A COMPOSITE LINEAR MODEL GENERATING A STATIONARY STOCHASTIC PROCESS WITH GIVEN THIRD‐ORDER AUTOCORRELATION FUNCTION

Fuminori Sakaguchi and Hideaki Sakai

Journal of Time Series Analysis, 1989, vol. 10, issue 2, 171-181

Abstract: Abstract. A composite linear model is proposed which generates a non‐Gaussian stationary stochastic process with a given third‐order autocorrelation function and a white power spectrum. The design of the model is based on the fact that a type of finite‐impulse‐response linear system with a non‐Gaussian white input series produces an output process whose third‐order correlations exist only for special time lags. An arbitrary third‐order autocorrelation function can be constructed by superposing output processes of this type. The model requires at most 2L2+ 4L+ 1 independent identically distributed (i.i.d.) input processes for the third‐order autocorrelation function with the largest time lag L. Results of numerical experiments confirm the validity of the model.

Date: 1989
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https://doi.org/10.1111/j.1467-9892.1989.tb00022.x

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