Bootstrapping Noncausal Autoregressions: With Applications to Explosive Bubble Modeling

Cavaliere, Giuseppe; Nielsen, Heino Bohn; Rahbek, Anders

doi:10.1080/07350015.2018.1448830

Cited by 32 publications

(29 citation statements)

References 34 publications

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“…for MAR processes, and byCavaliere et al (2018) using bootstrap inference for pure noncausal processes. We proposed an alternative strategy based on extreme clustering and leave its asymptotic properties for further investigations.…”

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confidence: 99%

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

Fries

Zakoïan²

2019

Econom. Theory

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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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confidence: 99%

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

Fries

Zakoïan²

2019

Econom. Theory

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“…For all commodity series we do not reject the null of no autocorrelation, but we still observe nonnormality and heteroskedasticity using standard diagnostic tests on the residuals of the identified MARX models. Tests for homoskedasticity proposed by Gouriéroux and Zakoïan (2016) and Cavaliere, Nielsen, and Rahbek (2020) assume that the true model is noncausal with i.i.d. Cauchy error term, which is not the case here, as most series are heteroskedastic both in direct and reverse time.…”

Section: Identification and Estimation Of Marxmentioning

confidence: 99%

Mixed causal–noncausal autoregressions with exogenous regressors

Hecq

Issler

Telg

2020

J of Applied Econometrics

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Mixed causal-noncausal autoregressive (MAR) models have been proposed to model time series exhibiting nonlinear dynamics. Possible exogenous regressors are typically substituted into the error term to maintain the MAR structure of the dependent variable. We introduce a representation including these covariates called MARX to study their direct impact. The asymptotic distribution of the MARX parameters is derived for a class of non-Gaussian densities. For a Student t likelihood, closed-form standard errors are provided. By simulations, we evaluate the MARX model selection procedure using information criteria. We examine the influence of the exchange rate and industrial production index on commodity prices.

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“…Hence, it is advisable to check the residuals of the pseudo-causal model for the presence of ARCH effects in the spirit of misspecification analysis. Cavaliere et al (2017) propose to use an alternative to the standard Lagrange multiplier test (Engle's ARCH LM test) as it is based on conventional asymptotic Gaussian p-values, which are not appropriate in this framework. To circumvent this problem, they suggest a test based on Spearman's rank statistic, which tests non-parametrically the relationship between the residuals and the square of the lagged residuals.…”

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confidence: 99%

Do Seasonal Adjustments Induce Noncausal Dynamics in Inflation Rates?

2017

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This paper investigates the effect of seasonal adjustment filters on the identification of mixed causal-noncausal autoregressive models. By means of Monte Carlo simulations, we find that standard seasonal filters induce spurious autoregressive dynamics on white noise series, a phenomenon already documented in the literature. Using a symmetric argument, we show that those filters also generate a spurious noncausal component in the seasonally adjusted series, but preserve (although amplify) the existence of causal and noncausal relationships. This result has has important implications for modelling economic time series driven by expectation relationships. We consider inflation data on the G7 countries to illustrate these results.

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Bootstrapping Noncausal Autoregressions: With Applications to Explosive Bubble Modeling

Abstract: This article may be used for non-commercial purposes in accordance with Taylor and Francis and Conditions for Use of Self-Archived Versions.

Cited by 32 publications

References 34 publications

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

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

Mixed causal–noncausal autoregressions with exogenous regressors

Do Seasonal Adjustments Induce Noncausal Dynamics in Inflation Rates?

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