Modeling high-frequency foreign exchange rate dynamics

In this thesis, I focus on the estimation and application of multivariate GARCH type model. Start with introduction of state-space model and Kalman filter technique, and modify them for the estimation of multivariate GARCH-type model. In addition, I also discuss the issues arising in implementation of Kalman filter iteration and provide the possible solutions. Another issue discussed here is the efficient model estimation with missing data. The technique introduced here is to take advantage of state-space model setting and Kalman filter iteration of information flow. It does not involve any imputation of missing value. Simulation results show the method work very well in recovery of true model even facing large proportion of missing observations.; Then I explore the model specifications and estimation of multivariate ARMA-GARCH model by introducing different specifications of covariance matrix in order to reduce the number of coefficients to be estimated to a workable level. The specifications include constant correlation GARCH, time-varying correlation GARCH, factor GARCH model and simultaneous ARMA-factor GARCH model. A simulation result is provided for the comparison of two stage estimations and simultaneous estimation of ARMA-factor GARCH model.; Another issue studied here is Bayesian approach and Bayesian Kalman filter. A Bayesian filter is derived for Gaussian density function. The Bayesian filter not only offer an alternative for model estimation but also demonstrates some robustness in dealing with large portion of missing data in estimation.; A set of computer program in MATLAB are developed for the full implementation of all type of model discussed in this thesis (User instruction is attached in Appendix).; Finally as an application of modeling and implementation method developed here, a two dimension of high frequency (at 3 minute interval) foreign exchange rate (JPY/USD and DEM/USD) are modeled and estimated. The missing data is introduced at non-trading periods. The application fully use the techniques developed in previous chapters. To avoid the estimation to be trapped into local optima, the optimization routine is combined with generic algorithm in order to search global optima. The results suggest the bivariate model is superior to the univariate model given strong evidence of correlation within two series.