Wavelet-domain test for long-range dependence in the presence of a trend. (English) Zbl 1148.62072

Summary: We propose a test to distinguish a weakly-dependent time series with a trend component from a long-memory process, possibly with a trend. The test uses a generalized likelihood ratio statistic based on wavelet domain likelihoods. The trend is assumed to be a polynomial whose order does not exceed a known value. The test is robust to trends which are piecewise polynomials. We study the empirical size and power by means of simulations and find that they are good and do not depend on specific choices of wavelet functions and models for the wavelet coefficients. The test is applied to annual minima of the Nile River and confirms the presence of long-range dependence in this time series.


62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F03 Parametric hypothesis testing
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
62M15 Inference from stochastic processes and spectral analysis
65C60 Computational problems in statistics (MSC2010)
Full Text: DOI


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