Seasonality in Mixed Causal-Noncausal Processes

TL;DR

This paper analyzes how seasonal roots influence mixed causal-noncausal autoregressive models, showing that no new seasonal effects arise from their multiplicative structure, with implications for model selection.

Contribution

It demonstrates that seasonal roots can be isolated in MAR models and that their multiplicative structure does not generate new seasonal effects, impacting model selection procedures.

Findings

Seasonal roots can be isolated in MAR models.

Multiplicative structure does not produce new seasonal effects.

Monte Carlo simulations validate the theoretical results.

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.