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Using Extraneous Information and GMM to Estimate Threshold Parameters in TAR Models

Author

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  • George Kapetanios

    (Queen Mary, University of London)

Abstract

A prominent class of nonlinear time series models are threshold autoregressive models. Recently work by Kapetanios (2000) has shown in a Monte Carlo setting that the superconsistency property of the threshold parameter estimates does not translate to superior performance in small samples. Another issue concerning inference for the threshold parameters relates to estimation of their standard errors. As the asymptotic distribution of the threshold parameters is neither normal nor nuisance parameter free, an outstanding issue is how to obtain standard errors and confidence intervals for them. This paper aims to address these issues. In particular, we suggest that using extraneous information on the location of the threshold parameters may lead to better estimates. The extraneous information comes in the form of moment conditions that relate residuals of standard threshold models to shocks driving other variables. Additionally the paper considers the problem of estimating standard errors and confidence intervals for threshold parameter estimates. We suggest use of the bootstrap for this problem.

Suggested Citation

  • George Kapetanios, 2003. "Using Extraneous Information and GMM to Estimate Threshold Parameters in TAR Models," Working Papers 494, Queen Mary University of London, School of Economics and Finance.
    • Handle: RePEc:qmw:qmwecw:494
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    File URL: https://www.qmul.ac.uk/sef/media/econ/research/workingpapers/2003/items/wp494.pdf
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    References listed on IDEAS

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    1. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    2. Kapetanios, George, 2000. "Small sample properties of the conditional least squares estimator in SETAR models," Economics Letters, Elsevier, vol. 69(3), pages 267-276, December.
    3. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
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    Cited by:

    1. Araujo-Enciso, Sergio Rene, 2011. "The Takayama and Judge Price and Allocation Model and its Application in Non-linear Techniques for Spatial Market Integration," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 114225, European Association of Agricultural Economists.

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    More about this item

    Keywords

    Threshold Models; GMM; Bootstrap;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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