 MIXED CAUSAL-NONCAUSAL AR PROCESSES AND THE MODELLING OF EXPLOSIVE BUBBLESSebastien Fries and Jean-Michel Zakoian Econometric Theory, 2019, vol. 35, issue 6, 1234-1270 Abstract: 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. Date: 2019 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:cup:etheor:v:35:y:2019:i:6:p:1234-1270_5 Access Statistics for this article More articles in Econometric Theory from Cambridge University Press Cambridge University Press, UPH, Shaftesbury Road, Cambridge CB2 8BS UK. |
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