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<p>Simple processes are a class of spectrally correlated time series which constitutes a novel category of non-stationary time series that their Loeve bi-frequency spectrum includes a countable collection of curves. Since autocovariance function is an important tool in both theoretical and practical time series analysis, this paper deals with the estimation of the autocovariance function for simple processes. For this purpose, we apply an auxiliary process which converges to main simple process in quadratic mean. The theoretical results will be justified through Monte Carlo simulations.</p>

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On the covariance estimation of the simple processes

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月25日

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  • Mohammadreza Mahmoudi

摘要

Simple processes are a class of spectrally correlated time series which constitutes a novel category of non-stationary time series that their Loeve bi-frequency spectrum includes a countable collection of curves. Since autocovariance function is an important tool in both theoretical and practical time series analysis, this paper deals with the estimation of the autocovariance function for simple processes. For this purpose, we apply an auxiliary process which converges to main simple process in quadratic mean. The theoretical results will be justified through Monte Carlo simulations.