The plot below shows the autocorrelation (ACF) and partial autocorrelation (PACF) functions of VXX returns. It’s interesting to note that VXX returns are positively auto-correlated at 3-day lag.

A.D.M. Hilton, J.B. Roberts, O. Hadded, Autocorrelation Based Analysis of Ensemble Averaged LDA Engine Data for Bias-Free Turbulence Estimates: A Unified Approach ...

An extended sample autocorrelation function based on these consistent estimates is then defined and used for order determination. One of the advantages of this new approach is that it eliminates the ...