Periodic Autoregressive Models for Stochastic Seasonality

Book cover Mathematical and Statistical Methods for Actuarial Sciences and Finance pp 79–85Cite as Periodic Autoregressive Models for Stochastic Seasonality Roberto Baragona, Francesco Battaglia & Domenico Cucina Conference paper First Online: 14 December 2021 238 Accesses Abstract The periodic autoregressive (PAR) models for seasonal time series data seem able to take into account simultaneously many issues, e.g. the mean level and the second order moments. The problem naturally arises if seasonal unit roots have to be imposed on the model structure for taking into account stochastic seasonality. Statistical tests for the presence of seasonal unit roots have been developed, but in this environment they may suffer from some drawbacks. The approach can be advantageously reversed, that is the attention may focus on model building in the first place, then the goodness of fit may be checked according to some suitable criterion. The effectiveness of the suggested procedure has been confirmed by a comprehensive simulation study that includes a comparison with some well-known widely used seasonal unit roots tests. An application to the monthly Italian general industrial production index (1993–2016) is also presented