Unified quasi-maximum likelihood estimation theory for stable and unstable Markov bilinear processes

Abdelhakim Aknouche

MPRA Paper from University Library of Munich, Germany

Abstract: A unified quasi-maximum 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.

Keywords: Markov bilinear process; random coefficient process; stability; instability; Quasi-maximum likelihood; knife edge effect; strict stationarity testing. (search for similar items in EconPapers)
JEL-codes: C10 C13 C18 C19 (search for similar items in EconPapers)
Date: 2015
New Economics Papers: this item is included in nep-ecm and nep-ets
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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:69572

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