Holt-Winters Forecasting Algorithm

holtWinters.js

function holtWinters(alpha, beta, gamma, period, data) {
  let seasonals = {};
  let r = [];
  let initialSeasonals = [];
  let detrended = [];
  let forecast = [];
  let dataPoints = data.length;
  let avgSmooth = [];
  let trendSmooth = [];
  let seasonalSmooth = [];

  //initialize seasonals to the average of each cycle
  for (let i = 0; i < period; i++) {
    seasonals[i] = [];
    for (let j = i; j < dataPoints; j += period) {
      seasonals[i].push(data[j]);
    }
    initialSeasonals[i] = (seasonals[i].reduce((a, b) => a + b, 0) / seasonals[i].length);
  }

  //initialize first level of smoothed averages
  for (let i = 0; i < period; i++) {
    avgSmooth[i] = (data.slice(i, i + period).reduce((a, b) => a + b, 0) / period);
  }

  //initialize first level of smoothed trends
  for (let i = 0; i < period; i++) {
    trendSmooth[i] = ((data[period + i] - data[i]) / period);
  }

  //initialize seasonalSmooth
  for (let i = 0; i < period; i++) {
    seasonalSmooth[i] = initialSeasonals[i] - avgSmooth[i];
  }

  //determine r
  for (let i = 0; i < dataPoints - period; i++) {
    r[i] = data[period + i] - (avgSmooth[i] + trendSmooth[i]);
  }

  //smooth the detrended values
  for (let i = 0; i < dataPoints - period; i++) {
    detrended[i] = (alpha * (data[period + i] - seasonalSmooth[i])) + ((1 - alpha) * (detrended[i - 1] || r[0]));
  }

  //smooth the trend
  for (let i = 0; i < period; i++) {
    trendSmooth[period + i] = (beta * (detrended[i] - detrended[i - period])) + ((1 - beta) * trendSmooth[i]);
  }

  //smooth the seasonals
  for (let i = 0; i < period; i++) {
    seasonalSmooth[i] = (gamma * (data[period + i] - avgSmooth[i] - detrended[i])) + ((1 - gamma) * seasonalSmooth[i]);
  }

  //calculate the forecast
  for (let i = 0; i < period; i++) {
    forecast[i] = avgSmooth[i] + ((i + 1) * trendSmooth[period + i]) + seasonalSmooth[i - period];
  }

  return forecast;
}


// Input data for the time series
const data = [
  100,
  120,
  130,
  140,
  150,
  160,
  170,
  180,
  190,
  200,
  210,
  220,
  230,
  240,
  250,
  260,
  270,
  280,
  290,
  300,
];

// Apply Holt-Winters method with alpha=0.2, beta=0.1, gamma=0.1, and period=4
const forecast = hw(data, {
  alpha: 0.2,
  beta: 0.1,
  gamma: 0.1,
  period: 4,
  forecastLength: 5,
});

// Output the forecast values
console.log(forecast);

// Level: L(t) = alpha * Y(t) + (1 - alpha) * (L(t-1) + T(t-1))
// Trend: T(t) = beta * (L(t) - L(t-1)) + (1 - beta) * T(t-1)
// Seasonality: S(t) = gamma * (Y(t) - L(t)) + (1 - gamma) * S(t-m)
// F(t+h) = L(t) + h * T(t) + S(t-m+1+(h-1)modm)