AUTOHWS_FORECAST

Holt-Winters Seasonal (HWS) Forecasting

The Holt-Winters Seasonal (HWS) method, also known as Triple Exponential Smoothing, is a popular technique for forecasting time series data that exhibits trend and seasonality. It extends the Holt-Winters method by incorporating a seasonal component, making it suitable for data with recurring patterns over fixed intervals (e.g., monthly, quarterly, or yearly data).

Components of Holt-Winters Seasonal Model

The HWS model consists of three main components:

  1. Level (L): Represents the baseline value of the series at a given point in time.
  2. Trend (T): Captures the increasing or decreasing trend in the data.
  3. Seasonality (S): Accounts for periodic fluctuations or patterns in the data.

The model is defined by three smoothing parameters:

  • Alpha (α): Controls the smoothing of the level.
  • Beta (β): Controls the smoothing of the trend.
  • Gamma (γ): Controls the smoothing of the seasonality.

Types of Holt-Winters Seasonal Models

There are two variants of the HWS model, depending on the nature of the seasonality:

  1. Additive Model:

    • Used when the seasonal fluctuations are roughly constant throughout the series.
    • Formula:

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    • Here, mm is the length of the seasonal period (e.g., 12 for monthly data with yearly seasonality).

  2. Multiplicative Model:

    • Used when the seasonal fluctuations grow or shrink proportionally with the level of the series.
    • Formula:

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Parameters of AUTO_HWS_FORECAST

The AUTO_HWS_FORECAST technique automates the process of selecting the best parameters for the Holt-Winters Seasonal model. It determines:

  1. Smoothing Parameters (α, β, γ):

    • These are optimized to minimize the forecast error (e.g., Mean Squared Error or MSE).

    • Possible values: Between 0 and 1.

      • A value closer to 1 gives more weight to recent observations.
      • A value closer to 0 gives more weight to past observations.

  2. Seasonal Period (m):

    • The length of the seasonal cycle (e.g., 12 for monthly data with yearly seasonality, 4 for quarterly data).
    • This is typically inferred from the data or specified by the user.

  3. Model Type (Additive or Multiplicative):

    • The algorithm automatically selects the appropriate model type based on the characteristics of the data.