Advances in applied nonlinear time series modeling

Time series modeling and forecasting are of vital importance in many real world applications. Recently nonlinear time series models have gained much attention, due to the fact that linear time series models faced various limitations in many empirical applications. In this thesis, a large variety of standard and extended linear and nonlinear time series models is considered in order to compare their out-of-sample forecasting performance. We examined the out-of-sample forecast accuracy of linear Autoregressive (AR), Heterogeneous Autoregressive (HAR), Autoregressive Conditional Duration (ACD), Threshold Autoregressive (TAR), Self-Exciting Threshold Autoregressive (SETAR), Logistic Smooth Transition Autoregressive (LSTAR), Additive Autoregressive (AAR) and Artificial Neural Network (ANN) models and also the extended Heterogeneous Threshold Autoregressive (HTAR) or Heterogeneous Self-Exciting Threshold Autoregressive (HSETAR) model for financial, economic and seismic time series. We also extended the previous studies by using Vector Autoregressive (VAR) and Threshold Vector Autoregressive (TVAR) models and compared their forecasting accuracy with linear models for the above mentioned time series. Unlike previous studies that typically consider the threshold models specifications by using internal threshold variable, we specified the threshold models with external transition variables and compared their out-of-sample forecasting performance with the linear benchmark HAR and AR models by using the financial, economic and seismic time series. According to our knowledge, this is the first study of its kind that extends the usage of linear and nonlinear time series models in the field of seismology by utilizing the seismic data from the Hindu Kush region of Pakistan. The question addressed in this study is whether nonlinear models produce 1 through 4 step-ahead forecasts that improve upon linear models. The answer is that linear model mostly yields more accurate forecasts than nonlinear ones for financial, economic and seismic time series. Furthermore, while modeling and forecasting the financial (DJIA, FTSE100, DAX and Nikkei), economic (the USA GDP growth rate) and seismic (earthquake magnitudes, consecutive elapsed times and consecutive distances between earthquakes occurred in the Hindu Kush region of Pakistan) time series, it appears that using various external threshold variables in threshold models improve their out-of-sample forecasting performance. The results of this study suggest that constructing the nonlinear models with external threshold variables has a positive effect on their forecasting accuracy. Similarly for seismic time series, in some cases, TVAR and VAR models provide improved forecasts over benchmark linear AR model. The findings of this study could somehow bridge the analytical gap between statistics and seismology through the potential use of linear and nonlinear time series models. Secondly, we extended the linear Heterogeneous Autoregressive (HAR) model in a nonlinear framework, namely Heterogeneous Threshold Autoregressive (HTAR) model, to model and forecast a time series that contains simultaneously nonlinear and long-range dependence phenomena. The model has successfully been applied to financial data (DJIA, FTSE100, DAX and Nikkei) and the results show that HTAR model has improved 1-step-ahead forecasting performance than linear HAR model by utilizing the financial data of DJIA. For DJIA, the combination of the forecasts from HTAR and linear HAR models are improved over those obtained from the benchmark HAR model. Furthermore, we conducted a simulated study to assess the performance of HAR and HSETAR models in the presence of spurious long-memory type phenomena contains by a time series. The main purpose of this study is to answer the question, for a time series, whether the HAR and HSETAR models have an ability to detect spurious long-memory type phenomena. The simulation results show that HAR model is completely unable to discriminate between true and spurious long-memory type phenomena. However the extended HSETAR model is capable of detecting spurious long-memory type phenomena. This study provides an evidence that it is better to use HSETAR model, when it is suspected that the underlying time series contains some spurious long-memory type phenomena. To sum up, this thesis is a vital tool for researchers who have to choose the best forecasting model from a large variety of models discussed in this thesis for modeling and forecasting the economic, financial, and mainly seismic time series.