New recursive estimators of the time-average variance constant. (English) Zbl 1420.62365
Summary: Estimation of the time-average variance constant (TAVC) of a stationary process plays a fundamental role in statistical inference for the mean of a stochastic process. W. B. Wu [Ann. Appl. Probab. 19, No. 4, 1529–1552 (2009; Zbl 1171.62048)] proposed an efficient algorithm to recursively compute the TAVC with \(O(1)\) memory and computational complexity. In this paper, we propose two new recursive TAVC estimators that can compute TAVC estimate with \(O(1)\) computational complexity. One of them is uniformly better than Wu’s estimator in terms of asymptotic mean squared error (MSE) at a cost of slightly higher memory complexity. The other preserves the \(O(1)\) memory complexity and is better then Wu’s estimator in most situations. Moreover, the first estimator is nearly optimal in the sense that its asymptotic MSE is \(2^{10/3}3^{-2} \fallingdotseq 1.12\) times that of the optimal off-line TAVC estimator.
MSC:
| 62M09 | Non-Markovian processes: estimation |
| 60G10 | Stationary stochastic processes |
| 68Q25 | Analysis of algorithms and problem complexity |
Keywords:
batch means; long-run variance; physical dependence measure; predictive dependence measure; sequential estimationCitations:
Zbl 1171.62048Software:
ASAP3References:
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