ONE-SIDED TESTING FOR ARCH EFFECTS USING WAVELETS
提出一种基于小波谱密度估计的单侧检验方法，用于检测时间序列中的自回归条件异方差（ARCH）效应，尤其适用于ARCH效应持久或分布滞后较长的小样本情形。
There has been increasing interest recently in hypothesis testing with inequality restrictions. An important example in time series econometrics is hypotheses on autoregressive conditional heteroskedasticity (ARCH). We propose a one-sided test for ARCH effects using a wavelet spectral density estimator at frequency zero of a squared regression residual series. The square of an ARCH process is positively correlated at all lags, resulting in a spectral mode at frequency zero. In particular, it has a spectral peak at frequency zero when ARCH effects are persistent or when ARCH effects are small at each individual lag but carry over a long distributional lag. As a joint time-frequency decomposition method, wavelets can effectively capture spectral peaks. We expect that wavelets are more powerful than kernels in small samples when ARCH effects are persistent or when ARCH effects have a long distributional lag. This is confirmed in a simulation study.