Serial Correlation and Serial Dependence
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.
KeywordsARMA 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
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.
- 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
- 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
- Campbell, J.Y., A.W. Lo, and A.C. MacKinlay. 1997. The econometrics of financial markets. Princeton: Princeton University Press.Google Scholar
- Durbin, J., and G.S. Watson. 1950. Testing for serial correlation in least squares regression: I. Biometrika 37: 409–428.Google Scholar
- Granger, C.J.W., and T. Terasvirta. 1993. Modeling nonlinear economic relationships. Oxford: Oxford University Press.Google Scholar
- Hayashi, F. 2000. Econometrics. Princeton: Princeton University Press.Google Scholar
- Hong, Y., and T.H. Lee. 2003b. Diagnostic checking for the adequacy of nonlinear time series models. Econometric Theory 19: 1065–1121.Google Scholar
- 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
- Priestley, M.B. 1988. Non-linear and non-stationary time series analysis. London: Academic Press.Google Scholar
- 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
- 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
- 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