Method for determining covariance functions of time series

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 non-periodic 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.