Unbiased Time-Average Estimators for Markov Chains

Nabil Kahalé ()
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Nabil Kahalé: ESCP Business School, 75011 Paris, France

Mathematics of Operations Research, 2024, vol. 49, issue 4, 2136-2165

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.

Keywords: Primary: 65C05; secondary: 60J05; 60J22; multilevel Monte Carlo; unbiased estimator; steady state; Markov chain; time-average estimator (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:49:y:2024:i:4:p:2136-2165

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