Simulation, Estimation and Selection of Mixed Causal-Noncausal Autoregressive Models: The MARX Package

Hecq, Alain; Lieb, Lenard; Telg, Sean

doi:10.2139/ssrn.3015797

Cited by 11 publications

(8 citation statements)

References 15 publications

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“…Portmanteau tests are however not designed to select an «optimal» model. To go further, we report in Table Q.3 the orders that minimise Akaike's information criterion (AIC) using the R package 'MARX' available on CRAN (see Hecq, Telg and Lieb (2017b)). The validity of such AIC's for innovations in the domain of attraction of a stable law has been studied by Knight (1989).…”

Section: R Real Data: Complementary Results Using the R Package 'Marxmentioning

confidence: 99%

“…including deconvolution of seismic signals [Wiggins (1978), Donoho (1981), Hsueh and Mendel (1985)], and analysis of astronomical data [Scargle (1981)]. Recent years have witnessed the emergence of a significant line of research on noncausal models in the econometric literature [see e.g., Lanne, Nyberg and Saarinen (2012), Lanne, Saikkonen (2011), Davis and Song (2012), Chen, Choi and Escanciano (2012), Hencic and Gouriéroux (2015), Velasco and Lobato (2015), Hecq, Lieb and Telg (2016, 2017a, 2017b, Cavaliere, Nielsen and Rahbek (2017)]. The distinction between causal and noncausal processes is only meaningful in a non-Gaussian framework, and the increasing interest in Mixed causal-noncausal AR processes (MAR) parallels the widespread use of non-Gaussian heavy-tailed processes in economic or financial applications.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: R Real Data: Complementary Results Using the R Package 'Marxmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Fries

Zakoïan²

2019

Econom. Theory

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“…When the distribution of innovations is known, a non-Gaussian likelihood approach can be used to discriminate between lag and lead polynomials of the dependent variable. For instance, the R package MARX developed by (Hecq, Lieb, and Telg 2017a) estimates univariate mixed models under the assumption of a Student's t-distribution with v degrees of freedom (see also Saikkonen 2011, 2013) as well as the Cauchy distribution as a special case of the Student's t when v = 1. Gouriéroux and Zakoian (2016) privilege the latter distribution to derive analytical results.…”

Section: Motivationmentioning

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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“…sequence, often referred to as anticipative, have witnessed a recent surge of attention from the statistical and econometric literatures. This gain of interest is driven in particular by their convenience for modelling exotic patterns in time series, such as explosive bubbles in financial prices [6,10,13,14,17,19,20,21,22,23] (see also [1,4,5,7,15,16,26,27,31]). The attractive flexibility of anticipative processes cannot yet be fully leveraged however, as their dynamics, and especially the conditional distribution of future paths given the observed past trajectory, remains largely mysterious.…”

Section: Introductionmentioning

confidence: 99%

Path prediction of aggregated $α$-stable moving averages using semi-norm representations

Fries¹

2018

Preprint

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For (X t ) a two-sided α-stable moving average, this paper studies the conditional distribution of future paths given a piece of observed trajectory when the process is far from its central values.Under this framework, vectors of the form X t = (X t−m , . . . , X t , X t+1 , . . . , X t+h ), m ≥ 0, h ≥ 1, are multivariate α-stable and the dependence between the past and future components is encoded in their spectral measures. A new representation of stable random vectors on unit cylinders -sets {s ∈ R m+h+1 : s = 1} for • an adequate semi-norm-is proposed in order to describe the tail behaviour of vectors X t when only the first m + 1 components are assumed to be observed and large in norm. Not all stable vectors admit such a representation and (X t ) will have to be «anticipative enough» for X t to admit one. The conditional distribution of future paths can then be explicitly derived using the regularly varying tails property of stable vectors and has a natural interpretation in terms of pattern identification. The approach extends to processes resulting from the linear combination of stable moving averages and applied to several examples.

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Simulation, Estimation and Selection of Mixed Causal-Noncausal Autoregressive Models: The MARX Package

Cited by 11 publications

References 15 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

Path prediction of aggregated $α$-stable moving averages using semi-norm representations

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