Multi-scale test procedure for non-stationarity in short and long memory time series

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 and between scales. We also propose an application to electric power consumption monitoring.

[1]  B. E. Brodsky,et al.  Non-Parametric Statistical Diagnosis: Problems and Methods , 2000 .

[2]  Thomas Mikosch,et al.  Changes of structure in financial time series and the GARCH model , 2004 .

[3]  Q. Shao,et al.  On discriminating between long-range dependence and changes in mean , 2006, math/0607803.

[4]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[5]  J. Kiefer,et al.  K-Sample Analogues of the Kolmogorov-Smirnov and Cramer-V. Mises Tests , 1959 .

[6]  Robert Tibshirani,et al.  The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd Edition , 2001, Springer Series in Statistics.

[7]  G. C. Tiao,et al.  Use of Cumulative Sums of Squares for Retrospective Detection of Changes of Variance , 1994 .

[8]  Yves Lechevallier,et al.  Exploratory analysis of functional data via clustering and optimal segmentation , 2010, Neurocomputing.

[9]  R. Bhattacharya,et al.  THE HURST EFFECT UNDER TRENDS , 1983 .

[10]  On the laws of homogeneous functionals of the Brownian bridge , 1999 .

[11]  Klaus Nordhausen,et al.  The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Second Edition by Trevor Hastie, Robert Tibshirani, Jerome Friedman , 2009 .

[12]  Jan Beran,et al.  Statistics for long-memory processes , 1994 .

[13]  B. E. Brodsky,et al.  Non-Parametric Statistical Diagnosis , 2000 .

[14]  R. Bass,et al.  Review: P. Billingsley, Convergence of probability measures , 1971 .

[15]  P. Guttorp,et al.  Testing for homogeneity of variance in time series: Long memory, wavelets, and the Nile River , 2002 .

[16]  François Roueff,et al.  On the Spectral Density of the Wavelet Coefficients of Long‐Memory Time Series with Application to the Log‐Regression Estimation of the Memory Parameter , 2005, math/0512635.

[17]  Philippe Soulier,et al.  Estimation of Long Memory in the Presence of a Smooth Nonparametric Trend , 2002 .