Estimation and identification of periodic autoregressive models with one exogenous variable

This paper analyzes the identification and estimation procedures for periodic autoregressive models with one exogenous variable (PARX). The identification of the optimal PARX model is based on the use of a genetic algorithm combined with the Bayes information criterion. The estimation of the parameters relies on the least squares method and their asymptotic properties are studied. Two simulation experiments are performed and indicate the success of the suggested method. A PARX model is used to study the relationship between the catch-per-unit-effort and the sea surface temperature as exogenous variable for the shrimp French Guiana fishery from January 1989 to December 2012.