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.