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Maximum likelihood estimation and forecasting for GARCH, Markov switching, and locally stationary wavelet processes

Xie, Yingfu (2007). Maximum likelihood estimation and forecasting for GARCH, Markov switching, and locally stationary wavelet processes. Diss. (sammanfattning/summary) Umeå : Sveriges lantbruksuniv., Acta Universitatis agriculturae Sueciae, 1652-6880 ; 2007:107
ISBN 978-91-85913-06-0
[Doctoral thesis]

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Abstract

Financial time series are frequently met both in daily life and the scientific world. It is clearly of importance to study the financial time series, to understand the mechanism giving rise to the data, and/or predict the future values of a series. This thesis is dedicated to statistical inferences of a number of models for financial time series. Financial time series often exhibit time-varying and clustering volatility (conditional variance), which were not handled well by traditional models, until the development of the autoregressive conditionally heteroscedastic (ARCH) and the generalized ARCH (GARCH) models. We prove the consistency and asymptotic normality of the quasi-maximum likelihood estimators for a GARCH(1,2) model with dependent innovations, which extends the results for the GARCH(1,1) model in the literature under weaker conditions. The regime-switching GARCH (RS-GARCH) model extends the GARCH models by incorporating a Markov switching into the variance structure. The statistical inferences for the RS-GARCH model are difficult due to the complex dependence structure. One alternative is to take average over all regimes at every step, and adapt the integrated conditional variances. Another one is to transform the GARCH into an ARCH model. The maximum likelihood (ML) estimation of these two cases is considered. Consistency of the ML estimators is proved, and the asymptotic normality is suggested by simulation studies. The results are further generalized to a general autoregressive model with Markov switching, in which the autoregression can be of infinite order. Consistency of the ML estimators is obtained and the asymptotic normality is conjectured. Time series analysis can also be conducted in frequency domain, i.e. to analyze their spectral values obtained by e.g. Fourier or wavelet transforms. Locally stationary wavelet (LSW) processes are a class of processes defined on a set of non-decimated wavelets. We first address the problem on how to select a wavelet in practice, and some guidelines are suggested by simulation studies. The existing forecasting algorithm for LSW processes is found vulnerable to outliers, and a new forecasting algorithm is proposed to overcome this weakness. The new algorithm is shown stable and outperforms the existing algorithm when applied to real financial data. The volatility forecasting ability of LSW model based on our new algorithm is then discussed and is shown to be competitive with GARCH models. Algorithms and functions for data generation, calculation and maximization of the likelihoods for RS-GARCH models, and for the new forecasting algorithm of LSW processes are appended.

Authors/Creators:Xie, Yingfu
Title:Maximum likelihood estimation and forecasting for GARCH, Markov switching, and locally stationary wavelet processes
Series/Journal:Acta Universitatis agriculturae Sueciae (1652-6880)
Year of publishing :2007
Volume:2007:107
Number of Pages:35
Papers/manuscripts:
NumberReferences
ALLI Xie, Y. and Yu, J. 2003. Asymptotics for quasi-maximum likelihood estimators of GARCH(1,2) model under dependent innovations. Research report 2003:5, Centre of Biostochastics, Swedish University of Agricultural Sciences (submitted). II Xie, Y. and Yu, J. 2005. Consistency of maximum likelihood estimators for the reduced regime-switching GARCH models. Research report 2005:2, Centre of Biostochastics, Swedish University of Agricultural Sciences (submitted). III Xie, Y. 2007. Consistency of maximum likelihood estimators for the regime-switching GARCH model. Statistics (to appear). IV Xie, Y., Yu, J. and Ranneby, B. 2007. Forecasting using locally stationary wavelet processes. Research report 2007:2, Centre of Biostochastics, Swedish University of Agricultural Sciences (submitted). V Xie, Y., Yu, J. and Ranneby, B. 2007. A general autoregressive model with Markov switching: estimation and consistency. Research report 2007:6, Centre of Biostochastics, Swedish University of Agricultural Sciences.
Place of Publication:Umeå
Publisher:Department of Forest Economics, Swedish University of Agricultural Sciences
ISBN for printed version:978-91-85913-06-0
ISSN:1652-6880
Language:English
Publication Type:Doctoral thesis
Full Text Status:Public
Agrovoc terms:time series analysis, statistical methods, forecasting, simulation models
Keywords:Consistency, Financial time series, Forecasting, GARCH, LSW process, Maximum likelihood estimation, Markov switching, Non-decimated wavelet, Volatility forecasting
URN:NBN:urn:nbn:se:slu:epsilon-1840
Permanent URL:
http://urn.kb.se/resolve?urn=urn:nbn:se:slu:epsilon-1840
ID Code:1594
Faculty:S - Faculty of Forest Sciences
Department:(S) > Dept. of Forest Economics
Deposited By: Yingfu Xie
Deposited On:16 Oct 2007 00:00
Metadata Last Modified:11 Jun 2015 08:51

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