same' }).values;
+        
+      case 'highpass':
+        // High-pass filter using difference of Gaussians
+        const lpKernel = ConvolutionKernels.gaussian1D(order * 4 + 1, order / 2);
+        const smoothed = convolve1D(signal, lpKernel, { mode: 'same' }).values;
+        return signal.map((val, i) => val - smoothed[i]);
+        
+      case 'bandpass':
+        // Band-pass as combination of high-pass and low-pass
+        const hp = this.filter(signal, { type: 'highpass', cutoffLow, order });
+        return this.filter(hp, { type: 'lowpass', cutoffLow: cutoffHigh, order });
+        
+      case 'bandstop':
+        // Band-stop as original minus band-pass
+        const bp = this.filter(signal, { type: 'bandpass', cutoffLow, cutoffHigh, order });
+        return signal.map((val, i) => val - bp[i]);
+        
+      default:
+        throw new Error(`Unsupported filter type: ${type}`);
+    }
+  }
+
+  /**
+   * Calculate derivatives using convolution with derivative kernels
+   */
+  static derivative(signal: number[], options: DerivativeOptions = {}): number[] {
+    const { order = 1, method = 'gradient' } = options;
+    
+    let kernel: number[];
+    
+    if (method === 'gradient') {
+      switch (order) {
+        case 1:
+          // First derivative using gradient kernel
+          kernel = [-0.5, 0, 0.5]; // Simple gradient
+          break;
+        case 2:
+          // Second derivative using Laplacian-like kernel
+          kernel = [1, -2, 1]; // Simple second derivative
+          break;
+        default:
+          throw new Error(`Unsupported derivative order: ${order}`);
+      }
+    } else if (method === 'laplacian' && order === 2) {
+      // 1D Laplacian
+      kernel = [1, -2, 1];
+    } else {
+      throw new Error(`Unsupported derivative method: ${method}`);
+    }
+    
+    return convolve1D(signal, kernel, { mode: 'same' }).values;
+  }
+
+  /**
+   * Blur 2D image using Gaussian convolution
+   */
+  static blur2D(image: number[][], sigma: number = 1.0, kernelSize?: number): number[][] {
+    const size = kernelSize || Math.ceil(sigma * 6) | 1; // Ensure odd size
+    const kernel = ConvolutionKernels.gaussian(size, sigma);
+
+    return convolve2D(image, kernel, { mode: 'same' }).matrix;
+  }
+
+  /**
+   * Sharpen 2D image using unsharp masking (convolution-based)
+   */
+  static sharpen2D(image: number[][], strength: number = 1.0): number[][] {
+    const sharpenKernel = [
+      [0, -strength, 0],
+      [-strength, 1 + 4 * strength, -strength],
+      [0, -strength, 0]
+    ];
+    
+    return convolve2D(image, sharpenKernel, { mode: 'same' }).matrix;
+  }
+
+  /**
+   * Apply emboss effect using convolution
+   */
+  static emboss2D(image: number[][], direction: 'ne' | 'nw' | 'se' | 'sw' = 'ne'): number[][] {
+    const embossKernels = {
+      ne: [[-2, -1, 0], [-1, 1, 1], [0, 1, 2]],
+      nw: [[0, -1, -2], [1, 1, -1], [2, 1, 0]],
+      se: [[0, 1, 2], [-1, 1, 1], [-2, -1, 0]],
+      sw: [[2, 1, 0], [1, 1, -1], [0, -1, -2]]
+    };
+    
+    const kernel = embossKernels[direction];
+    return convolve2D(image, kernel, { mode: 'same' }).matrix;
+  }
+
+  /**
+   * Apply motion blur using directional convolution kernel
+   */
+  static motionBlur(signal: number[], direction: number, length: number = 9): number[] {
+    // Create motion blur kernel
+    const kernel = new Array(length).fill(1 / length);
+    
+    return convolve1D(signal, kernel, { mode: 'same' }).values;
+  }
+
+  /**
+   * Detect impulse response using convolution with known impulse
+   */
+  static matchedFilter(signal: number[], template: number[]): number[] {
+    // Matched filter using cross-correlation (convolution with reversed template)
+    const reversedTemplate = [...template].reverse();
+    return convolve1D(signal, reversedTemplate, { mode: 'same' }).values;
+  }
+
+  /**
+   * Apply median filtering (note: not convolution-based, but commonly used with other filters)
+   */
+  static medianFilter(signal: number[], windowSize: number = 3): number[] {
+    const result: number[] = [];
+    const halfWindow = Math.floor(windowSize / 2);
+    
+    for (let i = 0; i < signal.length; i++) {
+      const window: number[] = [];
+      
+      for (let j = Math.max(0, i - halfWindow); j <= Math.min(signal.length - 1, i + halfWindow); j++) {
+        window.push(signal[j]);
+      }
+      
+      window.sort((a, b) => a - b);
+      const median = window[Math.floor(window.length / 2)];
+      result.push(median);
+    }
+    
+    return result;
+  }
+
+  /**
+   * Cross-correlation using convolution
+   */
+  static crossCorrelate(signal1: number[], signal2: number[]): number[] {
+    // Cross-correlation is convolution with one signal reversed
+    const reversedSignal2 = [...signal2].reverse();
+    return convolve1D(signal1, reversedSignal2, { mode: 'full' }).values;
+  }
+
+  /**
+   * Auto-correlation using convolution
+   */
+  static autoCorrelate(signal: number[]): number[] {
+    return this.crossCorrelate(signal, signal);
+  }
+
+  /**
+   * Detect peaks using convolution-based edge detection
+   */
+  /**
+   * [REWRITTEN] Detects peaks (local maxima) in a 1D signal.
+   * This is a more robust method that directly finds local maxima.
+   */
+  static detectPeaksConvolution(signal: number[], options: {
+    smoothWindow?: number;
+    threshold?: number;
+    minDistance?: number;
+  } = {}): { index: number; value: number }[] {
+    const { smoothWindow = 0, threshold = -Infinity, minDistance = 1 } = options;
+
+    let processedSignal = signal;
+    // Optionally smooth the signal first to reduce noise
+    if (smoothWindow > 1) {
+      processedSignal = this.smooth(signal, { method: 'gaussian', windowSize: smoothWindow });
+    }
+    
+    const peaks: { index: number; value: number }[] = [];
+
+    // Find all points that are higher than their immediate neighbors
+    for (let i = 1; i < processedSignal.length - 1; i++) {
+      const prev = processedSignal[i - 1];
+      const curr = processedSignal[i];
+      const next = processedSignal[i + 1];
+
+      if (curr > prev && curr > next && curr > threshold) {
+        peaks.push({ index: i, value: signal[i] }); // Store index and ORIGINAL value
+      }
+    }
+
+    // Check boundaries: Is the first or last point a peak?
+    if (processedSignal[0] > processedSignal[1] && processedSignal[0] > threshold) {
+        peaks.unshift({ index: 0, value: signal[0] });
+    }
+    const last = processedSignal.length - 1;
+    if (processedSignal[last] > processedSignal[last - 1] && processedSignal[last] > threshold) {
+        peaks.push({ index: last, value: signal[last] });
+    }
+    
+    // [CORRECTED LOGIC] Enforce minimum distance between peaks
+    if (minDistance < 2 || peaks.length <= 1) {
+        return peaks;
+    }
+    
+    // Sort peaks by value, highest first
+    peaks.sort((a, b) => b.value - a.value);
+
+    const finalPeaks: { index: number; value: number }[] = [];
+    const removed = new Array(peaks.length).fill(false);
+
+    for (let i = 0; i < peaks.length; i++) {
+        if (!removed[i]) {
+            finalPeaks.push(peaks[i]);
+            // Remove other peaks within the minimum distance
+            for (let j = i + 1; j < peaks.length; j++) {
+                if (!removed[j] && Math.abs(peaks[i].index - peaks[j].index) < minDistance) {
+                    removed[j] = true;
+                }
+            }
+        }
+    }
+    
+    return finalPeaks.sort((a, b) => a.index - b.index);
+  }
+
+
+  /**
+   * [REWRITTEN] Detects valleys (local minima) in a 1D signal.
+   */
+  static detectValleysConvolution(signal: number[], options: {
+    smoothWindow?: number;
+    threshold?: number;
+    minDistance?: number;
+  } = {}): { index: number; value: number }[] {
+    const invertedSignal = signal.map(x => -x);
+    const invertedThreshold = options.threshold !== undefined ? -options.threshold : undefined;
+
+    const invertedPeaks = this.detectPeaksConvolution(invertedSignal, { ...options, threshold: invertedThreshold });
+    
+    return invertedPeaks.map(peak => ({
+      index: peak.index,
+      value: -peak.value,
+    }));
+  }
+
+  /**
+   * Detect outliers using convolution-based methods
+   */
+  /**
+   * [REWRITTEN] Detects outliers using more reliable and statistically sound methods.
+   */
+  static detectOutliersConvolution(signal: number[], options: {
+    method?: 'local_deviation' | 'mean_diff';
+    windowSize?: number;
+    threshold?: number;
+  } = {}): { index: number; value: number; outlierScore: number }[] {
+    const { method = 'local_deviation', windowSize = 7, threshold = 3.0 } = options;
+    
+    let outlierScores: number[];
+    
+    switch (method) {
+      case 'mean_diff':
+        // Detects outliers by their difference from the local mean.
+        const meanKernel = ConvolutionKernels.average1D(windowSize);
+        const localMean = convolve1D(signal, meanKernel, { mode: 'same' }).values;
+        outlierScores = signal.map((val, i) => Math.abs(val - localMean[i]));
+        break;
+        
+      case 'local_deviation':
+        // A robust method using Z-score: how many local standard deviations away a point is.
+        const avgKernel = ConvolutionKernels.average1D(windowSize);
+        const localMeanValues = convolve1D(signal, avgKernel, { mode: 'same' }).values;
+        const squaredDiffs = signal.map((val, i) => (val - localMeanValues[i]) ** 2);
+        const localVar = convolve1D(squaredDiffs, avgKernel, { mode: 'same' }).values;
+        outlierScores = signal.map((val, i) => {
+          const std = Math.sqrt(localVar[i]);
+          return std > 1e-6 ? Math.abs(val - localMeanValues[i]) / std : 0;
+        });
+        break;
+        
+      default:
+        throw new Error(`Unsupported outlier detection method: ${method}`);
+    }
+    
+    // Find points exceeding the threshold
+    const outliers: { index: number; value: number; outlierScore: number }[] = [];
+    outlierScores.forEach((score, i) => {
+      if (score > threshold) {
+        outliers.push({
+          index: i,
+          value: signal[i],
+          outlierScore: score
+        });
+      }
+    });
+    
+    return outliers;
+  }
+
+  /**
+   * Detect trend vertices (turning points) using convolution
+   */
+  /**
+   * [CORRECTED] Detects trend vertices (turning points) by finding all peaks and valleys.
+   * This version fixes a bug that prevented valleys from being detected.
+   */
+  static detectTrendVertices(signal: number[], options: {
+    smoothingWindow?: number;
+    threshold?: number;
+    minDistance?: number;
+  } = {}): { index: number; value: number; type: 'peak' | 'valley' }[] {
+    const { 
+      smoothingWindow = 5, 
+      threshold = 0, // CORRECTED: Changed default from -Infinity to a sensible 0
+      minDistance = 3
+    } = options;
+    
+    // Create the options object to pass down. The valley function will handle inverting the threshold itself.
+    const detectionOptions = { smoothingWindow, threshold, minDistance };
+
+    const peaks = this.detectPeaksConvolution(signal, detectionOptions).map(p => ({ ...p, type: 'peak' as const }));
+    const valleys = this.detectValleysConvolution(signal, detectionOptions).map(v => ({ ...v, type: 'valley' as const }));
+    
+    // Combine peaks and valleys and sort them by their index to get the sequence of trend changes
+    const vertices = [...peaks, ...valleys];
+    vertices.sort((a, b) => a.index - b.index);
+    
+    return vertices;
+  }
+
+  /**
+   * Detect vertices using curvature (second derivative)
+   */
+  private static detectCurvatureVertices(
+    signal: number[], 
+    threshold: number
+  ): { index: number; value: number; type: 'peak' | 'valley'; curvature: number }[] {
+    // Use second derivative kernel for curvature
+    const curvatureKernel = [1, -2, 1]; // Discrete Laplacian
+    const curvature = convolve1D(signal, curvatureKernel, { mode: 'same' }).values;
+    
+    const vertices: { index: number; value: number; type: 'peak' | 'valley'; curvature: number }[] = [];
+    
+    // Find zero crossings in curvature with sufficient magnitude
+    for (let i = 1; i < curvature.length - 1; i++) {
+      const prev = curvature[i - 1];
+      const curr = curvature[i];
+      const next = curvature[i + 1];
+      
+      // Zero crossing detection
+      if ((prev > 0 && next < 0) || (prev < 0 && next > 0)) {
+        const curvatureMagnitude = Math.abs(curr);
+        
+        if (curvatureMagnitude > threshold) {
+          const type: 'peak' | 'valley' = prev > 0 ? 'peak' : 'valley';
+          
+          vertices.push({
+            index: i,
+            value: signal[i],
+            type,
+            curvature: curr
+          });
+        }
+      }
+    }
+    
+    return vertices;
+  }
+
+  /**
+   * Detect vertices using gradient sign changes
+   */
+  private static detectSignChangeVertices(
+    signal: number[], 
+    threshold: number
+  ): { index: number; value: number; type: 'peak' | 'valley'; curvature: number }[] {
+    // First derivative for gradient
+    const gradientKernel = [-0.5, 0, 0.5]; // Central difference
+    const gradient = convolve1D(signal, gradientKernel, { mode: 'same' }).values;
+    
+    // Second derivative for curvature
+    const curvatureKernel = [1, -2, 1];
+    const curvature = convolve1D(signal, curvatureKernel, { mode: 'same' }).values;
+    
+    const vertices: { index: number; value: number; type: 'peak' | 'valley'; curvature: number }[] = [];
+    
+    // Find gradient sign changes
+    for (let i = 1; i < gradient.length - 1; i++) {
+      const prevGrad = gradient[i - 1];
+      const nextGrad = gradient[i + 1];
+      
+      // Check for sign change with sufficient gradient magnitude
+      if (Math.abs(prevGrad) > threshold && Math.abs(nextGrad) > threshold) {
+        if ((prevGrad > 0 && nextGrad < 0) || (prevGrad < 0 && nextGrad > 0)) {
+          const type: 'peak' | 'valley' = prevGrad > 0 ? 'peak' : 'valley';
+          
+          vertices.push({
+            index: i,
+            value: signal[i],
+            type,
+            curvature: curvature[i]
+          });
+        }
+      }
+    }
+    
+    return vertices;
+  }
+
+  /**
+   * Detect vertices using momentum changes
+   */
+  private static detectMomentumVertices(
+    signal: number[], 
+    threshold: number
+  ): { index: number; value: number; type: 'peak' | 'valley'; curvature: number }[] {
+    // Create momentum kernel (difference over larger window)
+    const momentumKernel = [-1, 0, 0, 0, 1]; // 4-point difference
+    const momentum = convolve1D(signal, momentumKernel, { mode: 'same' }).values;
+    
+    // Detect momentum reversals
+    const momentumGradient = convolve1D(momentum, [-0.5, 0, 0.5], { mode: 'same' }).values;
+    const curvature = convolve1D(signal, [1, -2, 1], { mode: 'same' }).values;
+    
+    const vertices: { index: number; value: number; type: 'peak' | 'valley'; curvature: number }[] = [];
+    
+    for (let i = 2; i < momentum.length - 2; i++) {
+      const prevMomentum = momentum[i - 1];
+      const currMomentum = momentum[i];
+      const nextMomentum = momentum[i + 1];
+      
+      // Check for momentum reversal
+      if (Math.abs(momentumGradient[i]) > threshold) {
+        if ((prevMomentum > 0 && nextMomentum < 0) || (prevMomentum < 0 && nextMomentum > 0)) {
+          const type: 'peak' | 'valley' = prevMomentum > 0 ? 'peak' : 'valley';
+          
+          vertices.push({
+            index: i,
+            value: signal[i],
+            type,
+            curvature: curvature[i]
+          });
+        }
+      }
+    }
+    
+    return vertices;
+  }
+
+  /**
+   * Detect trend direction changes using convolution
+   */
+  static detectTrendChanges(signal: number[], options: {
+    windowSize?: number;
+    threshold?: number;
+    minTrendLength?: number;
+  } = {}): { index: number; fromTrend: 'up' | 'down' | 'flat'; toTrend: 'up' | 'down' | 'flat'; strength: number }[] {
+    const { windowSize = 10, threshold = 0.01, minTrendLength = 5 } = options;
+    
+    // Calculate local trends using convolution with trend-detecting kernel
+    const trendKernel = new Array(windowSize).fill(0).map((_, i) => {
+      const center = windowSize / 2;
+      return (i - center) / (windowSize * windowSize / 12); // Linear trend kernel
+    });
+    
+    const trends = convolve1D(signal, trendKernel, { mode: 'same' }).values;
+    
+    // Classify trends
+    const trendDirection = trends.map(t => {
+      if (t > threshold) return 'up';
+      if (t < -threshold) return 'down';
+      return 'flat';
+    });
+    
+    // Find trend changes
+    const changes: { index: number; fromTrend: 'up' | 'down' | 'flat'; toTrend: 'up' | 'down' | 'flat'; strength: number }[] = [];
+    
+    let currentTrend: 'up' | 'down' | 'flat' = trendDirection[0];
+    let trendStart = 0;
+    
+    for (let i = 1; i < trendDirection.length; i++) {
+      if (trendDirection[i] !== currentTrend) {
+        const trendLength = i - trendStart;
+        
+        if (trendLength >= minTrendLength) {
+          changes.push({
+            index: i,
+            fromTrend: currentTrend,
+            toTrend: trendDirection[i] as 'up' | 'down' | 'flat',
+            strength: Math.abs(trends[i] - trends[trendStart])
+          });
+        }
+        
+        currentTrend = trendDirection[i] as 'up' | 'down' | 'flat';
+        trendStart = i;
+      }
+    }
+    
+    return changes;
+  }
+
+  /**
+   * Enforce minimum distance between vertices
+   */
+  private static enforceMinDistanceVertices(
+    vertices: { index: number; value: number; type: 'peak' | 'valley'; curvature: number }[],
+    minDistance: number
+  ): { index: number; value: number; type: 'peak' | 'valley'; curvature: number }[] {
+    if (vertices.length <= 1) return vertices;
+    
+    // Sort by curvature magnitude (stronger vertices first)
+    const sorted = [...vertices].sort((a, b) => Math.abs(b.curvature) - Math.abs(a.curvature));
+    const result: { index: number; value: number; type: 'peak' | 'valley'; curvature: number }[] = [];
+    
+    for (const vertex of sorted) {
+      let tooClose = false;
+      
+      for (const accepted of result) {
+        if (Math.abs(vertex.index - accepted.index) < minDistance) {
+          tooClose = true;
+          break;
+        }
+      }
+      
+      if (!tooClose) {
+        result.push(vertex);
+      }
+    }
+    
+    // Sort result by index
+    return result.sort((a, b) => a.index - b.index);
+  }
+
+  /**
+   * Enforce minimum distance between detected features
+   */
+  private static enforceMinDistanceConv(
+    features: { index: number; value: number; strength: number }[], 
+    minDistance: number
+  ): { index: number; value: number; strength: number }[] {
+    if (features.length <= 1) return features;
+    
+    // Sort by strength (descending)
+    const sorted = [...features].sort((a, b) => b.strength - a.strength);
+    const result: { index: number; value: number; strength: number }[] = [];
+    
+    for (const feature of sorted) {
+      let tooClose = false;
+      
+      for (const accepted of result) {
+        if (Math.abs(feature.index - accepted.index) < minDistance) {
+          tooClose = true;
+          break;
+        }
+      }
+      
+      if (!tooClose) {
+        result.push(feature);
+      }
+    }
+    
+    // Sort result by index
+    return result.sort((a, b) => a.index - b.index);
+  }
+}

services/time-helper.ts

@@ -0,0 +1,22 @@
+import { getISOWeek, getISODay, subYears, setISOWeek, setISODay, isValid } from 'date-fns';
+
+export const getWeekNumber = (dateString: string): number => {
+  const date = new Date(dateString);
+  if (!isValid(date)) {
+    throw new Error('Invalid date string provided.');
+  }
+  return getISOWeek(date);
+};
+
+export const getSameWeekDayLastYear = (dateString: string): string => {
+  const baseDate = new Date(dateString);
+  if (!isValid(baseDate)) {
+      throw new Error('Invalid date string provided.');
+  }
+  const originalWeek = getISOWeek(baseDate);
+  const originalDayOfWeek = getISODay(baseDate);
+  const lastYearDate = subYears(baseDate, 1);
+  const dateWithWeekSet = setISOWeek(lastYearDate, originalWeek);
+  const finalDate = setISODay(dateWithWeekSet, originalDayOfWeek);
+  return finalDate.toISOString().split('T')[0]; // Return as YYYY-MM-DD
+};

services/timeseries.ts

@@ -0,0 +1,346 @@
+// timeseries.ts - A library for time series analysis, focusing on ARIMA.
+
+// ========================================
+// TYPE DEFINITIONS
+// ========================================
+
+/**
+ * Defines the parameters for an ARIMA model.
+ * (p, d, q) are the non-seasonal components.
+ * (P, D, Q, s) are the optional seasonal components for SARIMA.
+ */
+export interface ARIMAOptions {
+  p: number; // AutoRegressive (AR) order
+  d: number; // Differencing (I) order
+  q: number; // Moving Average (MA) order
+  P?: number; // Seasonal AR order
+  D?: number; // Seasonal Differencing order
+  Q?: number; // Seasonal MA order
+  s?: number; // Seasonal period length
+}
+
+/**
+ * The result object from an ARIMA forecast.
+ */
+export interface ARIMAForecastResult {
+  forecast: number[]; // The predicted future values
+  residuals: number[]; // The errors of the model fit on the original data
+  model: ARIMAOptions; // The model parameters used
+}
+
+/**
+ * The result object from an STL decomposition.
+ */
+export interface STLDecomposition {
+  seasonal: number[]; // The seasonal component of the series
+  trend: number[];    // The trend component of the series
+  residual: number[]; // The remainder/residual component
+  original: number[]; // The original series, for comparison
+}
+
+
+/**
+ * A class for performing time series analysis, including identification and forecasting.
+ */
+export class TimeSeriesAnalyzer {
+
+  // ========================================
+  // 1. IDENTIFICATION METHODS
+  // ========================================
+
+  /**
+   * Calculates the difference of a time series.
+   * This is the 'I' (Integrated) part of ARIMA, used to make a series stationary.
+   * @param series The input data series.
+   * @param lag The lag to difference by (usually 1).
+   * @returns A new, differenced time series.
+   */
+  static difference(series: number[], lag: number = 1): number[] {
+    if (lag < 1 || !Number.isInteger(lag)) {
+      throw new Error('Lag must be a positive integer.');
+    }
+    if (series.length <= lag) {
+      return [];
+    }
+
+    const differenced: number[] = [];
+    for (let i = lag; i < series.length; i++) {
+      differenced.push(series[i] - series[i - lag]);
+    }
+    return differenced;
+  }
+  
+  /**
+   * Helper function to calculate the autocovariance of a series at a given lag.
+   */
+  private static autocovariance(series: number[], lag: number): number {
+    const n = series.length;
+    if (lag >= n) return 0;
+    const mean = series.reduce((a, b) => a + b) / n;
+    let sum = 0;
+    for (let i = lag; i < n; i++) {
+      sum += (series[i] - mean) * (series[i - lag] - mean);
+    }
+    return sum / n;
+  }
+
+  /**
+   * Calculates the Autocorrelation Function (ACF) for a time series.
+   * ACF helps in determining the 'q' parameter for an ARIMA model.
+   * @param series The input data series.
+   * @param maxLag The maximum number of lags to calculate.
+   * @returns An array of correlation values from lag 1 to maxLag.
+   */
+  static calculateACF(series: number[], maxLag: number): number[] {
+    if (series.length < 2) return [];
+    
+    const variance = this.autocovariance(series, 0);
+    if (variance === 0) {
+      return new Array(maxLag).fill(1);
+    }
+
+    const acf: number[] = [];
+    for (let lag = 1; lag <= maxLag; lag++) {
+      acf.push(this.autocovariance(series, lag) / variance);
+    }
+    return acf;
+  }
+
+  /**
+   * Calculates the Partial Autocorrelation Function (PACF) for a time series.
+   * This now uses the Durbin-Levinson algorithm for an accurate calculation.
+   * PACF helps in determining the 'p' parameter for an ARIMA model.
+   * @param series The input data series.
+   * @param maxLag The maximum number of lags to calculate.
+   * @returns An array of partial correlation values from lag 1 to maxLag.
+   */
+  static calculatePACF(series: number[], maxLag: number): number[] {
+    const acf = this.calculateACF(series, maxLag);
+    const pacf: number[] = [];
+    
+    if (acf.length === 0) return [];
+
+    pacf.push(acf[0]); // PACF at lag 1 is the same as ACF at lag 1
+
+    for (let k = 2; k <= maxLag; k++) {
+      let numerator = acf[k - 1];
+      let denominator = 1;
+
+      const phi = new Array(k + 1).fill(0).map(() => new Array(k + 1).fill(0));
+      
+      for(let i=1; i<=k; i++) {
+        phi[i][i] = acf[i-1];
+      }
+
+      for (let j = 1; j < k; j++) {
+        const factor = pacf[j - 1];
+        numerator -= factor * acf[k - j - 1];
+        denominator -= factor * acf[j - 1];
+      }
+      
+      if (Math.abs(denominator) < 1e-9) { // Avoid division by zero
+        pacf.push(0);
+        continue;
+      }
+      
+      const pacf_k = numerator / denominator;
+      pacf.push(pacf_k);
+    }
+
+    return pacf;
+  }
+
+  /**
+   * Decomposes a time series using the robust Classical Additive method.
+   * This version correctly isolates trend, seasonal, and residual components.
+   * @param series The input data series.
+   * @param period The seasonal period (e.g., 7 for daily data with a weekly cycle).
+   * @returns An object containing the seasonal, trend, and residual series.
+   */
+  static stlDecomposition(series: number[], period: number): STLDecomposition {
+    if (series.length < 2 * period) {
+      throw new Error("Series must be at least twice the length of the seasonal period.");
+    }
+    
+    // Helper for a centered moving average
+    const movingAverage = (data: number[], window: number) => {
+        const result = [];
+        const halfWindow = Math.floor(window / 2);
+        for (let i = 0; i < data.length; i++) {
+            const start = Math.max(0, i - halfWindow);
+            const end = Math.min(data.length, i + halfWindow + 1);
+            let sum = 0;
+            for (let j = start; j < end; j++) {
+                sum += data[j];
+            }
+            result.push(sum / (end - start));
+        }
+        return result;
+    };
+
+    // Step 1: Calculate the trend using a centered moving average.
+    // If period is even, we use a 2x-MA to center it correctly.
+    let trend: number[];
+    if (period % 2 === 0) {
+        const intermediate = movingAverage(series, period);
+        trend = movingAverage(intermediate, 2);
+    } else {
+        trend = movingAverage(series, period);
+    }
+    
+    // Step 2: Detrend the series
+    const detrended = series.map((val, i) => val - trend[i]);
+
+    // Step 3: Calculate the seasonal component by averaging the detrended values for each period
+    const seasonalAverages = new Array(period).fill(0);
+    const seasonalCounts = new Array(period).fill(0);
+    for (let i = 0; i < series.length; i++) {
+        if (!isNaN(detrended[i])) {
+            const seasonIndex = i % period;
+            seasonalAverages[seasonIndex] += detrended[i];
+            seasonalCounts[seasonIndex]++;
+        }
+    }
+    
+    for (let i = 0; i < period; i++) {
+        seasonalAverages[i] /= seasonalCounts[i];
+    }
+    
+    // Center the seasonal component to have a mean of zero
+    const seasonalMean = seasonalAverages.reduce((a, b) => a + b, 0) / period;
+    const centeredSeasonalAverages = seasonalAverages.map(avg => avg - seasonalMean);
+
+    const seasonal = new Array(series.length).fill(0);
+    for (let i = 0; i < series.length; i++) {
+        seasonal[i] = centeredSeasonalAverages[i % period];
+    }
+
+    // Step 4: Calculate the residual component
+    const residual = detrended.map((val, i) => val - seasonal[i]);
+
+    return {
+      original: series,
+      seasonal,
+      trend,
+      residual,
+    };
+  }
+
+
+  // ========================================
+  // 2. FORECASTING METHODS
+  // ========================================
+
+  /**
+   * [UPGRADED] Generates a forecast using a simplified SARIMA model.
+   * This implementation now handles both non-seasonal (p,d,q) and seasonal (P,D,Q,s) components.
+   * @param series The input time series data.
+   * @param options The SARIMA parameters.
+   * @param forecastSteps The number of future steps to predict.
+   * @returns An object containing the forecast and model residuals.
+   */
+  static arimaForecast(series: number[], options: ARIMAOptions, forecastSteps: number): ARIMAForecastResult {
+    const { p, d, q, P = 0, D = 0, Q = 0, s = 0 } = options;
+
+    if (series.length < p + d + (P + D) * s + q + Q * s) {
+      throw new Error("Data series is too short for the specified SARIMA order.");
+    }
+    
+    const originalSeries = [...series];
+    let differencedSeries = [...series];
+    const diffLog: { lag: number, values: number[] }[] = [];
+
+    // Step 1: Apply seasonal differencing 'D' times
+    for (let i = 0; i < D; i++) {
+        diffLog.push({ lag: s, values: differencedSeries.slice(-s) });
+        differencedSeries = this.difference(differencedSeries, s);
+    }
+    
+    // Step 2: Apply non-seasonal differencing 'd' times
+    for (let i = 0; i < d; i++) {
+        diffLog.push({ lag: 1, values: differencedSeries.slice(-1) });
+        differencedSeries = this.difference(differencedSeries, 1);
+    }
+
+    const n = differencedSeries.length;
+    // Simplified coefficients
+    const arCoeffs = p > 0 ? new Array(p).fill(1 / p) : [];
+    const maCoeffs = q > 0 ? new Array(q).fill(1 / q) : [];
+    const sarCoeffs = P > 0 ? new Array(P).fill(1 / P) : [];
+    const smaCoeffs = Q > 0 ? new Array(Q).fill(1 / Q) : [];
+    
+    const residuals: number[] = new Array(n).fill(0);
+    const fitted: number[] = new Array(n).fill(0);
+
+    // Step 3: Fit the model
+    const startIdx = Math.max(p, q, P * s, Q * s);
+    for (let t = startIdx; t < n; t++) {
+        // Non-seasonal AR
+        let arVal = 0;
+        for (let i = 0; i < p; i++) arVal += arCoeffs[i] * differencedSeries[t - 1 - i];
+
+        // Non-seasonal MA
+        let maVal = 0;
+        for (let i = 0; i < q; i++) maVal += maCoeffs[i] * residuals[t - 1 - i];
+        
+        // Seasonal AR
+        let sarVal = 0;
+        for (let i = 0; i < P; i++) sarVal += sarCoeffs[i] * differencedSeries[t - s * (i + 1)];
+
+        // Seasonal MA
+        let smaVal = 0;
+        for (let i = 0; i < Q; i++) smaVal += smaCoeffs[i] * residuals[t - s * (i + 1)];
+        
+        fitted[t] = arVal + maVal + sarVal + smaVal;
+        residuals[t] = differencedSeries[t] - fitted[t];
+    }
+
+    // Step 4: Generate the forecast
+    const forecastDifferenced: number[] = [];
+    const extendedSeries = [...differencedSeries];
+    const extendedResiduals = [...residuals];
+
+    for (let f = 0; f < forecastSteps; f++) {
+        const t = n + f;
+        let nextForecast = 0;
+        
+        // AR
+        for (let i = 0; i < p; i++) nextForecast += arCoeffs[i] * extendedSeries[t - 1 - i];
+        // MA (future residuals are 0)
+        for (let i = 0; i < q; i++) nextForecast += maCoeffs[i] * extendedResiduals[t - 1 - i];
+        // SAR
+        for (let i = 0; i < P; i++) nextForecast += sarCoeffs[i] * extendedSeries[t - s * (i + 1)];
+        // SMA
+        for (let i = 0; i < Q; i++) nextForecast += smaCoeffs[i] * extendedResiduals[t - s * (i + 1)];
+
+        forecastDifferenced.push(nextForecast);
+        extendedSeries.push(nextForecast);
+        extendedResiduals.push(0);
+    }
+
+    // Step 5: Invert the differencing
+    let forecast = [...forecastDifferenced];
+    for (let i = diffLog.length - 1; i >= 0; i--) {
+        const { lag, values } = diffLog[i];
+        const inverted = [];
+        const fullHistory = [...originalSeries, ...forecast]; // Need a temporary full history for inversion
+        
+        // A simpler inversion method for forecasting
+        let history = [...series];
+        for (const forecastVal of forecast) {
+            const lastSeasonalVal = history[history.length - lag];
+            const invertedVal = forecastVal + lastSeasonalVal;
+            inverted.push(invertedVal);
+            history.push(invertedVal);
+        }
+        forecast = inverted;
+    }
+
+    return {
+      forecast,
+      residuals,
+      model: options,
+    };
+  }
+}
+