School of Mathematics and Statistics

Postgraduate research

Research being undertaken by our current postgraduates:


Muhammad Jaffri Mohd Nasir


Start date

Mar 2015

Submission date

Oct 2018

Muhammad Jaffri Mohd Nasir

Muhammad Jaffri Mohd Nasir profile photo


Statistical Inference for Multiple Threshold Autoregressive Model with Heteroscedasticity


Time series data especially in finance and economics are known to exhibit various nonlinear behaviors such as asymmetries, jumps phenomenon and time irreversibility for both data series and their volatility. For example, financial data series with their volatility such as log of return of a stock exchange might behaves differently when the log of return is in different states (either positive, negative or zero return). In addition, it is also common for the time series data to exhibit heavy tails or skewed distributions. Thus, these characteristics need to be taken under scrupulous consideration when conducting statistical inference.

The threshold autoregressive model (TAR) of Tong and Lim (1980) and Tong (1990) is well-known and widely applied in various fields such as statistics, psychology and econometrics due to its capabilities in explaining multiple nonlinear behaviors existed in time series data and can provides much direct and easier interpretations of analysis outcomes compared to other class of nonlinear time series models. However, further rigorous work can be done to improve inference of TAR model with volatility effect in terms of computational speed and accuracy in detecting the exact number and location of thresholds. This work can be further extended to the multivariate time-series model with volatility effect which is still in an early stage. Involvement of heavy-tail distributions are also considered to assess the robustness of TAR inference for case of time series with skewed distribution.

Why my research is important

Efficient asymmetric identification and estimation of multiple thresholds via TAR model, with volatility effect, are crucial for several applications (etc. in finance, economics,...) in order to explain or to forecast various nonlinear behaviors existed in time series data more accurately.

In previous time, modeling time series for multiple regimes are difficult via traditional approach since multidimensional grid search coupled with data segregation approach is required for the purpose. Furthermore, the traditional approach is complex, time consuming and infeasible for large sample size. Based on these arguments, this research will develop more feasible modeling procedures and algorithms to minimize the aforementioned problems while gaining more accurate estimation for the TAR model.


  • Ministry of Higher Education (Malaysia)

Statistics clinic

Assistance in statistics is available for Postgraduates students by research at the UWA Centre for Applied Statistics.


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Monday, 16 June, 2014 2:41 PM