Model order selection in seasonal/cyclical long memory models

We propose an automatic model order selection procedure for k-factor GARMA processes. The procedure is based on sequential tests of the maximum of the periodogram and semiparametric estimators of the model parameters. As a byproduct, we introduce a generalized version of Walker's large sample g-test that allows to test for persistent periodicity in stationary ARMA processes. Our simulation studies show that the procedure performs well in identifying the correct model order under various circumstances. An application to Californian electricity load data illustrates its value in empirical analyses and allows new insights into the periodicity of this process that has been subject of several forecasting exercises.