Testing variances in wavelet regression models

In this paper we develop an asymptotically locally optimal partial score test for testing the suitability of a homoscedastic wavelet model against a general heteroscedastic wavelet model. As the construction of the partial score test requires a consistent estimate for the nuisance parameter, namely the constant variance estimate under the null hypothesis, we conduct a comprehensive investigation in order to choose its best possible estimate among some competitors. The size and power performances of the partial score test are reported for testing for heteroscedasticity in a time series of finite length.