Length and Quality of Lagged-Product Autocorrelation Estimates

The sample autocorrelation function is defined with the mean lagged products of random observations. It is the inverse Fourier transform of the raw periodogram. Both contain the same information and the quality of the sample autocorrelation, as a representation of data, is as poor as that of a raw periodogram. The autocorrelation function can be estimated much more accurately with a parametric time series method. A MATLABreg computer program automatically selects the type and the order of the best time series model for stochastic observations with unknown characteristics. The parametric estimate of the autocorrelation function has always a better accuracy than the mean-lagged-product estimates. Parametric estimates will die out eventually. They allow an objective answer to the question how long the autocorrelation function really is.