Automatic ARIMA selection

A popular criterion for comparing autoregressive-moving average (ARMA) models with different lags is a measure known as Akaike’s Information Criterion (AIC). The AIC for an ARMA univariate series is calculated by

$$AIC = -2 \cdot ln(L) + 2r$$

where L = the value of the maximum likelihood function for the fitted model, and r = p+q+1, the number of parameters in the ARMA model. To use the criterion, several choices for p and q are fit to a time series and the fit with the smallest AIC is considered best.

Another criterion often used in the ARMA model selection is the Corrected AIC (AICC), defined as

$$AICC = -2 \cdot ln(L) + 2r(n/(n-r-1))$$

where n denotes the number of data points in the series.

A third criterion, the Bayesian Information Criterion (BIC), is computed as

$$BIC = -2 \cdot ln(L) + r \cdot ln(n)$$

Function imsl.timeseries.auto_arima() uses one of these criteria to select a best fitting ARIMA model, considering not only the ARMA parameters, but also the appropriate Box-Cox transformation, degree of differencing and seasonal adjustment. The function also filters the data for outliers.

For a detailed study of model selection criteria, see [1].

[1]	Burnham, Kenneth P. and David R. Anderson (2002), Model Selection and Multimodel Inference, second Edition, Springer-Verlag, New York.