Scandinavian Working Papers in Economics

SSE/EFI Working Paper Series in Economics and Finance,
Stockholm School of Economics

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

Marcelo Medeiros (), Alvaro Veiga () and Mauricio Resende ()
Additional contact information
Marcelo Medeiros: Dept. of Economic Statistics, Stockholm School of Economics, Postal: Stockholm School of Economics, P.O. Box 6501, S-113 83 Stockholm, Sweden
Alvaro Veiga: Dept. of Electrical Engineering, Postal: Catholic University of Rio de Janeiro (PUC-Rio), Rua Marquês de São Vicente 225, Rio de Janeiro, RJ, Brazil, 22453-900
Mauricio Resende: Information Sciences Research Center, Algorithms and Optimization Research Department, Postal: AT&T Labs Research, Room C241, 180 Park Avenue, P. O. Box 971, Florham Park, NJ 07932-0971, USA

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

JEL-codes: C22; C51

30 pages, June 26, 2000

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