Comparing ARIMA Models

Since there is some guesswork in deciding which ARIMA(p,d,q) process to use (i.e. which value to choose for p, q and d), we may need to look at various processes. As for other regression processes, Akaike Information Criterion (AIC) and Schwarz Bayesian Criterion (SBC), aka Schwarz Information Criterion (SIC) or Bayesian Information Criteria (BIC), can be used for this purpose. Generally, the process with the lower AIC or BIC value should be selected. Here

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where n = the sample size and k = the number of parameters (including σ2) = p+q+c+1 where c = 1 if there is a constant term and c = 0 otherwise.

The above measures leave out the constant term n(1+LN(2π).

Example 1: Which produces a better model for the data in Example 1 of Real Statistics ARMA Tool, the ARIMA(2,0,1) model with constant or the ARIMA(2,1,1) model with zero constant.

Based on the Akaike Information Criterion, AIC = 16.682 for the ARIMA(2,0,1) model (see Figure 2 of Real Statistics ARMA Tool), while AIC = 26.768 for the ARIMA(2,1,1) model (see Figure 1 of Calculating ARIMA Model Coefficients). Thus, we choose the ARIMA(2,0,1) as the better model.

We get the same result using the Bayesian Information Criteria: BIC = 29.856 vs. BIC = 37.267.

8 thoughts on “Comparing ARIMA Models”

  1. Hi Charles,

    I’ve noticed that the AIC and BIC values are given in OLS regressions. I’m holding a single variable x constant in ten models, but varying all the remaining variables j through t-5 to t+5. As such these are causal models where I test the effect of j on x and x on j. I am wondering whether the AIC and BIC values will be useful for comparison between the models, as an indicator of an ‘optimal lag’, where the smallest AIC/BIC values imply those lag periods of which the causal effect is strongest? (assuming the variables are found to be statistically significant in the regressions)

    Thank you

    Reply

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