Premium
A COMPOSITE LINEAR MODEL GENERATING A STATIONARY STOCHASTIC PROCESS WITH GIVEN THIRD‐ORDER AUTOCORRELATION FUNCTION
Author(s) -
Sakaguchi Fuminori,
Sakai Hideaki
Publication year - 1989
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1989.tb00022.x
Subject(s) - autocorrelation , mathematics , moving average model , impulse response , white noise , autocorrelation technique , third order , partial autocorrelation function , spectral density , gaussian process , stationary process , gaussian , independent and identically distributed random variables , function (biology) , lag , statistical physics , statistics , random variable , mathematical analysis , time series , computer science , computer network , philosophy , physics , theology , quantum mechanics , evolutionary biology , biology , autoregressive integrated moving average
. 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 2 L 2 + 4 L + 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.