Abstract
A one-sided asymptotically normal test for non-correlation between two stationary time series is proposed based on the spectral coherence function. The test statistic is a properly standardized version of the integrated spectral coherency and has similar asymptotic properties as a previously introduced time domain based test for non-correlation. Unlike its time domain counterpart, the proposed test does not require prewhitening of the time series and, thus, is a truly nonparametric test for non-correlation. In a simulation study, we evaluate the small sample performance of the proposed test in comparison with the time domain test and address the problem of bandwidth selection. Furthermore, we present a modification of the test statistic that allows to test for non-correlation over frequency bands. This version shows higher power of detecting interrelationships restricted to the frequency band of interest.
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References
Beltrão KI, Bloomfield P (1987) Determining the bandwidth of a kernel spectrum estimate. J Time Ser Anal 8:21–38
Brillinger DR (1981) Time series: data analysis and theory. McGraw Hill, New York
Bühlmann P (1996) Locally adaptive lag-window spectral estimation. J Time Ser Anal 17:247–270
Dahlhaus R (1983) Spectral analysis with tapered data. J Time Ser Anal 4:163–175
Dahlhaus R (1990) Nonparametric high resolution spectral estimation. Probab Theory Relat Fields 85:147–180
Dahlhaus R, Eichler M (2003) Causality and graphical models in time series analysis. In: Green P, Hjort N, Richardson S (eds) Highly structured stochastic systems. University Press, Oxford, pp 1–1
Dahlhaus R, Eichler M, Sandkühler J (1997) Identification of synaptic connections in neural ensembles by graphical models. J Neurosci Methods 77:93–107
Duchesne P, Roy R (2003) Robust test for independence of two time series. Stat Sinica 13:827–852
El Himdi K, Saidi A (1997) Tests for noncorrelation of two multivariate ARMA time series. Can J Stat 25:233–256
Fortin I, Kuzmics C (2000) Optimal window width choice in spectral density estimation. J Stat Comput Simul 67:109–131
Hallin M, Saidi A (2005) Testing non-correlation and non-causality between multivariate ARMA time series. J Time Ser Anal 26:83–105
Haugh LD (1976) Checking the independence of two covariance-stationary time series: a univariate residual covariance approach. J Am Stat Assoc 71:378–385
Hong Y (1996) Testing for independence between two covariance stationary time series. Biometrika 83:615–625
Koch PD, Yang SS (1986) A method for testing the independence of two time series that accounts for a potential pattern in the cross-correlation function. J Am Stat Assoc 81:533–544
Lee TCM (2001) A stabilized bandwidth selection method for kernel smoothing of the periodogram. Signal Process 81:419–430
Priestley MB (1981) Spectral analysis and time series vol 1. Academic, London
Taniguchi M, Puri ML, Kondo M (1996) Nonparametric approach for non-gaussian vector stationary processes. J Multivar Anal 56:259–283
Timmer J, Lauk M, Köster B, Hellwig B, Häußler S, Guschlbauer B, Radt V, Eichler M, Deuschl G, Lücking CH (2000) Cross-spectral analysis of tremor time series. Int J Bifurcat Chaos 10:2595–2610
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This work has been carried out at the Institute of Applied Mathematics at the University of Heidelberg and partly while the author was visiting the Department of Statistics at the University of Chicago.
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Eichler, M. A Frequency-domain Based Test for Non-correlation between Stationary Time Series. Metrika 65, 133–157 (2007). https://doi.org/10.1007/s00184-006-0065-8
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DOI: https://doi.org/10.1007/s00184-006-0065-8