One-sided testing for arch effects using wavelets

There has been increasing interest recently in hypothesis testing with ineq uality restrictions. An important example in time series econometrics is hy potheses on autoregressive conditional heteroskedasticity (ARCH). We propos e a one-sided test for ARCH effects using a wavelet spectral density estima tor at frequency zero of a squared regression residual series. The square o f an ARCH process is positively correlated at all lags, resulting in a spec tral mode at frequency zero. In particular, it has a spectral peak at frequ ency zero when ARCH effects are persistent or when ARCH effects are small a t each individual lag but carry over a long distributional lag. As a joint time-frequency decomposition method, wavelets can effectively capture spect ral 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 d istributional lag. This is confirmed in a simulation study.