A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ten lectures on wavelets
On consistent testing for serial correlation of unknown form in vector time series models
Journal of Multivariate Analysis
Preface: Special Issue on Nonlinear Modelling and Financial Econometrics
Computational Statistics & Data Analysis
Wavelet analysis of stock returns and aggregate economic activity
Computational Statistics & Data Analysis
Applications of the characteristic function-based continuum GMM in finance
Computational Statistics & Data Analysis
On wavelet-based testing for serial correlation of unknown form using Fan's adaptive Neyman method
Computational Statistics & Data Analysis
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Test statistics for autoregressive conditional heteroskedasticity (ARCH) in the residuals from a possibly nonlinear and dynamic multivariate regression model are considered. The new approach is based on estimation of the multivariate spectral density of squared and cross-residuals. A simple wavelet-based spectral density estimator is advocated, which is a particularly suitable analytic tool when the spectral density exhibits peaks or kinks that may arise from strong cross-dependence, seasonal patterns and other forms of periodic behaviors. In several circumstances, the spectral density may have peaks at various frequencies, such as seasonal frequencies, and the wavelet method may capture them effectively. Compared to kernel-based test statistics for multivariate ARCH effects, the weighting scheme offered by the new wavelet-based test statistics differs in several important aspects. An asymptotic analysis under the null hypothesis of no ARCH effects shows that the wavelet-based test statistic converges in distribution to a convenient standard normal distribution. Under fixed alternatives, the consistency of the wavelet-based test statistics is established in a class of static regression models with uncorrelated but dependent errors. In a Monte Carlo study comparisons are made under various alternatives between the proposed wavelet-based test statistics, the kernel-based test statistics for ARCH effects, and several popular portmanteau test statistics for ARCH effects available in the literature.