时均方差常数的递推估计
Recursive estimation of time-average variance constants
摘要：
对于平稳过程均值的统计推断，需要估计其时间平均方差常数（TAVC）或长期方差。对于一个平稳过程，它的TAVC是它所有协方差的和，它是零处谱密度的倍数。经典的TAVC估计是基于批处理均值，不允许递归更新，所需的内存复杂度为O（n）。我们提出了一个更快的算法，递归计算的TAVC，从而具有O（1）阶的内存复杂度和计算复杂性度的规模线性$n$。在短相依条件下，我们建立了递归TAVC估计的矩和几乎必然收敛。并给出了收敛速度。
英文摘要：
For statistical inference of means of stationary processes, one needs to estimate their time-average variance constants (TAVC) or long-run variances. For a stationary process, its TAVC is the sum of all its covariances and it is a multiple of the spectral density at zero. The classical TAVC estimate which is based on batched means does not allow recursive updates and the required memory complexity is O(n). We propose a faster algorithm which recursively computes the TAVC, thus having memory complexity of order O(1) and the computational complexity scales linearly in $n$. Under short-range dependence conditions, we establish moment and almost sure convergence of the recursive TAVC estimate. Convergence rates are also obtained.
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