On processes with hyperbolically decaying autocorrelations ∗ Łukasz Dębowski Institute of Computer Science, Polish Academy of Sciences ul. Ordona 21, 01-237 Warszawa, Poland Abstract We discuss some relations between autocorrelations (ACF) and partial autocorrelations (PACF) of weakly stationary processes. Firstly, we con- struct an extension of a process ARIMA(0, d, 0) for d ∈ (−∞, 0), which enjoys nonsummable partial autocorrelations and autocorrelations decay- ing as rapidly as ρn ≍ n -1+2d . Such a situation is impossible if the absolute sum of autocorrelations is sufficiently small. We show that then the PACF is less than the ACF up to a multiplicative constant. Our sec- ond result complements a similar result of Baxter (1962). Key words: autocorrelation, partial autocorrelation, ARIMA processes * The work was partially supported by the Polish Ministry of Scientific Research and In- formation Technology, grant no. 1/P03A/045/28. 1