Mixed causal–noncausal autoregressions with exogenous regressors

Noncausal autoregressive models with heavy-tailed errors generate locally explosive processes and, therefore, provide a convenient framework for modelling bubbles in economic and financial time series. We investigate the probability properties of mixed causal-noncausal autoregressive processes, assuming the errors follow a stable non-Gaussian distribution. Extending the study of the noncausal AR(1) model by Gouriéroux and Zakoian (2017), we show that the conditional distribution in direct time is lighter-tailed than the errors distribution, and we emphasize the presence of ARCH effects in a causal representation of the process. Under the assumption that the errors belong to the domain of attraction of a stable distribution, we show that a causal AR representation with non-i.i.d. errors can be consistently estimated by classical least-squares. We derive a portmanteau test to check the validity of the estimated AR representation and propose a method based on extreme residuals clustering to determine whether the AR generating process is causal, noncausal, or mixed. An empirical study on simulated and real data illustrates the potential usefulness of the results.

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“…MAR processes have been considered, among others, by Lanne and Saikkonen (2011), Gouriéroux and Jasiak (2016), Hecq, Issler, and Telg (2017).…”

Section: Stable Mar(p Q) Processesmentioning

confidence: 99%

Mixed Causal-Noncausal Ar Processes and the Modelling of Explosive Bubbles

Fries

Zakoïan²

2019

Econom. Theory

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“…It would be interesting to extend our modelling to investigate theoretical models with both forward and backward behaviours such as backward-and forward-looking Taylor rule for instance. To do that however we have to introduce additional regressors and extend the approach of Hecq, Issler, and Telg (2020) to quantile regressions, which can be further investigated by future research and is out of the scope of this paper.…”

Section: Modelling Hyperinflation In Latin America 61 the Model Specmentioning

confidence: 99%

Selecting between causal and noncausal models with quantile autoregressions

Hecq

Sun

2020

Studies in Nonlinear Dynamics &Amp; Econometrics

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We propose a model selection criterion to detect purely causal from purely noncausal models in the framework of quantile autoregressions (QAR). We also present asymptotics for the i.i.d. case with regularly varying distributed innovations in QAR. This new modelling perspective is appealing for investigating the presence of bubbles in economic and financial time series, and is an alternative to approximate maximum likelihood methods. We illustrate our analysis using hyperinflation episodes of Latin American countries.

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“…Lanne and Saikkonen (2011a) propose a two-step approach to identify MAR models; a procedure that got extended to MARX models in Hecq et al (2017a). In the proposed model selection procedure, it is assumed that the exogenous variables are chosen a priori.…”

Section: Modelling Proceduresmentioning

confidence: 99%

“…However, we did not yet discuss the marx() function, which completely integrates the two steps of the model selection procedure. In this section, we will apply the function to commodity prices in relation to the U.S. exchange rate, similar to Hecq et al (2017a). They consider the growth rate of commodity prices, as these series are believed to potentially contain a forward-looking component similar to more general measures of inflation.…”

Section: An Application On Commodity Pricesmentioning

confidence: 99%

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Mixed causal-noncausal models

Telg

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Mixed causal–noncausal autoregressions with exogenous regressors

Cited by 16 publications

References 21 publications

Mixed Causal-Noncausal Ar Processes and the Modelling of Explosive Bubbles

Mixed Causal-Noncausal Ar Processes and the Modelling of Explosive Bubbles

Selecting between causal and noncausal models with quantile autoregressions

Mixed causal-noncausal models

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