Stationarity for a Markov-switching Box-Cox transformed threshold GARCH process
In order to capture three important dynamic characteristics of time series, the asymmetry, regimes, and conditional heteroskedasticity, based on Hwang and Basawa's [2004. Stationarity and moment structure for Box-Cox transformed threshold GARCH(1,1) processes. Statist. Probab. Lett. 68, 209-220] and Haas et al. [2004. A new approach to Markov-switching GARCH models. J. Financial Econometrics 2, 493-530] models, this paper proposes a Markov-switching Box-Cox transformed threshold GARCH model. Some structural properties of this new GARCH process are considered. First, a sufficient and necessary condition for the existence of the weakly and strictly stationary solution of the process is presented, respectively. Second, the general conditions for the existence of high-order moments of the process are derived. The technique used in this paper for the weak stationarity and the high-order moments of the process is different from that used in Haas et al. [2004. A new approach to Markov-switching GARCH models. J. Financial Econometrics 2, 493-530], and avoids the assumption that the process started in the infinite past with finite variance.
Year of publication: |
2007
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Authors: | Liu, Ji-Chun |
Published in: |
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 77.2007, 13, p. 1428-1438
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Publisher: |
Elsevier |
Keywords: | Markov-switching GARCH Threshold GARCH Weak stationarity Strict stationarity Existence of moments |
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