Periodic autoregressive models with multiple structural changes by genetic algorithms

We present a model and a computational procedure for dealing with seasonality and regime changes in time series. In this work we are interested in time series which in addition to trend display seasonality in mean, in autocorrelation and in variance. These type of series appears in many areas, including hydrology, meteorology, economics and finance. The seasonality is accounted for by subset PAR modelling, for which each season follows a possibly different Autoregressive model. Levels, trend, autoregressive parameters and residual variances are allowed to change their values at fixed unknown times. The identification of number and location of structural changes, as well as $PAR$ lags indicators, is based on Genetic Algorithms, which are suitable because of high dimensionality of the discrete search space. An application to Italian industrial production index time series is also proposed.