A new one-sided test for serial correlation in multivariate time series models is proposed.The test is based on a comparison between a multivariate spectral density estimator and the spectral density under the null hypothesis of no serial correlation.Duchesne and Roy(2004,Journal of Multivariate Analysis 89,148- 180)considered a multivariate kernel-based spectral density estimator.However,when the spectral density exhibits irregular features(because of strong autocorrelation or seasonality,among other factors),it is expected that a multivariate wavelet-based spectral density estimator will capture more effectively the local behavior of the spectral density.We consider a test based on a wavelet spectral density estimator,which represents a generalization of a test proposed by Lee and Hong(2001,Econometric Theory 17,386-423).The asymptotic distribution of the new test is established under the null hypothesis,which is N(0,1).We propose and justify a suitable data-driven method to choose the smoothing parameter of the wavelet estimator(called the finest scale in that context).The new test should be powerful when the spectral density contains peaks or bumps.This is confirmed in a simulation study,where kernel-based and wavelet-based estimators are compared.
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机译：提出了一种新的多变量时间序列模型中序列相关性的单面检验，该检验基于多元谱密度估计量与无序列相关零假设下的谱密度的比较.Duchesne and Roy（2004，Journal多元分析89,148-180）考虑了基于多元核的光谱密度估计器。然而，当光谱密度表现出不规则特征（由于强自相关性或季节性，以及其他因素）时，可以预期基于多元小波的光谱密度估计器将更有效地捕获频谱密度的局部行为。我们考虑基于小波谱密度估计器的检验，该检验代表了Lee和Hong（2001，Econometric Theory 17,386-423）提出的检验的一般化。在零假设N（0,1）下建立了新检验的检验结果。我们提出并证明了一种合适的数据驱动方法来选择t小波估计器的平滑参数（在这种情况下称为最佳尺度）。当光谱密度包含峰或波峰时，新测试应具有强大的功能。这在仿真研究中得到了证实，其中基于核和基于小波的估计器都是比较。
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