Fries, Sébastien and Zakoian, JeanMichel (2017): Mixed CausalNoncausal AR Processes and the Modelling of Explosive Bubbles.
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Abstract
Noncausal autoregressive models with heavytailed 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 causalnoncausal autoregressive processes, assuming the errors follow a stable nonGaussian 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 lightertailed 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 noni.i.d. errors can be consistently estimated by classical leastsquares. 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.
Item Type:  MPRA Paper 

Original Title:  Mixed CausalNoncausal AR Processes and the Modelling of Explosive Bubbles 
Language:  English 
Keywords:  Noncausal process, Stable process, Extreme clustering, Explosive bubble, Portmanteau test. 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C52  Model Evaluation, Validation, and Selection C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C53  Forecasting and Prediction Methods ; Simulation Methods 
Item ID:  86926 
Depositing User:  Sébastien Fries 
Date Deposited:  28 May 2018 18:56 
Last Modified:  03 Oct 2019 15:13 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/86926 
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Mixed CausalNoncausal AR Processes and the Modelling of Explosive Bubbles. (deposited 16 Sep 2017 09:01)
 Mixed CausalNoncausal AR Processes and the Modelling of Explosive Bubbles. (deposited 28 May 2018 18:56) [Currently Displayed]