A method for determining covariance functions of time series is presented.First

it can construct a series of cross covariance

cross correlation

auto-covariance or auto-correlation function according to the time series.Then

it can determine the trend term of the cross covariance

the cross correlation

the auto-covariance or the auto-correlation function series

which obtains not only the periodic function of the trend term by the spectral analysis but also the nonperiodic function by multiple-point averaging

and synthesizes the integral function of the trend term.The functional form of the cross covariance

the cross correlation

the auto-covariance or the auto-correlation function can be derived from the trend function.Besides

its parameters are estimated by the least squares method.The presented method is credible and easily available for modeling

analysis and forecast of the covariance and the correlation function of time series.