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04

Time Series Stock Price Forecasting

Forecasts next-day returns on 500 days of synthetic prices with lagged returns and technical indicators as features. Linear regression and ridge regression are compared with a mean baseline.

Features

  • Synthetic prices with a small upward trend, mean reversion to 100 and random noise
  • Indicators: 20 and 50 day moving averages, 20 day volatility, 14 day RSI, 10 day momentum
  • Time-ordered train and test split, with no shuffling
  • Metrics: MSE, RMSE, MAE, R2 and directional accuracy
  • Autocorrelation of returns with pearsonr

What you will learn

  • Synthetic prices with a small upward trend, mean reversion to 100 and random noise
  • Indicators: 20 and 50 day moving averages, 20 day volatility, 14 day RSI, 10 day momentum
  • Time-ordered train and test split, with no shuffling
  • Metrics: MSE, RMSE, MAE, R2 and directional accuracy
  • Use deepbox/ndarray for tensor, toArray, item.
  • Use deepbox/stats for mean, std, pearsonr.

Source

index.ts
/** * Time Series Stock Price Forecasting * * Forecasts next-day returns on synthetic prices from lagged returns and technical indicators. * * Deepbox Modules Used: * - deepbox/ndarray: Tensor operations * - deepbox/stats: Statistical analysis * - deepbox/ml: Regression models * - deepbox/metrics: Forecasting metrics * - deepbox/dataframe: Data manipulation * - deepbox/plot: Visualization */ import { existsSync, mkdirSync, writeFileSync } from "node:fs";import { DataFrame } from "deepbox/dataframe";import { mae, mse, r2Score, rmse } from "deepbox/metrics";import { LinearRegression, Ridge } from "deepbox/ml";import { tensor } from "deepbox/ndarray";import { Figure } from "deepbox/plot";import { StandardScaler } from "deepbox/preprocess";import { mean, pearsonr, std } from "deepbox/stats"; // ============================================================================// Configuration// ============================================================================ const OUTPUT_DIR = "docs/projects/04-stock-price-forecasting/output";const NUM_DAYS = 500;const LOOKBACK = 20; // ============================================================================// Data Generation// ============================================================================ /** * Generate synthetic stock price data: a small trend, mean reversion to 100 and random noise */function generateStockData(  numDays: number,  seed = 42): {  dates: string[];  prices: number[];  returns: number[];  volume: number[];} {  let randomSeed = seed;  const seededRandom = () => {    randomSeed = (randomSeed * 1103515245 + 12345) & 0x7fffffff;    return randomSeed / 0x7fffffff;  };   const randomNormal = (mean: number, std: number) => {    const u1 = seededRandom();    const u2 = seededRandom();    const z = Math.sqrt(-2 * Math.log(u1)) * Math.cos(2 * Math.PI * u2);    return mean + std * z;  };   const dates: string[] = [];  const prices: number[] = [];  const returns: number[] = [];  const volume: number[] = [];   let price = 100; // Starting price  const startDate = new Date("2023-01-01");   for (let i = 0; i < numDays; i++) {    // Generate date    const date = new Date(startDate);    date.setDate(date.getDate() + i);    dates.push(date.toISOString().split("T")[0]);     // Generate return with trend, volatility, and mean reversion    const trend = 0.0002; // Slight upward trend    const volatility = 0.02;    const meanReversion = (-0.01 * (price - 100)) / 100; // Pull back to 100     const dailyReturn = trend + meanReversion + randomNormal(0, volatility);    returns.push(dailyReturn);     // Update price    price = price * (1 + dailyReturn);    prices.push(price);     // Generate volume with some correlation to volatility    const baseVolume = 1000000;    const volumeMultiplier = 1 + Math.abs(dailyReturn) * 10;    volume.push(Math.round(baseVolume * volumeMultiplier * (0.8 + seededRandom() * 0.4)));  }   return { dates, prices, returns, volume };} /** * Calculate technical indicators */function calculateIndicators(  prices: number[],  returns: number[]): {  sma20: number[];  sma50: number[];  volatility20: number[];  rsi14: number[];  momentum10: number[];} {  const n = prices.length;   // Simple Moving Averages  const sma20: number[] = [];  const sma50: number[] = [];  for (let i = 0; i < n; i++) {    if (i >= 19) {      const window = prices.slice(i - 19, i + 1);      sma20.push(window.reduce((a, b) => a + b, 0) / 20);    } else {      sma20.push(NaN);    }    if (i >= 49) {      const window = prices.slice(i - 49, i + 1);      sma50.push(window.reduce((a, b) => a + b, 0) / 50);    } else {      sma50.push(NaN);    }  }   // Rolling Volatility (20-day)  const volatility20: number[] = [];  for (let i = 0; i < n; i++) {    if (i >= 19) {      const window = returns.slice(i - 19, i + 1);      const mean = window.reduce((a, b) => a + b, 0) / 20;      const variance = window.reduce((sum, r) => sum + (r - mean) ** 2, 0) / 20;      volatility20.push(Math.sqrt(variance) * Math.sqrt(252)); // Annualized    } else {      volatility20.push(NaN);    }  }   // RSI (14-day)  const rsi14: number[] = [];  for (let i = 0; i < n; i++) {    if (i >= 14) {      const gains: number[] = [];      const losses: number[] = [];      for (let j = i - 13; j <= i; j++) {        if (returns[j] > 0) {          gains.push(returns[j]);          losses.push(0);        } else {          gains.push(0);          losses.push(-returns[j]);        }      }      const avgGain = gains.reduce((a, b) => a + b, 0) / 14;      const avgLoss = losses.reduce((a, b) => a + b, 0) / 14;      const rs = avgLoss === 0 ? 100 : avgGain / avgLoss;      rsi14.push(100 - 100 / (1 + rs));    } else {      rsi14.push(NaN);    }  }   // Momentum (10-day price change)  const momentum10: number[] = [];  for (let i = 0; i < n; i++) {    if (i >= 10) {      momentum10.push((prices[i] - prices[i - 10]) / prices[i - 10]);    } else {      momentum10.push(NaN);    }  }   return { sma20, sma50, volatility20, rsi14, momentum10 };} /** * Create features for forecasting */function createFeatures(  prices: number[],  returns: number[],  indicators: ReturnType<typeof calculateIndicators>,  lookback: number): { X: number[][]; y: number[]; validIndices: number[] } {  const X: number[][] = [];  const y: number[] = [];  const validIndices: number[] = [];   const startIdx = Math.max(lookback, 50); // Start late enough for every indicator to be defined   for (let i = startIdx; i < prices.length - 1; i++) {    // Check if all indicators are valid    if (      Number.isNaN(indicators.sma20[i]) ||      Number.isNaN(indicators.sma50[i]) ||      Number.isNaN(indicators.volatility20[i]) ||      Number.isNaN(indicators.rsi14[i]) ||      Number.isNaN(indicators.momentum10[i])    ) {      continue;    }     const features: number[] = [];     // Lagged returns    for (let j = 0; j < lookback; j++) {      features.push(returns[i - j]);    }     // Technical indicators    features.push((prices[i] - indicators.sma20[i]) / indicators.sma20[i]); // Price vs SMA20    features.push((prices[i] - indicators.sma50[i]) / indicators.sma50[i]); // Price vs SMA50    features.push(indicators.volatility20[i]);    features.push(indicators.rsi14[i] / 100); // Normalize RSI    features.push(indicators.momentum10[i]);     X.push(features);    y.push(returns[i + 1]); // Next day return    validIndices.push(i);  }   return { X, y, validIndices };} // ============================================================================// Main Execution// ============================================================================ console.log("═".repeat(70));console.log("  TIME SERIES STOCK PRICE FORECASTING");console.log("  Built with Deepbox: TypeScript toolkit for AI & numerical computing");console.log("═".repeat(70)); // Create output directoryif (!existsSync(OUTPUT_DIR)) {  mkdirSync(OUTPUT_DIR, { recursive: true });} // ============================================================================// Step 1: Generate Data// ============================================================================ console.log("\nSTEP 1: Generating Stock Price Data");console.log("─".repeat(70)); const { dates, prices, returns, volume: _volume } = generateStockData(NUM_DAYS); console.log(`\nGenerated ${NUM_DAYS} days of synthetic stock data`);console.log(`  Date Range: ${dates[0]} to ${dates[dates.length - 1]}`);console.log(`  Starting Price: $${prices[0].toFixed(2)}`);console.log(`  Ending Price: $${prices[prices.length - 1].toFixed(2)}`);console.log(`  Total Return: ${((prices[prices.length - 1] / prices[0] - 1) * 100).toFixed(2)}%`); // Basic statisticsconst returnsTensor = tensor(returns);const meanReturn = Number(mean(returnsTensor).item());const stdReturn = Number(std(returnsTensor).item()); console.log(`\nReturn Statistics:`);console.log(`  Mean Daily Return: ${(meanReturn * 100).toFixed(4)}%`);console.log(`  Daily Volatility:  ${(stdReturn * 100).toFixed(4)}%`);console.log(`  Annualized Return: ${(meanReturn * 252 * 100).toFixed(2)}%`);console.log(`  Annualized Vol:    ${(stdReturn * Math.sqrt(252) * 100).toFixed(2)}%`); // ============================================================================// Step 2: Calculate Technical Indicators// ============================================================================ console.log("\nSTEP 2: Calculating Technical Indicators");console.log("─".repeat(70)); const indicators = calculateIndicators(prices, returns); // Show sample of indicatorsconst sampleIdx = prices.length - 1;console.log(`\nLatest Indicators (${dates[sampleIdx]}):`);console.log(`  Price:       $${prices[sampleIdx].toFixed(2)}`);console.log(`  SMA(20):     $${indicators.sma20[sampleIdx].toFixed(2)}`);console.log(`  SMA(50):     $${indicators.sma50[sampleIdx].toFixed(2)}`);console.log(`  Volatility:  ${(indicators.volatility20[sampleIdx] * 100).toFixed(2)}%`);console.log(`  RSI(14):     ${indicators.rsi14[sampleIdx].toFixed(2)}`);console.log(`  Momentum:    ${(indicators.momentum10[sampleIdx] * 100).toFixed(2)}%`); // ============================================================================// Step 3: Feature Engineering// ============================================================================ console.log("\nSTEP 3: Feature Engineering");console.log("─".repeat(70)); const { X, y, validIndices: _validIndices } = createFeatures(prices, returns, indicators, LOOKBACK); console.log(`\nCreated feature matrix`);console.log(`  Samples: ${X.length}`);console.log(`  Features per sample: ${X[0].length}`);console.log(`  Feature breakdown:`);console.log(`    - ${LOOKBACK} lagged returns`);console.log(`    - 5 technical indicators`); // ============================================================================// Step 4: Train/Test Split// ============================================================================ console.log("\nSTEP 4: Train/Test Split");console.log("─".repeat(70)); const splitIdx = Math.floor(X.length * 0.8);const XTrain = X.slice(0, splitIdx);const XTest = X.slice(splitIdx);const yTrain = y.slice(0, splitIdx);const yTest = y.slice(splitIdx); console.log(`\nTime-based split (no shuffle to preserve temporal order)`);console.log(`  Training: ${XTrain.length} samples`);console.log(`  Testing:  ${XTest.length} samples`); // Scale featuresconst scaler = new StandardScaler();scaler.fit(tensor(XTrain));const XTrainScaled = scaler.transform(tensor(XTrain));const XTestScaled = scaler.transform(tensor(XTest)); console.log(`Applied StandardScaler`); // ============================================================================// Step 5: Model Training// ============================================================================ console.log("\nSTEP 5: Model Training");console.log("─".repeat(70)); // Linear Regressionconsole.log("\nTraining Linear Regression...");const lr = new LinearRegression();lr.fit(XTrainScaled, tensor(yTrain));const yPredLR = lr.predict(XTestScaled); // Ridge Regressionconsole.log("Training Ridge Regression (alpha=0.1)...");const ridge = new Ridge({ alpha: 0.1 });ridge.fit(XTrainScaled, tensor(yTrain));const yPredRidge = ridge.predict(XTestScaled); // Baseline: Predict meanconst meanPred = yTrain.reduce((a, b) => a + b, 0) / yTrain.length;const yPredBaseline = tensor(Array(yTest.length).fill(meanPred)); console.log("Both models trained"); // ============================================================================// Step 6: Model Evaluation// ============================================================================ console.log("\nSTEP 6: Model Evaluation");console.log("─".repeat(70)); const yTestTensor = tensor(yTest); // Calculate metricsconst results = [  {    name: "Mean Baseline",    mse: mse(yTestTensor, yPredBaseline),    rmse: rmse(yTestTensor, yPredBaseline),    mae: mae(yTestTensor, yPredBaseline),    r2: r2Score(yTestTensor, yPredBaseline),    pred: yPredBaseline,  },  {    name: "Linear Regression",    mse: mse(yTestTensor, yPredLR),    rmse: rmse(yTestTensor, yPredLR),    mae: mae(yTestTensor, yPredLR),    r2: r2Score(yTestTensor, yPredLR),    pred: yPredLR,  },  {    name: "Ridge Regression",    mse: mse(yTestTensor, yPredRidge),    rmse: rmse(yTestTensor, yPredRidge),    mae: mae(yTestTensor, yPredRidge),    r2: r2Score(yTestTensor, yPredRidge),    pred: yPredRidge,  },]; console.log("\nModel Comparison:\n");const metricsDF = new DataFrame({  Model: results.map((r) => r.name),  "MSE (×10⁻⁵)": results.map((r) => (r.mse * 100000).toFixed(4)),  "RMSE (%)": results.map((r) => (r.rmse * 100).toFixed(4)),  "MAE (%)": results.map((r) => (r.mae * 100).toFixed(4)),  "R² Score": results.map((r) => r.r2.toFixed(4)),});console.log(metricsDF.toString()); // Directional accuracyconsole.log("\nDirectional Accuracy (predicting up/down):");for (const result of results) {  const predData = result.pred.toArray() as number[];  let correct = 0;  for (let i = 0; i < yTest.length; i++) {    const actualDirection = yTest[i] > 0 ? 1 : -1;    const predDirection = predData[i] > 0 ? 1 : -1;    if (actualDirection === predDirection) correct++;  }  const dirAcc = correct / yTest.length;  console.log(`  ${result.name.padEnd(20)}: ${(dirAcc * 100).toFixed(2)}%`);} // ============================================================================// Step 7: Autocorrelation Analysis// ============================================================================ console.log("\nSTEP 7: Autocorrelation Analysis");console.log("─".repeat(70)); // Calculate autocorrelation of returnsconsole.log("\nReturn Autocorrelation:");for (const lag of [1, 5, 10, 20]) {  const returns1 = returns.slice(0, returns.length - lag);  const returns2 = returns.slice(lag);  const [corr] = pearsonr(tensor(returns1), tensor(returns2));  console.log(`  Lag ${String(lag).padStart(2)}: ${corr.toFixed(4)}`);} // ============================================================================// Step 8: Visualizations// ============================================================================ console.log("\nSTEP 8: Generating Visualizations");console.log("─".repeat(70)); // Price charttry {  const fig = new Figure({ width: 1000, height: 400 });  const ax = fig.addAxes();   const xValues = Array.from({ length: prices.length }, (_, i) => i);  ax.plot(tensor(xValues), tensor(prices), { color: "#2196F3", linewidth: 1 });  ax.setTitle("Stock Price Over Time");  ax.setXLabel("Day");  ax.setYLabel("Price ($)");   const svg = fig.renderSVG();  writeFileSync(`${OUTPUT_DIR}/price-chart.svg`, svg.svg);  console.log(`  Saved: ${OUTPUT_DIR}/price-chart.svg`);} catch (e) {  console.log(`  Warning: could not generate price chart: ${e}`);} // Returns distributiontry {  const fig = new Figure({ width: 800, height: 400 });  const ax = fig.addAxes();   // Create histogram  const numBins = 30;  const minRet = Math.min(...returns);  const maxRet = Math.max(...returns);  const binWidth = (maxRet - minRet) / numBins;   const bins: number[] = [];  const counts: number[] = [];  for (let i = 0; i < numBins; i++) {    const binCenter = minRet + (i + 0.5) * binWidth;    const count = returns.filter(      (r) => r >= minRet + i * binWidth && r < minRet + (i + 1) * binWidth    ).length;    bins.push(binCenter * 100);    counts.push(count);  }   ax.bar(tensor(bins), tensor(counts), { color: "#4CAF50" });  ax.setTitle("Daily Returns Distribution");  ax.setXLabel("Return (%)");  ax.setYLabel("Frequency");   const svg = fig.renderSVG();  writeFileSync(`${OUTPUT_DIR}/returns-distribution.svg`, svg.svg);  console.log(`  Saved: ${OUTPUT_DIR}/returns-distribution.svg`);} catch (e) {  console.log(`  Warning: could not generate returns distribution: ${e}`);} // ============================================================================// Step 9: Summary// ============================================================================ console.log(`\n${"═".repeat(70)}`);console.log("  FORECASTING COMPLETE - SUMMARY");console.log("═".repeat(70)); const bestModel = results.reduce((best, r) => (r.r2 > best.r2 ? r : best)); console.log("\nKey Findings:\n");console.log("  1. Data Overview:");console.log(`     • ${NUM_DAYS} days of price data`);console.log(`     • Annualized return: ${(meanReturn * 252 * 100).toFixed(2)}%`);console.log(`     • Annualized volatility: ${(stdReturn * Math.sqrt(252) * 100).toFixed(2)}%`); console.log("\n  2. Best Model:");console.log(`     • ${bestModel.name}`);console.log(`     • R² Score: ${bestModel.r2.toFixed(4)}`);console.log(`     • RMSE: ${(bestModel.rmse * 100).toFixed(4)}%`); console.log("\n  3. Observations:");console.log("     • The synthetic returns are close to white noise, so autocorrelation is low");console.log("     • R² is near zero, so the models barely beat the mean baseline");console.log("     • Directional accuracy stays near 50%"); console.log("\nOutput Files:");console.log(`   • ${OUTPUT_DIR}/price-chart.svg`);console.log(`   • ${OUTPUT_DIR}/returns-distribution.svg`); console.log(`\n${"═".repeat(70)}`);console.log("  Stock Price Forecasting Complete!");console.log("═".repeat(70));

Output

Console output
Return statistics, indicator values and the model comparison table on the console
`output/price-chart.svg`
`output/returns-distribution.svg`