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Asymptotic normality of the spectral density estimators for almost periodically correlated stochastic processes

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  • Léskow, Jacek

Abstract

A stochastic process is almost periodically correlated (APC) when its first and second moments exhibit periodicity in some approximative sense. The mathematical framework conveniently expressing such approximate periodicity is based on the theory of almost periodic functions (see Besicovitch, 1953). It is known that when APC process is strongly harmonizable then its covariance function may be represented by a countable family of distributions {G[lambda]}. In the event when the distributions {G[lambda]} have densities {g[lambda]} we can consider the problem of estimating distributions of the APC process in terms of estimating corresponding spectral densities {g[lambda]}. Following the previous results of Hurd and Leskow (1992a, b) we present here estimators of densities {g[lambda]} of the APC process and show their asymptotic normality when the process has a [phi]-mixing property.

Suggested Citation

  • Léskow, Jacek, 1994. "Asymptotic normality of the spectral density estimators for almost periodically correlated stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 52(2), pages 351-360, August.
    • Handle: RePEc:eee:spapps:v:52:y:1994:i:2:p:351-360
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    Cited by:

    1. Dehay, Dominique & Leskow, Jacek, 1996. "Testing stationarity for stock market data," Economics Letters, Elsevier, vol. 50(2), pages 205-212, February.
    2. Makagon, A. & Miamee, A. G., 1997. "On the spectrum of correlation autoregressive sequences," Stochastic Processes and their Applications, Elsevier, vol. 69(2), pages 179-193, September.

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