A Combinatorial Approach to Piecewise Linear Time Series Analysis
AbstractOver 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 InfoPaper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 393.
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.
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nonlinear time series; piecewise linear models; combinatorial optimization; search heuristic; GRASP;
Find related papers by JEL classification:
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
This paper has been announced in the following NEP Reports:
- NEP-ALL-2000-09-01 (All new papers)
- NEP-ECM-2000-09-18 (Econometrics)
- NEP-ETS-2000-09-01 (Econometric Time Series)
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- 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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