A wavelet-based consistent test for serial correlation
of unknown form is proposed. As a spatially adaptive estimation
method, wavelets can effectively detect local features
such as peaks and spikes in a spectral density, which can
arise as a result of strong autocorrelation or seasonal
or business cycle periodicities in economic and financial
time series. The proposed test statistic is constructed
by comparing a wavelet-based spectral density estimator
and the null spectral density. It is asymptotically one-sided
N(0,1) under the null hypothesis of no serial correlation
and is consistent against serial correlation of unknown form.
The test is expected to have better power than a kernel-based
test (e.g., Hong, 1996, Econometrica 64, 837–864)
when the true spectral density has significant spatial inhomogeneity.
This is confirmed in a simulation study. Because the spectral
densities of time series arising in practice usually have
unknown smoothness, the wavelet-based test is a useful
complement to the kernel-based test in practice.
On consistent testing for serial correlation of unknown form in vector time series models
