Hostname: page-component-f554764f5-c4bhq Total loading time: 0 Render date: 2025-04-09T23:16:41.526Z Has data issue: false hasContentIssue false
  • English
  • Français

Discrimination between monotonic trends and long-range dependence

Published online by Cambridge University Press:  24 August 2016

H. Künsch
H. Künsch*
Affiliation:
ΕTH Zurich
*
∗Postal address: Seminar für Statistik, ETH-Zentrum, CH-8092 Zurich, Switzerland.
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that the periodogram behaves differently for a weakly dependent process with a small monotonic trend and a stationary strongly dependent process. In the former case it has a non-central -distribution with noncentrality parameter tending to 0 uniformly outside intervals . In the latter case it has λα −1 times a central -distribution, 0 < α < 1.

Keywords

HURST EFFECTWEAK AND STRONG DEPENDENCETRENDSPERIODOGRAMGEOPHYSICAL MODELS
Type
Short Communications
Information
Journal of Applied Probability , Volume 23 , Issue 4 , December 1986 , pp. 1025 - 1030
Copyright
Copyright © Applied Probability Trust 1986 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Anderson, T. W. (1971) The Statistical Analysis of Time Series. Wiley, New York.Google Scholar
Bhattacharya, R. N., Gupta, V. K. and Waymire, E. (1983) The Hurst effect under trends. J. Appl. Prob. 20, 649–662.Google Scholar
Feller, W. (1951) The asymptotic distribution of the range of sums of independent random variables. Ann. Math. Statist. 22, 427–432.Google Scholar
Geweke, J. and Porter-Hudak, S. (1983). The estimation and application of long memory time series models. J. Time Series Anal. 4, 221–238.Google Scholar
Graf, H. (1983) Long Range Correlations and Estimation of the Self-similarity Parameter. , ETH Zurich.Google Scholar
Graf, H., Hampel, F. R. and Tacier, J.-D. (1984) The problem of unsuspected serial correlations. In Robust and Nonlinear Time Series Analysis, eds. Franke, J., Hardie, W. and Martin, D., Lecture Notes in Statistics 26, Springer-Verlag, Berlin, 127–145.Google Scholar
Hurst, H. E. (1951) Long term storage capacity of reservoirs. Trans. Amer. Soc. Civil Engrs. 116, 770–779.Google Scholar
Mandelbrot, B. B. and Taqqu, M. (1979) Robust R/S analysis of long run serial correlation. 42nd Internat. Statist. Inst., Manila, 1–38.Google Scholar
Mandelbrot, B. B. and Wallis, J. (1968) Noah, Joseph and operational hydrology. Water Resources Res. 4, 909–918.Google Scholar
Mohr, D. L. (1981) Modeling Data as Fractional Gaussian Noise. , Princeton University, Princeton, N.J. Google Scholar
Zygmund, A. (1959) Trigonometric Series, Vol. 1. Cambridge University Press.Google Scholar