Testing for independence between two covariance stationary time series

Hong, Yongmiao (1996): Testing for independence between two covariance stationary time series. Published in: Biometrika , Vol. 83, No. 3 (September 1996): pp. 615-625.

Abstract

A one-sided asymptotically normal test for independence between two stationary time series is proposed by first prewhitening the two time series and then basing the test on the residual cross-correlation function. The test statistic is a properly standardised version of the sum of weighted squares of residual cross-correlations, with weights depending on a kernel function. Haugh's (1976) test can be viewed as a special case of our approach in the sense that it corresponds to the use of the truncated kernel. Many kernels deliver better power than Haugh's test. A simulation study shows that the new test has good power against short and long cross-correlations.

• Item Type: MPRA Paper
• Language: English
• Keywords: Coherency; Cross-correlation; Independence; Kernel function; Multivariate time series.
• Subjects: C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models

References

ANDREWS, D. W. K. (1991). Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59, 817-58.

BAHADUR, R. R. (1960). Stochastic comparison of tests. Ann. Math. Statist. 31, 276-95.

BERK, K. N. (1974). Consistent autoregressive spectral estimates. Ann. Statist. 2, 489-502.

CHAN, N. H. & TRAN, L. T. (1992). Nonparametric tests for serial dependence. J. Time Ser. Anal. 13, 102-13.

GALLANT, A. R. & JORGENSON, D. (1979). Statistical inference for a system of simultaneous nonlinear implicit equations in the context of instrumental variables estimation. J. Economet. 11, 275-302.

GALLANT, A. R. & WHITE, H. (1988). A Unified Theory of Estimation and Inference for Nonlinear Dynamic Models. Oxford: Basil Blackwell.

GEWEKE, J. (1981a). The approximate slopes of econometric tests. Econometrica 49, 1427-42.

GEWEKE, J. (1981b). A comparison of tests of independence of two covariance stationary time series. J. Am. Statist. Assoc. 76, 363-73.

HAUGH, L. D. (1976). Checking the independence of two covariance-stationary time series: a univariate residual cross correlation approach. J. Am. Statist. Assoc. 71, 378-85.

HONG, Y. (1996). Consistent testing for serial correlation of unknown form. Econometrica 64, 837-64.

PIERCE, A. (1977). Lack of dependence among economic variables. J. Am. Statist. Assoc. 72, 11-22.

PITMAN, E. J. G. (1979). Some Basic Theory for Statistical Inference. London: Chapman Hall.

PRIESTLEY, M. B. (1962). Basic considerations in the estimation of spectra. Technometrics 4, 551-64.

PRIESTLEY, M. B. (1981). Spectral Analysis and Time Series, 1, 2. London: Academic Press.

ROBINSON, P. M. (1991). Consistent nonparametric entropy-based testing. Rev. Econ. Studies 58, 437-53.

SKAUG, H. J. & TJOSTHEM, D. (1993a). A nonparametric test of serial independence based on the empirical distribution function. Biometrika 80, 591-602.

SKAUG, H. J. & TJOSTHEIM, D. (1993b). Nonparametric tests of serial independence. In Developments in Time Series Analysis, the M. B. Priestley Birthday Volume, Ed. T. Subba Rao, pp. 207-29. London: Academic Press.