This thesis develops the systematic procedures of statistical inference for the heavy-tailed threshold autoregressive (TAR) models and heavy-tailed multiple threshold double autoregressive (MTDAR) models, respectively. The asymptotic theory of the self-weighted least absolute deviation (SLAD) estimation for the TAR models and quasi-maximum exponential likelihood estimation (QMELE) for the MTDAR models are obtained. Since the objective functions of these two models involves the discontinuous threshold parameters, the arguments in this thesis are more demanding than the usual LAD estimation. To our knowledge, this is the first attempt to study the asymptotic theory for the estimation of the heavy-tailed threshold time series in the literature. This thesis also investigates the l...[ Read more ]

This thesis develops the systematic procedures of statistical inference for the heavy-tailed threshold autoregressive (TAR) models and heavy-tailed multiple threshold double autoregressive (MTDAR) models, respectively. The asymptotic theory of the self-weighted least absolute deviation (SLAD) estimation for the TAR models and quasi-maximum exponential likelihood estimation (QMELE) for the MTDAR models are obtained. Since the objective functions of these two models involves the discontinuous threshold parameters, the arguments in this thesis are more demanding than the usual LAD estimation. To our knowledge, this is the first attempt to study the asymptotic theory for the estimation of the heavy-tailed threshold time series in the literature. This thesis also investigates the large sample theory of quasi-maximum likelihood estimator (QMLE) for a threshold GARCH model with unknown threshold parameter. Three empirical examples are given to illustrate the usefulness of these threshold models. All of these results are new and bridge a gap in the statistical literature of nonlinear time series.