The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Serial Correlation and Serial Dependence

  • Yongmiao Hong
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_2157

Abstract

In this article we discuss serial correlation in a linear time series regression context and serial dependence in a nonlinear time series context. We first discuss various tests for serial correlation for both estimated regression residuals and observed raw data. Particular attention is paid to the impact of parameter estimation uncertainty and conditional heteroskedasticity on the asymptotic distribution of test statistics. We discuss the drawback of serial correlation in nonlinear time series models and introduce a number of measures that can capture nonlinear serial dependence and reveal useful information about serial dependence.

Keywords

ARMA models Durbin–Watson statistic Efficient market hypothesis Entropy;generalized spectral density Homoskedasticity Heteroskedasticity Kernel estimators;Lagrange multipliers Rational expectations Serial correlation Serial dependence Spectral density Statistical inference Time series analysis 

JEL Classifications

C22 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgment

I thank Steven Durlauf (editor) for suggesting this topic and comments on an earlier version, and Jing Liu for excellent research assistance and references. This research is supported by the Cheung Kong Scholarship of the Chinese Ministry of Education and Xiamen University. All remaining errors are solely mine.

Bibliography

  1. Andrews, D.W.K. 1991. Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59: 817–858.CrossRefGoogle Scholar
  2. Bollerslev, T. 1986. Generalized autoregressive conditional heteroskedastcity. Journal of Econometrics 31: 307–327.CrossRefGoogle Scholar
  3. Box, G.E.P., and D.A. Pierce. 1970. Distribution of residual autocorrelations in autoregressive moving average time series models. Journal of the American Statistical Association 65: 1509–1526.CrossRefGoogle Scholar
  4. Breusch, T.S. 1978. Testing for autocorrelation in dynamic linear models. Australian Economic Papers 17: 334–355.CrossRefGoogle Scholar
  5. Breusch, T.S., and A. Pagan. 1980. The Lagrange multiplier test and its applications to model specification in econometrics. Review of Economic Studies 47: 239–253.CrossRefGoogle Scholar
  6. Brillinger, D.R., and M. Rosenblatt. 1967a. Asymptotic theory of estimates of kth order spectra. In Spectral analysis of time series, ed. B. Harris. New York: Wiley.Google Scholar
  7. Brillinger, D.R., and M. Rosenblatt. 1967b. Computation and interpretation of the kth order spectra. In Spectral analysis of time series, ed. B. Harris. New York: Wiley.Google Scholar
  8. Brooks, C., S. Burke, and G. Persand. 2005. Autoregressive conditional kurtosis. Journal of Financial Econometrics 3: 399–421.CrossRefGoogle Scholar
  9. Campbell, J.Y., A.W. Lo, and A.C. MacKinlay. 1997. The econometrics of financial markets. Princeton: Princeton University Press.Google Scholar
  10. Chen, W., and R. Deo. 2004. A generalized portmanteau goodness-of-fit test for time series models. Econometric Theory 20: 382–416.CrossRefGoogle Scholar
  11. Cochrane, J.H. 1988. How big is the random walk in GNP? Journal of Political Economy 96: 893–920.CrossRefGoogle Scholar
  12. Delgado, M.A. 1996. Testing serial independence using the sample distribution function. Journal of Time Series Analysis 17: 271–285.CrossRefGoogle Scholar
  13. Deo, R.S. 2000. Spectral tests of the martingale hypothesis under conditional heteroscedasticity. Journal of Econometrics 99: 291–315.CrossRefGoogle Scholar
  14. Durbin, J. 1970. Testing for serial correlation in least squares regression when some of the regressors are lagged dependent variables. Econometrica 38: 422–421.CrossRefGoogle Scholar
  15. Durbin, J., and G.S. Watson. 1950. Testing for serial correlation in least squares regression: I. Biometrika 37: 409–428.Google Scholar
  16. Durbin, J., and G.S. Watson. 1951. Testing for serial correlation in least squares regression: II. Biometrika 38: 159–178.CrossRefGoogle Scholar
  17. Durlauf, S.N. 1991. Spectral based testing of the martingale hypothesis. Journal of Econometrics 50: 355–376.CrossRefGoogle Scholar
  18. Engle, R. 1982. Autoregressive conditional hetersokedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50: 987–1008.CrossRefGoogle Scholar
  19. Engle, R., D. Lilien, and R.P. Robins. 1987. Estimating time varying risk premia in the term structure: The ARCH-M model. Econometrica 55: 391–407.CrossRefGoogle Scholar
  20. Engle, R., and S. Manganelli. 2004. CARViaR: Conditional autoregressive value at risk by regression quantiles. Journal of Business and Economic Statistics 22: 367–391.CrossRefGoogle Scholar
  21. Fan, J., and W. Zhang. 2004. Generalized likelihood ratio tests for spectral density. Biometrika 91: 195–209.CrossRefGoogle Scholar
  22. Glosten, R., R. Jagannathan, and D. Runkle. 1993. On the relation between the expected value and the volatility of the nominal excess return on stocks. Journal of Finance 48: 1779–1801.CrossRefGoogle Scholar
  23. Godfrey, L.G. 1978. Testing against general autoregressive and moving average error models when the regressors include lagged dependent variables. Econometrica 46: 1293–1301.CrossRefGoogle Scholar
  24. Granger, C.W.J., and J.L. Lin. 1994. Using the mutual information coefficient to identify lags in nonlinear models. Journal of Time Series Analysis 15: 371–384.CrossRefGoogle Scholar
  25. Granger, C.J.W., and T. Terasvirta. 1993. Modeling nonlinear economic relationships. Oxford: Oxford University Press.Google Scholar
  26. Harvey, C.R., and A. Siddique. 2000. Conditional skewness in asset pricing tests. Journal of Finance 51: 1263–1295.CrossRefGoogle Scholar
  27. Hayashi, F. 2000. Econometrics. Princeton: Princeton University Press.Google Scholar
  28. Hong, Y. 1996. Consistent testing for serial correlation of unknown form. Econometrica 64: 837–864.CrossRefGoogle Scholar
  29. Hong, Y. 1998. Testing for pairwise serial independence via the empirical distribution function. Journal of the Royal Statistical Society, Series B 60: 429–453.CrossRefGoogle Scholar
  30. Hong, Y. 1999. Hypothesis testing in time series via the empirical characteristic function: A generalized spectral density approach. Journal of the American Statistical Association 94: 1201–1220.CrossRefGoogle Scholar
  31. Hong, Y. 2000. Generalized spectral tests for serial dependence. Journal of the Royal Statistical Society, Series B 62: 557–574.CrossRefGoogle Scholar
  32. Hong, Y., and T.H. Lee. 2003a. Inference on predictability of foreign exchange rates via generalized spectrum and nonlinear time series models. Review of Economics and Statistics 85: 1048–1062.CrossRefGoogle Scholar
  33. Hong, Y., and T.H. Lee. 2003b. Diagnostic checking for the adequacy of nonlinear time series models. Econometric Theory 19: 1065–1121.Google Scholar
  34. Hong, Y., and Y.J. Lee. 2005. Generalized spectral testing for conditional mean models in time series with conditional heteroskedasticity of unknown form. Review of Economic Studies 72: 499–451.CrossRefGoogle Scholar
  35. Hong, Y., and Y.J. Lee. 2007. Consistent testing for serial correlation of unknown form under general conditional heteroskedasticity. Working paper, Department of Economics, Cornell University, and Department of Economics, Indiana University.Google Scholar
  36. Hong, Y., and H. White. 2005. Asymptotic distribution theory for nonparametric entropy measures of serial dependence. Econometrica 73: 837–901.CrossRefGoogle Scholar
  37. Hsieh, D.A. 1989. Testing for nonlinear dependence in daily foreign exchange rates. Journal of Business 62: 339–368.CrossRefGoogle Scholar
  38. Ljung, G.M., and G.E.P. Box. 1978. On a measure of lack of fit in time series models. Biometrika 65: 297–303.CrossRefGoogle Scholar
  39. Lo, A.W., and A.C. MacKinlay. 1988. Stock market prices do not follow random walks: Evidence from a simple specification test. Review of Financial Studies 1: 41–66.CrossRefGoogle Scholar
  40. Nelson, D. 1991. Conditional heteroskedasticity in asset returns: A new approach. Econometrica 59: 347–370.CrossRefGoogle Scholar
  41. Newey, W.K., and K.D. West. 1987. A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix. Econometrica 55: 703–708.CrossRefGoogle Scholar
  42. Paparoditis, E. 2000. Spectral density based goodness-of-fit tests for time series models. Scandinavian Journal of Statistics 27: 143–176.CrossRefGoogle Scholar
  43. Priestley, M.B. 1988. Non-linear and non-stationary time series analysis. London: Academic Press.Google Scholar
  44. Robinson, P.M. 1991. Consistent nonparametric entropy-based testing. Review of Economic Studies 58: 437–453.CrossRefGoogle Scholar
  45. Robinson, P.M. 1994. Time series with strong dependence. In Advances in econometrics, sixth world congress, ed. C. Sims, Vol. 1. Cambridge: Cambridge University Press.Google Scholar
  46. Skaug, H.J., and D. Tjøstheim. 1993a. Nonparametric tests of serial independence. In Developments in time series analysis, ed. S. Rao. London: Chapman and Hall.Google Scholar
  47. Skaug, H.J., and D. Tjøstheim. 1993b. A nonparametric test of serial independence based on the empirical distribution function. Biometrika 80: 591–602.CrossRefGoogle Scholar
  48. Skaug, H.J., and D. Tjøstheim. 1996. Measures of distance between densities with application to testing for serial independence. In Time series analysis in memory of E.J. Hannan, ed. P. Robinson and M. Rosenblatt. New York: Springer.Google Scholar
  49. Tjøstheim, D. 1996. Measures and tests of independence: A survey. Statistics 28: 249–284.CrossRefGoogle Scholar
  50. Vinod, H.D. 1973. Generalization of the Durbin–Watson statistic for higher order autoregressive processes. Communications in Statistics 2: 115–144.CrossRefGoogle Scholar
  51. Wallis, K.F. 1972. Testing for fourth order autocorrelation in quarterly regression equations. Econometrica 40: 617–636.CrossRefGoogle Scholar
  52. Whang, Y.J. 1998. A test of autocorrelation in the presence of heteroskedasticity of unknown form. Econometric Theory 14: 87–122.CrossRefGoogle Scholar
  53. Wooldridge, J.M. 1990. An encompassing approach to conditional mean tests with applications to testing nonnested hypotheses. Journal of Econometrics 45: 331–350.CrossRefGoogle Scholar
  54. Wooldridge, J.M. 1991. On the application of robust, regression-based diagnostics to models of conditional means and conditional variances. Journal of Econometrics 47: 5–46.CrossRefGoogle Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Yongmiao Hong
    • 1
  1. 1.