ESTIMATION OF THE AUTOCORRELATION COEFFICIENTS IN A STATIONARY LOGNORMAL PROCESS

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  • Tanaka Minoru
    Department of Information Sciences, Science University of Tokyo

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  • Estimation of the Autocorrelation Coeff

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Abstract

The sequence of positive random variables {Yt} is called a stationary lognormal process with parameters μ, σ2 and ρh, h=0, ±1, ±2, …, if the sequence of logarithmic variables {ln Yt} is stationary and Gaussian with mean μ, variance σ2 and autocorrelation coefficients ρh. This paper deals with the problem of estimating the autocorrelation coefficients of a stationary lognormal process with known μ and σ2. Efficiency of the usual sample autocorrelations relative to a simplified estimate is studied under the assumption that the transformed process is Markovian. The result leads to the choice of the biased simplified estimate as a better estimate than the unbiased sample autocorrelations for small lag h and small σ. Other unbiased estimates are constructed and their variances are evaluated.

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