ABSTRACTIn this dissertation, firstly, I study spatial quantile regression estimation of multivariate threshold time series models. Asymptotic normality of the proposed spatial quantile regression estimator is established. Simulations and a real example are used to evaluate the performance of the proposed estimator. Secondly, I study the multivariate time-varying coefficient models for time series data. An explicit solution of the coefficient estimators is given in the paper. Furthermore, I propose generalized likelihood ratio test for the multivariate time-varying coefficient models, my aim is to construct some test statistics to test whether the coefficients are constants or of some specific parametric functional for the time-varying coefficient model. The asymptotic null distribution of the proposed test statistics is presented and shown to be independent of the nuisance parameters. Simulation results for the power of the test and a real example are reported at the end of this dissertation.