Mathematics and Statistics Vol. 8(4), pp. 430 - 436
DOI: 10.13189/ms.2020.080409
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Variance Homogeneity Test Based on Cumulative Wavelet Coefficients

Abdeslam Serroukh 1,*, Khudhayr A. Rashedi 2,3
1 Polydisciplinary Faculty of Larache, University Abdelmalek Essaadi, Morocco
2 College of Sciences, University of Hail, Saudi Arabia
3 School of Mathematical Sciences, University Sains Malaysia, 11800, Minden, Malaysia


The aim of this paper is to address the problem of variance break detection in time series in wavelet domain. The maximal overlapped discrete wavelet transform (MODWT) decomposes the series variance across scales into components known as the wavelet variances. We introduce all scale wavelet coefficients based test statistic that allows detecting a break in the homogeneity of the variance of a series through changes in the mean of wavelet variances. The statistic makes use of the traditional CUSUM (cumulative sum) based test designed to test for a break in the mean and constructed using cumulative sums of the square of wavelet coefficients. Under moments and mixing conditions, the test statistic satisfies the functional central limit theorem (FCLT) for a broad class of time series models. The overall performance of our test statistic is compared to the traditional Inclan [8] test statistic. The effectiveness of our statistic is supported by good performances reported in simulations and is as reliable as the traditional statistic. Our method provides a nonparametric test procedure that can be applied to a large class of linear and non linear models. We illustrate the practical use of our test procedure with the quarterly percentage changes in the Americans personal savings data set over the period 1970-2016. Both statistics detect a break in the variance in the second quarter of 2001.

Cumulative Wavelet Variance, Maximal Overlaped Discrete Wavelet Transform, Test for Homogeneity of Variance, Time Series

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Abdeslam Serroukh , Khudhayr A. Rashedi , "Variance Homogeneity Test Based on Cumulative Wavelet Coefficients," Mathematics and Statistics, Vol. 8, No. 4, pp. 430 - 436, 2020. DOI: 10.13189/ms.2020.080409.

(b). APA Format:
Abdeslam Serroukh , Khudhayr A. Rashedi (2020). Variance Homogeneity Test Based on Cumulative Wavelet Coefficients. Mathematics and Statistics, 8(4), 430 - 436. DOI: 10.13189/ms.2020.080409.