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A Combinatorial Approach to Piecewise Linear Time Series Analysis

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Author Info

  • Medeiros, Marcelo

    ()
    (Dept. of Economic Statistics, Stockholm School of Economics)

  • Veiga, Alvaro

    ()
    (Dept. of Electrical Engineering)

  • Resende, Mauricio

    ()
    (Information Sciences Research Center, Algorithms and Optimization Research Department)

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.

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Bibliographic Info

Paper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 393.

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Length: 30 pages
Date of creation: 26 Jun 2000
Date of revision:
Publication status: Published in Journal of Computational and Graphical Statistics, 2002, pages 236-258.
Handle: RePEc:hhs:hastef:0393

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Related research

Keywords: nonlinear time series; piecewise linear models; combinatorial optimization; search heuristic; GRASP;

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Cited by:
  1. Roberto Baragona & Domenico Cucina, 2013. "Multivariate Self-Exciting Threshold Autoregressive Modeling by Genetic Algorithms," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), Justus-Liebig University Giessen, Department of Statistics and Economics, vol. 233(1), pages 3-21, January.
  2. Strikholm, Birgit & Teräsvirta, Timo, 2005. "Determining the Number of Regimes in a Threshold Autoregressive Model Using Smooth Transition Autoregressions," Working Paper Series in Economics and Finance 578, Stockholm School of Economics, revised 11 Feb 2005.

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