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:
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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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