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The Economic Research Institute, Stockholm School of Economics SSE/EFI Working Paper Series in Economics and Finance

No 393:
A Combinatorial Approach to Piecewise Linear Time Series Analysis

Marcelo Medeiros (), Alvaro Veiga () and Mauricio Resende ()

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 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.

Keywords: nonlinear time series; piecewise linear models; combinatorial optimization; search heuristic; GRASP; (follow links to similar papers)

JEL-Codes: C22; C51; (follow links to similar papers)

30 pages, June 26, 2000

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This paper is published as:
Medeiros, Marcelo, Alvaro Veiga and Mauricio Resende, (2002), 'A Combinatorial Approach to Piecewise Linear Time Series Analysis', Journal of Computational and Graphical Statistics, Vol. 11, March, No. 1, pages 236-258

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