Nonparametric Detection of a Time‐Varying Mean
提出一种基于周期图比值的非参数检验方法，用于检测单变量时间序列中无条件均值的变化，适用于长记忆或短记忆序列，且对多种时变均值模型具有检验功效。
ABSTRACT We propose a nonparametric portmanteau test for detecting changes in the unconditional mean of a univariate time series which may display either long or short memory. Our approach is designed to have power against, among other things, cases where the mean component of the series displays abrupt level shifts, deterministic trending behaviour, or is subject to some form of time‐varying, continuous change. The test we propose is simple to compute, being based on ratios of periodogram ordinates, has a pivotal limiting null distribution of known form which reduces to the multiple of a random variable in the case where the series is short memory, and has power against a wide class of time‐varying mean models. A Monte Carlo simulation study into the finite sample behaviour of the test shows it to have both good size properties under the null for a range of long and short memory series and to exhibit good power against a variety of plausible time‐varying mean alternatives. Because of its simplicity, we recommend our periodogram ratio test as a routine portmanteau test for whether the mean component of a time series can reasonably be treated as constant.