We prove a representation of the partial autocorrelation function (PACF) of a stationary process, or of the Verblunsky coefficients of its normalized spectral measure, in terms of the Fourier coefficients of the phase function. It is not of fractional form, whence simpler than the existing one...

Important results in prediction theory dealing with missing values have been obtained traditionally using difficult techniques based on duality in Hilbert spaces of analytic functions [Nakazi, T., 1984. Two problems in prediction theory. Studia Math. 78, 7-14; Miamee, A.G., Pourahmadi, M., 1988....

We prove an analogue of Baxter's inequality for fractional Brownian motion-type processes with Hurst index less than 1/2. This inequality is concerned with the norm estimate of the difference between finite- and infinite-past predictor coefficients.

Let {Xn : n[set membership, variant]Z} be a fractional ARIMA(p,d,q) process with partial autocorrelation function [alpha](·). In this paper, we prove that if d[set membership, variant](-1/2,0) then [alpha](n)~d/n as n-->[infinity]. This extends the previous result for the case 0<d<1/2.