This thesis considers three important threshold time series models: threshold moving-average (TMA) models, threshold double autoregressive (TDAR) models and multiple-regime threshold autoregressive (MTAR) models. For the TMA model, I investigate its strict stationarity and ergodicity, and establish the asymptotic theory of its least squares estimation. I also develop the asymptotic theories on the quasi-maximum likelihood estimation of TDAR models and the least squares estimation of MTAR models. A simulation method is proposed for the limiting distribution of the estimated threshold. These models are illustrated with applications to three real examples. The most important contribution in the thesis is to develop some new asymptotic theories, especially the limiting distribution of the e...[ Read more ]

This thesis considers three important threshold time series models: threshold moving-average (TMA) models, threshold double autoregressive (TDAR) models and multiple-regime threshold autoregressive (MTAR) models. For the TMA model, I investigate its strict stationarity and ergodicity, and establish the asymptotic theory of its least squares estimation. I also develop the asymptotic theories on the quasi-maximum likelihood estimation of TDAR models and the least squares estimation of MTAR models. A simulation method is proposed for the limiting distribution of the estimated threshold. These models are illustrated with applications to three real examples. The most important contribution in the thesis is to develop some new asymptotic theories, especially the limiting distribution of the estimated threshold in TMA models and asymptotic independence among the estimated thresholds in MTAR models. These results have made quite a big step forward on statistical inference foundations of threshold time series models.