论文标题
基于全球小波的自举协方差测试
A Global Wavelet Based Bootstrapped Test of Covariance Stationarity
论文作者
论文摘要
我们提出了一个协方差的平稳性测试，以进行原本依赖的和可能是全球非平稳时间序列。我们在Jin，Wang和Wang（2015）的新环境的广义版本中工作，他们利用Walsh（1923）的功能将子样本协方差与完整的样本对应物进行比较。他们将严格的平稳性强加于零假设下的线性过程，以实现倒高维渐近协方差矩阵的参数估计器，并且不考虑任何其他正常基础。相反，我们在包括HAAR小波和沃尔什功能在内的轻度条件下与一般的正顺序基础合作；并且我们允许具有非IID创新的线性或非线性过程。这在宏观经济和金融中很重要，在许多情况下，非线性反馈和随机波动发生。我们通过引导最大相关差异统计量完全避开了渐近协方差矩阵估计和反转，其中最大值是在相关滞后$ h $以及基础生成的子样本计数器$ k $（系统样本的数量）上获取的。对于最大滞后和计数$ \ MATHCAL {H} _ {T} $和$ \ MATHCAL {K} _ {T} $，我们实现了更高的可行增加率。尤其值得注意的是，我们的测试能够检测出差异的断裂，远处或非常轻微的平稳性偏差。
We propose a covariance stationarity test for an otherwise dependent and possibly globally non-stationary time series. We work in a generalized version of the new setting in Jin, Wang and Wang (2015), who exploit Walsh (1923) functions in order to compare sub-sample covariances with the full sample counterpart. They impose strict stationarity under the null, only consider linear processes under either hypothesis in order to achieve a parametric estimator for an inverted high dimensional asymptotic covariance matrix, and do not consider any other orthonormal basis. Conversely, we work with a general orthonormal basis under mild conditions that include Haar wavelet and Walsh functions; and we allow for linear or nonlinear processes with possibly non-iid innovations. This is important in macroeconomics and finance where nonlinear feedback and random volatility occur in many settings. We completely sidestep asymptotic covariance matrix estimation and inversion by bootstrapping a max-correlation difference statistic, where the maximum is taken over the correlation lag $h$ and basis generated sub-sample counter $k$ (the number of systematic samples). We achieve a higher feasible rate of increase for the maximum lag and counter $\mathcal{H}_{T}$ and $\mathcal{K}_{T}$. Of particular note, our test is capable of detecting breaks in variance, and distant, or very mild, deviations from stationarity.
