A combinatorial approach to piecewise linear time series analysis

M.C. Medeiros, A. Veiga, and M.G.C. Resende

Journal of Computational and Graphical Statistics, vol. 11, pp. 236-258, 2002


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 paper, we propose a heuristic to estimate a more general SETAR model, where the thresholds are multivariate.  We formulated the task of finding multivariate thresholds as a combinatorial optimization problem. We developed 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.

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