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Specification testing for regression models with dependent data

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  • Hidalgo, Javier

Abstract

We describe and examine a consistent test for the correct specification of a regression function with dependent data. The test is based on the supremum of the difference between the parametric and nonparametric estimates of the regression model. Rather surprisingly, the behaviour of the test depends on whether the regressors are deterministic or stochastic. In the former situation, the normalization constants necessary to obtain the limiting Gumbel distribution are data dependent and difficult to estimate, so to obtain valid critical values may be difficult, whereas in 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 Carlo experiment.

Suggested Citation

  • Hidalgo, Javier, 2007. "Specification testing for regression models with dependent data," LSE Research Online Documents on Economics 6799, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:6799
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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. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
    3. Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-890, July.
    4. 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.
    5. Javier Hidalgo, 2000. "Nonparametric Test for Causality with Long-Range Dependence," Econometrica, Econometric Society, vol. 68(6), pages 1465-1490, November.
    6. 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.
    7. 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.
    8. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, vol. 59(5), pages 1329-1363, September.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    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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    1. Hidalgo, J., 2008. "Specification testing for regression models with dependent data," Journal of Econometrics, Elsevier, vol. 143(1), pages 143-165, March.

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    More about this item

    Keywords

    Functional specification. Variable selection. Nonparametric kernel regression. 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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