Testing for white noise under unknown dependence and its applications to goodness-of-fit for time series models

摘要: Testing for white noise has been well studied in the literature of econometrics and statistics. For most proposed test statistics, such as well-known Box-Pierce's statistic with fixed lag truncation number, asymptotic null distributions are obtained under independent identically distributed assumptions may not be valid dependent noise. Due to recent popularity conditional heteroscedastic models (e.g., GARCH models), which imply nonlinear dependence zero autocorrelation, there is a need understand properties existing statistics unknown dependence. In this paper, we showed that distribution general weights still holds weak so long number grows at an appropriate rate increasing sample size. Further applications diagnostic checking ARMA FARIMA errors also addressed. Our results go beyond earlier ones by allowing non-Gaussian provide theoretical support some empirical findings reported literature.