Score Test for Homogeneity of Variances in Longitudinal Time Series Via Wavelets

Abstract

We discuss the problem of testing for homogeneity of variances in a nonstationary longitudinal time series. The nonstationarity is assumed to arise from the dependence of the mean function on time and possibly nonconstancy in variance. We develop a partial score statistic for testing for equality of variances between the series in the longitudinal setup. We study the effect of using both the discrete wavelet transformation (DWT) approach and wavelet regression based on multiresolution analysis in estimating the time dependent mean function on the size and power of the test. We found that the DWT estimate is not consistent. Thus, the score test based on this approach fails in controlling the size of the test, whereas the score test based on the wavelet regression estimate performs well in controlling the size of the test. The power of the test is, however, not affected by the estimation method.

Keywords:

• Daubechies wavelet
• Discrete wavelet transformation
• Longitudinal time series
• Multiresolution analysis
• Score test
• Wavelet regression

Mathematics Subject Classification:

• Primary 62G05, 62G10
• Secondary 41A30

Acknowledgment

This research was partially supported by grants from the Natural Sciences and Engineering Research Council of Canada.