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Specification Testing Forregression Models Withdependent Data

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  • Javier Hidalgo

Abstract

We describe and examine a consistent test for the correct specification of aregression function with dependent data. The test is based on the supremum of thedifference between the parametric and nonparametric estimates of the regressionmodel. Rather surprisingly, the behaviour of the test depends on whether theregressors are deterministic or stochastic. In the former situation, the normalizationconstants necessary to obtain the limiting Gumbel distribution are data dependentand difficult to estimate, so to obtain valid critical values may be difficult, whereasin the latter, the asymptotic distribution may not be even known. Because of that,under very mild regularity conditions we describe a bootstrap analogue for the test,showing its asymptotic validity and finite sample behaviour in a small Monte Carloexperiment.

Suggested Citation

  • Javier Hidalgo, 2007. "Specification Testing Forregression Models Withdependent Data," STICERD - Econometrics Paper Series 518, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:518
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    References listed on IDEAS

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    1. Javier Hidalgo & Peter M Robinson, 1997. "Time Series Regression with Long Range Dependence - (Now published in 'Annals of Statistics', 25, (1997)pp.2054-2083.)," STICERD - Econometrics Paper Series 318, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. Johnston, Gordon J., 1982. "Probabilities of maximal deviations for nonparametric regression function estimates," Journal of Multivariate Analysis, Elsevier, vol. 12(3), pages 402-414, September.
    3. Hidalgo, Javier, 2003. "An alternative bootstrap to moving blocks for time series regression models," LSE Research Online Documents on Economics 6850, London School of Economics and Political Science, LSE Library.
    4. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, vol. 59(5), pages 1329-1363, September.
    5. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
    6. Javier Hidalgo, 1999. "Nonparametric tests for model selection with time series data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(2), pages 365-398, December.
    7. Javier Hidalgo, 2000. "Nonparametric Test for Causality with Long-Range Dependence - (Now published in Econometrica, 68, (2000) pp.1465-1490," STICERD - Econometrics Paper Series 387, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    8. Delgado, Miguel A. & Hidalgo, Javier & Velasco, Carlos, 2005. "Distribution free goodness-of-fit tests for linear processes," LSE Research Online Documents on Economics 6840, London School of Economics and Political Science, LSE Library.
    9. Javier Hidalgo, 2003. "An Alternative Bootstrap to Moving Blocks for Time Series Regression Models," STICERD - Econometrics Paper Series 452, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    10. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December.
    11. Hidalgo, Javier, 2003. "An alternative bootstrap to moving blocks for time series regression models," Journal of Econometrics, Elsevier, vol. 117(2), pages 369-399, December.
    12. Clifford M. Hurvich, 2001. "Model Selection for Broadband Semiparametric Estimation of Long Memory in Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(6), pages 679-709, November.
    13. Javier Hidalgo, 2000. "Nonparametric Test for Causality with Long-Range Dependence," Econometrica, Econometric Society, vol. 68(6), pages 1465-1490, November.
    14. Javier Hidalgo & Peter M. Robinson, 2002. "Adapting to Unknown Disturbance Autocorrelation in Regression with Long Memory," Econometrica, Econometric Society, vol. 70(4), pages 1545-1581, July.
    15. Javier Hidalgo, 1997. "Non‐Parametric Estimation With Strongly Dependent Multivariate Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(2), pages 95-122, March.
    16. Hidalgo, Javier, 2000. "Nonparametric test for causality with long-range dependence," LSE Research Online Documents on Economics 6866, London School of Economics and Political Science, LSE Library.
    17. Robinson, Peter M., 1997. "Large-sample inference for nonparametric regression with dependent errors," LSE Research Online Documents on Economics 302, London School of Economics and Political Science, LSE Library.
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    More about this item

    Keywords

    Functional specification. Variable selection. Nonparametric kernelregression. Frequency domain bootstrap.;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: 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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