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Seasonality in Mixed Causal-Noncausal Processes

Tomás del Barrio Castro, Alain Hecq, Sean Telg

arXiv 8 Apr 2026 · Econometrics

arXiv:2604.07040 · PDF · DOI · OpenAlex · Extracted main text

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.

Citation extraction

27
references
60
in-text mentions
27
distinct cited
6
self-citations
12,735
main-text words

appendix boundary found by appendix_titled_section at “Appendix” · 76% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Fries, S. and Zakoian, J.-M (2019) Mixed Causal-Noncausal AR Processes and the Modelling of Explosive Bubbles1.000103100%
2Lanne, M. and Saikkonen, P (2011) Noncausal Autoregressions for Economic Time Series1.00053100%
3Bec, F. and Nielsen, H.B. and Saïdi, S (2020) Mixed Causal-Noncausal Autoregressions: Bimodality Issues in Estimation and Unit Root Testing0.92844100%
4Hecq, A. and Lieb, L. and Telg, S (2016) Identification of Mixed Causal-Noncausal Models in Finite Samples self0.92843100%
5Gianluca Cubadda and Francesco Giancaterini and Alain Hecq and Joann… (2024) Optimization of the generalized covariance estimator in noncausal processes self0.84333100%
6Gouriéroux, C. and Zako\"ian, J.M (2017) Local explosion modelling by non-causal process0.84333100%
7Pollock, D.S.G (1999) A Handbook of Time-Series Analysis, Signal Processing and Dynamics0.64441100%
8del Barrio Castro, T. and Rodrigues, P.M.M. and Taylor, R.A.M (2019) Temporal Aggregation of Seasonally Near-Integrated Processes0.6443267%
9Gouriéroux, C. and Jasiak, J (2016) Filtering, Prediction and Simulation Methods for Noncausal Processes0.64422100%
10Hecq, Alain and Issler, Joao Victor and Telg, Sean (2020) Mixed causal-noncausal autoregressions with exogenous regressors self0.64422100%

Showing the top 10 of 27 scored citations.