Autoregressive (AR) Forecasting

The Autoregressive (AR) Forecasting technique is a statistical method used for time series forecasting. It models the relationship between a current observation and its past values, assuming that the current value depends linearly on its previous values. This method is particularly useful for stationary time series data, where the statistical properties (mean, variance, etc.) remain constant over time.

Key Concepts of Autoregressive Models

  1. Autoregressive Process:

    • An autoregressive model of order p, denoted as AR(p), predicts the current value of a time series based on its p previous values.
    • The general form of an AR(p) model is:

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Where:

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  1. Stationarity Requirement:

    • AR models require the time series to be stationary. If the data is non-stationary, differencing or transformation may be applied to achieve stationarity.

  2. Order of the Model (p):

    • The order p represents the number of lagged observations included in the model.
    • Selecting the appropriate value of p is critical for model performance.