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New recursive estimators of the time-average variance constant

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Abstract

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. Wu (2009) 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.

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Acknowledgments

Supported in part by HKSAR-RGC Grants CUHK405012, 405113.

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  1. Department of Statistics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong

    Chun Yip Yau & Kin Wai Chan

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  1. Chun Yip Yau
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Correspondence to Chun Yip Yau.

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Yau, C.Y., Chan, K.W. New recursive estimators of the time-average variance constant. Stat Comput 26, 609–627 (2016). https://doi.org/10.1007/s11222-015-9548-7

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