Lanne, Markku and Saikkonen, Pentti (2005): A Multivariate Generalized Orthogonal Factor GARCH Model.

PDF
MPRA_paper_23714.pdf Download (480Kb)  Preview 
Abstract
The paper studies a factor GARCH model and develops test procedures which can be used to test the number of factors needed to model the conditional heteroskedasticity in the considered time series vector. Assuming normally distributed errors the parameters of the model can be straightforwardly estimated by the method of maximum likelihood. Inefficient but computationally simple preliminary estimates are first obtained and used as initial values to maximize the likelihood function. Maximum likelihood estimation with nonnormal errors is also straightforward. Motivated by the empirical application of the paper a mixture of normal distributions is considered. An interesting feature of the implied factor GARCH model is that some parameters of the conditional covariance matrix which are not identifiable in the case of normal errors become identifiable when the mixture distribution is used. As an empirical example we consider a system of four exchange rate return series.
Item Type:  MPRA Paper 

Original Title:  A Multivariate Generalized Orthogonal Factor GARCH Model 
Language:  English 
Keywords:  Multivariate GARCH model; mixture of normal distributions; exchange rate 
Subjects:  C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C51  Model Construction and Estimation C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models; Multiple Variables > C32  TimeSeries Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models F  International Economics > F3  International Finance > F31  Foreign Exchange 
Item ID:  23714 
Depositing User:  Markku Lanne 
Date Deposited:  08. Jul 2010 19:28 
Last Modified:  15. Feb 2013 19:27 
References:  Aitchison, J. and S.D. Silvey (1959). Maximumlikelihoon estimation of parameters subject to restraints. Annals of Mathematical Statistics 29, 813828. Alexander, C. (2001). A primer on orthogonal GARCH model. Mimeo. ISMA Centre. Andrews, D.W.K. (1987). Asymptotic results for generalized Wald tests. Econometric Theory 3, 348358. Comte, F. and O. Lieberman (2003). Asymptotic theory for multivariate GARCH processes. Journal of Multivariate Analysis 84, 1, 6184. Bauwens, L., S. Laurent, and J.V.K. Rombouts (2003). Multivariate GARCH models: A survey. Journal of Applied Econometrics (forthcoming). Davidson, J. (2000). Econometric Theory. Blackwell Publishers Ltd, Oxford. Engle, R.F. and K.F. Kroner (1995). Multivariate simultaneous generalized GARCH. Econometric Theory 11, 122150. Engle, R.F., V.K. Ng, and M. Rotschield (1990). Asset pricing with a factor ARCH covariance structure: Empirical estimates for treasury bills. Journal of Econometrics 45, 213237. Franses, P.H., D. van Dijk, and A. Lucas (2004). Short patches of outliers, ARCH and volatility modelling. Applied Financial Economics 14, 221—231. Hafner, C.M. and H. Herwartz (2003). Analytical quasi maximum likelihood inference in multivariate volatility models, Econometric Institute Report 2003/21, Erasmus Universiteit Rotterdam. Horn, R.A. and C.H. Johnson (1985). Matrix Analysis. Cambridge University Press, Cambridge. Kawakatsu, H. (2003). Cholesky factor GARCH. Mimeo. Quantitative Micro Software. Klaassen, F. (2000). Have exchange rates become more closely tied? Evidence from a new multivariate GARCH model. Discussion Paper. University of Amsterdam. Ling, S. and W.K. Li (1997). Diagnostic checking of nonlinear multivariate time series with multivariate ARCH errors. Journal of Time Series Analysis 18, 447464. Lütkepohl, H. (1996). Handbook of Matrices. John Wiley & Sons. Chichester. Mencía, F.J., and E. Sentana (2004). Estimation and testing of dynamic models with generalised hyperbolic innovations. CEMFI Working Paper No. 0411. Silvey. S.D. (1959). The Lagrangian multiplier test. Annals of Mathematical Statistics 30, 389407. van der Weide, R. (2002). GOGARCH: A multivariate generalized orthogonal GARCH model. Journal of Applied Econometrics 17, 549564. Vrontos, I.D., P. Dellaportas and D.N. Politis (2003). A fullfactor multivariate GARCH model. Econometrics Journal 6, 312334. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/23714 