Parsimonious periodic autoregressive models for time series with evolving trend and seasonality

This paper proposes an extension of Periodic AutoRegressive (PAR) modelling for time series with evolving features. The large scale of modern datasets, in fact, implies that the time span may subtend several evolving patterns of the underlying series, affecting also seasonality. The proposed model allows several regimes in time and a possibly different PAR process with a trend term in each regime. The means, autocorrelations and residual variances may change both with the regime and the season, resulting in a very large number of parameters. Therefore as a second step we propose a grouping procedure on the PAR parameters, in order to obtain a more parsimonious and concise model. The model selection procedure is a complex combinatorial problem, and it is solved basing on genetic algorithms that optimize an information criterion. The model is tested in both simulation studies and real data analysis from different fields, proving to be effective for a wide range of series with evolving features, and competitive with respect to more specific models.