Aknouche, Abdelhakim (2015): Unified quasimaximum likelihood estimation theory for stable and unstable Markov bilinear processes. Published in: Nova Publisher Science (2015)

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Abstract
A unified quasimaximum likelihood (QML) estimation theory for stationary and nonstationary simple Markov bilinear (SMBL) models is proposed. Such models may be seen as generalized random coefficient autoregressions (GRCA) in which the innovation and the random coefficient processes are fully correlated. It is shown that the QML estimate (QMLE) for the SMBL model is always asymptotically Gaussian without assuming strict stationarity, meaning that there is no knife edge effect. The asymptotic variance of the QMLE is different in the stationary and nonstationary cases but is consistently estimated using the same estimator. A perhaps surprising result is that in the nonstationary domain, all SMBL parameters are consistently estimated in contrast with unstable GARCH and GRCA models where the QMLE of the conditional variance intercept is inconsistent. As a result, strict stationarity testing for the SMBL is studied. Simulation experiments and a real application to strict stationarity testing for some financial stock returns illustrate the theory in finite samples.
Item Type:  MPRA Paper 

Original Title:  Unified quasimaximum likelihood estimation theory for stable and unstable Markov bilinear processes 
English Title:  Unified quasimaximum likelihood estimation theory for stable and unstable Markov bilinear processes 
Language:  English 
Keywords:  Markov bilinear process, random coefficient process, stability, instability, Quasimaximum likelihood, knife edge effect, strict stationarity testing. 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C10  General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C18  Methodological Issues: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C19  Other 
Item ID:  69572 
Depositing User:  Prof. Abdelhakim Aknouche 
Date Deposited:  18 Feb 2016 12:04 
Last Modified:  10 Oct 2019 05:57 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/69572 