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Multi-scale tests for serial correlation

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  • Gençay, Ramazan
  • Signori, Daniele

Abstract

This paper introduces a new family of portmanteau tests for serial correlation. Using the wavelet transform, we decompose the variance of the underlying process into the variance of its low frequency and of its high frequency components and we design a variance ratio test of no serial correlation in the presence of dependence. Such decomposition can be carried out iteratively, each wavelet filter leading to a rich family of tests whose joint limiting null distribution is a multivariate normal. We illustrate the size and power properties of the proposed tests through Monte Carlo simulations.

Suggested Citation

  • Gençay, Ramazan & Signori, Daniele, 2015. "Multi-scale tests for serial correlation," Journal of Econometrics, Elsevier, vol. 184(1), pages 62-80.
    • Handle: RePEc:eee:econom:v:184:y:2015:i:1:p:62-80
    DOI: 10.1016/j.jeconom.2014.08.002
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    1. Lobato I. N., 2001. "Testing That a Dependent Process Is Uncorrelated," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1066-1076, September.
    2. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
    3. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    4. Hansen, Bruce E., 1991. "GARCH(1, 1) processes are near epoch dependent," Economics Letters, Elsevier, vol. 36(2), pages 181-186, June.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Breusch, T S, 1978. "Testing for Autocorrelation in Dynamic Linear Models," Australian Economic Papers, Wiley Blackwell, vol. 17(31), pages 334-355, December.
    7. Escanciano, J. Carlos & Lobato, Ignacio N., 2009. "An automatic Portmanteau test for serial correlation," Journal of Econometrics, Elsevier, vol. 151(2), pages 140-149, August.
    8. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    9. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    10. Davidson, James, 2004. "Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 16-29, January.
    11. Hong, Yongmiao, 1996. "Consistent Testing for Serial Correlation of Unknown Form," Econometrica, Econometric Society, vol. 64(4), pages 837-864, July.
    12. Efstathios Paparoditis, 2000. "Spectral Density Based Goodness‐of‐Fit Tests for Time Series Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(1), pages 143-176, March.
    13. Roll, Richard, 1984. "A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market," Journal of Finance, American Finance Association, vol. 39(4), pages 1127-1139, September.
    14. Yongmiao Hong & Chihwa Kao, 2004. "Wavelet-Based Testing for Serial Correlation of Unknown Form in Panel Models," Econometrica, Econometric Society, vol. 72(5), pages 1519-1563, September.
    15. Narasimhan Jegadeesh & Sheridan Titman, 2001. "Profitability of Momentum Strategies: An Evaluation of Alternative Explanations," Journal of Finance, American Finance Association, vol. 56(2), pages 699-720, April.
    16. Fan, Yanqin & Gençay, Ramazan, 2010. "Unit Root Tests With Wavelets," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1305-1331, October.
    17. Lee, Jin & Hong, Yongmiao, 2001. "Testing For Serial Correlation Of Unknown Form Using Wavelet Methods," Econometric Theory, Cambridge University Press, vol. 17(2), pages 386-423, April.
    18. de Jong, Robert M., 1997. "Central Limit Theorems for Dependent Heterogeneous Random Variables," Econometric Theory, Cambridge University Press, vol. 13(3), pages 353-367, June.
    19. Davidson, James, 2002. "Establishing conditions for the functional central limit theorem in nonlinear and semiparametric time series processes," Journal of Econometrics, Elsevier, vol. 106(2), pages 243-269, February.
    20. Deo, Rohit S. & Richardson, Matthew, 2003. "On The Asymptotic Power Of The Variance Ratio Test," Econometric Theory, Cambridge University Press, vol. 19(2), pages 231-239, April.
    21. Davidson, James, 1992. "A Central Limit Theorem for Globally Nonstationary Near-Epoch Dependent Functions of Mixing Processes," Econometric Theory, Cambridge University Press, vol. 8(3), pages 313-329, September.
    22. Duchesne, Pierre, 2006. "On Testing For Serial Correlation With A Wavelet-Based Spectral Density Estimator In Multivariate Time Series," Econometric Theory, Cambridge University Press, vol. 22(4), pages 633-676, August.
    23. Horowitz, Joel L. & Lobato, I.N. & Nankervis, John C. & Savin, N.E., 2006. "Bootstrapping the Box-Pierce Q test: A robust test of uncorrelatedness," Journal of Econometrics, Elsevier, vol. 133(2), pages 841-862, August.
    24. Duchesne, Pierre & Li, Linyuan & Vandermeerschen, Jill, 2010. "On testing for serial correlation of unknown form using wavelet thresholding," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2512-2531, November.
    25. Perron, Pierre & Vodounou, Cosme, 2005. "The Variance Ratio Test: An Analysis Of Size And Power Based On A Continuous-Time Asymptotic Framework," Econometric Theory, Cambridge University Press, vol. 21(3), pages 562-592, June.
    26. Lobato, I.N. & Nankervis, John C. & Savin, N.E., 2002. "Testing For Zero Autocorrelation In The Presence Of Statistical Dependence," Econometric Theory, Cambridge University Press, vol. 18(3), pages 730-743, June.
    27. 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.
    28. 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.
    29. Davidson, James, 1993. "The Central Limit Theorem for Globally Nonstationary Near-Epoch Dependent Functions of Mixing Processes: The Asymptotically Degenerate Case," Econometric Theory, Cambridge University Press, vol. 9(3), pages 402-412, June.
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    More about this item

    Keywords

    Serial correlation; Wavelets; Independence; Discrete wavelet transformation; Maximum overlap wavelet transformation; Variance ratio test; Variance decomposition;
    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
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • F31 - International Economics - - International Finance - - - Foreign Exchange
    • G0 - Financial Economics - - General
    • G1 - Financial Economics - - General Financial Markets

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