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Tests for serial correlation of unknown form in dynamic least squares regression with wavelets

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  • Li, Meiyu
  • Gençay, Ramazan

Abstract

This paper extends the multi-scale serial correlation tests of Gençay and Signori (2015) for observable time series to unobservable errors of unknown forms in a linear dynamic regression model. Our tests directly build on the variance ratio of the sum of squared wavelet coefficients of residuals over the sum of squared residuals, utilizing the equal contribution of each frequency of a white noise process to its variance and delivering higher empirical power than parametric tests. Our test statistics converge to the standard normal distribution at the parametric rate under the null hypothesis, faster than the nonparametric test using kernel estimators of the spectrum.

Suggested Citation

  • Li, Meiyu & Gençay, Ramazan, 2017. "Tests for serial correlation of unknown form in dynamic least squares regression with wavelets," Economics Letters, Elsevier, vol. 155(C), pages 104-110.
    • Handle: RePEc:eee:ecolet:v:155:y:2017:i:c:p:104-110
    DOI: 10.1016/j.econlet.2017.03.021
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    References listed on IDEAS

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    1. Wooldridge, Jeffrey M., 1991. "On the application of robust, regression- based diagnostics to models of conditional means and conditional variances," Journal of Econometrics, Elsevier, vol. 47(1), pages 5-46, January.
    2. Breusch, T S, 1978. "Testing for Autocorrelation in Dynamic Linear Models," Australian Economic Papers, Wiley Blackwell, vol. 17(31), pages 334-355, December.
    3. Chen, Willa W. & Deo, Rohit S., 2004. "A Generalized Portmanteau Goodness-Of-Fit Test For Time Series Models," Econometric Theory, Cambridge University Press, vol. 20(2), pages 382-416, April.
    4. Hong, Yongmiao, 1996. "Consistent Testing for Serial Correlation of Unknown Form," Econometrica, Econometric Society, vol. 64(4), pages 837-864, July.
    5. Willa W. Chen & Rohit S. Deo, 2004. "Power transformations to induce normality and their applications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 117-130, February.
    6. Godfrey, Leslie G, 1978. "Testing against General Autoregressive and Moving Average Error Models When the Regressors Include Lagged Dependent Variables," Econometrica, Econometric Society, vol. 46(6), pages 1293-1301, November.
    7. Gençay, Ramazan & Gençay, Ramazan & Selçuk, Faruk & Whitcher, Brandon J., 2001. "An Introduction to Wavelets and Other Filtering Methods in Finance and Economics," Elsevier Monographs, Elsevier, edition 1, number 9780122796708.
    8. Wooldridge, Jeffrey M., 1990. "An encompassing approach to conditional mean tests with applications to testing nonnested hypotheses," Journal of Econometrics, Elsevier, vol. 45(3), pages 331-350.
    9. Gençay, Ramazan & Signori, Daniele, 2015. "Multi-scale tests for serial correlation," Journal of Econometrics, Elsevier, vol. 184(1), pages 62-80.
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    More about this item

    Keywords

    Dynamic least squares regression; Serial correlation; Conditional heteroscedasticity; Maximum overlap discrete wavelet transformation;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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