LASSO-type estimations for threshold autoregressive and heteroscedastic time series models

This thesis proposes LASSO type estimators and develops associated algorithms to perform simultaneous parameter estimation and model selection for five specific univariate and multivariate time series models. Empirical studies based on the univariate and multivariate SETAR model show that the BCD algorithms estimate fewer irrelevant thresholds than the approximate group LASSO algorithms. Further, for both pure ARCH and pure multivariate BEKK-ARCH models, our CGD algorithms exclude irrelevant terms more often and have more stable parameter convergence than the existing modified shooting algorithms. CGD and weighted BCD algorithms are also proposed for pure GARCH and SETAR-GARCH models respectively.