A Recursive Algorithm of the Threshold Estimator in SETAR model

• Main Authors: Lee, Wen-ray, 李文瑞
• Other Authors: Guo, Mei-hui
• Format: Others
• Language: zh-TW
• Published: 1995
• Online Access: http://ndltd.ncl.edu.tw/handle/58883431687709282067

碩士 === 國立中山大學 === 應用數學研究所 === 83 === In this paper, the threshold estimator based on the least squares method in a two-pieces stationary and ergodic Self- Exciting Threshold Autoregressive(SETAR) model is considered. The traditional approach requires to compute n sums of squared residuals. In this paper, we shall consider a recursive algorithm to compute this estimator for a set of updated data when a preliminary estimator is available for the original data. It is shown that $|F_n(\hat{r}_n)-F_n(r)|$ is $O_p(1/n)$, where $F_n$ is the empirical distribution function and $\hat{r}_n$ is the least squares estimator of the threshold parameter r. This implies that $|(n+1)F_{n+1}(\hat{r}_n)-(n+1) F_{n+1}(\hat{r}_{n+1})| =O_p(1)$, which provides a new approach to compute $\hat{r}_{n+1}$ with a very reduced amount of computation of the sums of squared residuals. Some further discussion is also given.