Abstract
Over recent years, several nonlinear time series models have been proposed in the literature. One model that has found a large number of successful applications is the threshold autoregressive model (TAR). The TAR model is a piecewise linear process whose central idea is to change the parameters of a linear autoregressive model according to the value of an observable variable, called the threshold variable. If this variable is a lagged value of the time series, the model is called a self-exciting threshold autoregressive (SETAR) model. In this article, we propose a heuristic to estimate a more general SETAR model, where the thresholds are multivariate. We formulate the task of finding multivariate thresholds as a combinatorial optimization problem. We develop an algorithm based on a greedy randomized adaptive search procedure (GRASP) to solve the problem. GRASP is an iterative randomized sampling technique that has been shown to quickly produce good quality solutions for a wide variety of optimization problems. The proposed model performs well on both simulated and real data.
Original language | English (US) |
---|---|
Pages (from-to) | 236-258 |
Number of pages | 23 |
Journal | Journal of Computational and Graphical Statistics |
Volume | 11 |
Issue number | 1 |
DOIs | |
State | Published - 2002 |
Externally published | Yes |
Keywords
- Combinatorial optimization
- GRASP
- Nonlinear time series analysis
- Piecewise linear models
- Search heuristic
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Discrete Mathematics and Combinatorics