Logo
Munich Personal RePEc Archive

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

Fries, Sébastien and Zakoian, Jean-Michel (2017): Mixed Causal-Noncausal AR Processes and the Modelling of Explosive Bubbles.

This is the latest version of this item.

[thumbnail of MPRA_paper_86926.pdf]
Preview
PDF
MPRA_paper_86926.pdf

Download (890kB) | Preview

Abstract

Noncausal autoregressive models with heavy-tailed errors generate locally explosive processes and therefore provide a natural 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.

Available Versions of this Item

Atom RSS 1.0 RSS 2.0

Contact us: mpra@ub.uni-muenchen.de

This repository has been built using EPrints software.

MPRA is a RePEc service hosted by Logo of the University Library LMU Munich.