Tests for serial correlation of unknown form in dynamic least squares regression with wavelets

This paper extends the multi-scale serial correlation tests of Gençay and Signori (2015) for observable time series to unobservable errors of unknown forms in a linear dynamic regression model. Our tests directly build on the variance ratio of the sum of squared wavelet coefficients of residuals over the sum of squared residuals, utilizing the equal contribution of each frequency of a white noise process to its variance and delivering higher empirical power than parametric tests. Our test statistics converge to the standard normal distribution at the parametric rate under the null hypothesis, faster than the nonparametric test using kernel estimators of the spectrum.