an:01911753
Zbl 1017.62078
Hong, Yongmiao; Lee, Jin
One-sided testing for ARCH effects using wavelets
EN
Econom. Theory 17, No. 6, 1051-1081 (2001).
00079941
2001
j
62M10 62G08 62G10 62P20 62M15
Summary: There has recently been increasing interest 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.