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The danger of confusing long-range dependence with non-stationarity has been pointed out by many authors. Finding an answer to this difficult question is of importance to model time-series showing trend-like behavior, such as river runoff in hydrology, historical temperatures in the study of climates changes, or packet counts in network traffic engineering. The main goal of this paper is to...
In this paper, we develop a test procedure for non-stationarity for possibly long-memory processes. Contrary to most of the proposed methods, the test procedure has the same distribution for short-range and long-range dependence stationary processes. Such tests have been already proposed in [1], but these authors do not have taken into account the dependence of the wavelet coefficients within scales...
We propose in this paper robust estimators of the memory parameter d of a (possibly) non stationary Gaussian time series with generalized spectral density f. This generalized spectral density is characterized by the memory parameter d and by a function f∗ which specifies the short-range dependence structure of the process. The memory parameter d is estimated by regressing the logarithm of the estimated...
Consider the discrete wavelet transform (DWT) of a time series with weakly stationary th differences. Such time series are encountered in many situations, including unit root or long memory processes. If the wavelet has at least vanishing moments, the DWT is jointly stationary across scales provided that small scales coefficients are reshaped in appropriate blocks to cope...
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