TESTING FOR SERIAL CORRELATION OF UNKNOWN FORM USING WAVELET METHODS

Jin Lee and Yongmiao Hong

Econometric Theory, 2001, vol. 17, issue 02, pages 386-423

Abstract: 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.

Date: 2001
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