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Unbiased Time-Average Estimators for Markov Chains

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  • Nabil Kahalé

    (ESCP Business School, 75011 Paris, France)

Abstract

We consider a time-average estimator f k of a functional of a Markov chain. Under a coupling assumption, we show that the expectation of f k has a limit μ as the number of time steps goes to infinity. We describe a modification of f k that yields an unbiased estimator f ^ k of μ . It is shown that f ^ k is square integrable and has finite expected running time. Under certain conditions, f ^ k can be built without any precomputations and is asymptotically at least as efficient as f k , up to a multiplicative constant arbitrarily close to one. Our approach also provides an unbiased estimator for the bias of f k . We study applications to volatility forecasting, queues, and the simulation of high-dimensional Gaussian vectors. Our numerical experiments are consistent with our theoretical findings.

Suggested Citation

  • Nabil Kahalé, 2024. "Unbiased Time-Average Estimators for Markov Chains," Mathematics of Operations Research, INFORMS, vol. 49(4), pages 2136-2165, November.
    • Handle: RePEc:inm:ormoor:v:49:y:2024:i:4:p:2136-2165
    DOI: 10.1287/moor.2022.0326
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    References listed on IDEAS

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