Seasonality in Mixed Causal-Noncausal Processes

Abstract

This paper investigates the role of complex and negative roots in mixed causal-noncausal autoregressive (MAR) models. Using partial fraction decompositions, we show that seasonal roots can always be isolated in the moving average representation of purely causal and noncausal AR models. We find that this result extends to the MAR model, which means that no new joint seasonal effects can be generated despite the multiplicative structure of the causal and noncausal polynomials. This results has important consequences for the MAR model selection procedure and these are extensively studied in a Monte Carlo simulation study. An empirical application on COVID-19 and soybean data illustrates the main findings of the paper.