In case of seasonality in the data, autocorrelation in the model differ by season. For example, in case of quarterly sales data of a company, if the fourth autocorrelations of the error term differ significantly from 0 → This is a sign of seasonality in the model.
When t-statistic of the fourth lag of autocorrelations of the error > critical t-value → reject null hypothesis that fourth autocorrelations is 0. Thus, there is seasonality problem.
Correcting Seasonality: This problem can be solved by adding seasonal lags in an AR model i.e. after including a seasonal lag in case of quarterly sales data, the AR model becomes:
xt = b0 + b1x (t-1) + b2x(t-4) + et
NOTE: R(square) of the model without seasonal lag will be less than the R(square) of the model with seasonal lag. This implies that when time series exhibit seasonality, including a seasonal lag in the model improves the accuracy of the model.