Seasonality in Mixed Causal-Noncausal Processes
Tomás del Barrio Castro, Alain Hecq, Sean Telg
TLDR
This paper shows seasonal roots in Mixed Causal-Noncausal Autoregressive (MAR) models can be isolated, preventing new joint seasonal effects.
Key contributions
- Analyzes complex and negative roots in Mixed Causal-Noncausal Autoregressive (MAR) models.
- Demonstrates seasonal roots can be isolated in moving average representations of AR models.
- Proves this isolation extends to MAR models, preventing new joint seasonal effects.
- Studies implications for MAR model selection using simulations and real-world data.
Why it matters
This paper is important because it simplifies the understanding of seasonality in complex MAR models. By showing seasonal effects are isolable, it has significant consequences for MAR model selection procedures. This improves the accuracy and reliability of time series analysis.
Original 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.
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