论文标题
Volterra Bootstrap：重新采样严格固定单变量时间序列的高阶统计
Volterra bootstrap: Resampling higher-order statistics for strictly stationary univariate time series
论文作者
论文摘要
我们关注的是时间序列功能的非参数假设检验。众所周知，普遍流行的自动回归筛引导程序对于（渐近）分布的统计数据均无效，其（渐近）分布取决于高于两倍的秩序，而不论数据来自线性时间序列还是非线性。受非线性系统理论的启发，我们通过基于该过程的Volterra系列表示，引入了高阶的引导方案来规避这种非验证性。为了有效地估算这种表示的系数，我们依靠伏击运算符的替代表述来繁殖核希尔伯特空间。我们执行多项式内核回归，该回归与输入维度线性缩放，并且与非线性程度无关。我们在模拟研究中说明了建议的基于Volterra-prestressentation的引导程序的适用性，在该研究中，我们认为严格固定的线性和非线性过程。
We are concerned with nonparametric hypothesis testing of time series functionals. It is known that the popular autoregressive sieve bootstrap is, in general, not valid for statistics whose (asymptotic) distribution depends on moments of order higher than two, irrespective of whether the data come from a linear time series or a nonlinear one. Inspired by nonlinear system theory we circumvent this non-validity by introducing a higher-order bootstrap scheme based on the Volterra series representation of the process. In order to estimate coefficients of such a representation efficiently, we rely on the alternative formulation of Volterra operators in reproducing kernel Hilbert space. We perform polynomial kernel regression which scales linearly with the input dimensionality and is independent of the degree of nonlinearity. We illustrate the applicability of the suggested Volterra-representation-based bootstrap procedure in a simulation study where we consider strictly stationary linear and nonlinear processes.
