Analysis Method of Correlation Coefficient ARMA(p,q) Series

The correlation coefficient ARMA(p,q)series of which mean and variance may vary with time is widely used in engineering,such as pattern recognition,fault diagnosis,signal processing,automatic control,structure response analysis and so on.The traditional correlation function stationary ARMA(p,q) model is just a special case of that.The conditional maximum likelihood estimation (MLE) and exact MLE for the correlation coefficient ARMA(p,q) series are established in this paper,which can obtain its mean function,variance function and correlation coefficient function with high precision.The conditional MLE is simple and convenient for engineering application when the sample is large enough,and the exact MLE is still precise in the case of small sample. Base on analyzing in time domain,the spectral analysis of correlation coefficient ARMA(p,q) series can be done.