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.

We present a complete analysis of the weak limit behaviour of the sample autocovariance and autocorrelation functions of (Xt), (|Xt|) and (Xt 2). The results in this paper can be seen as a natural ...

Peter R. Hansen, Asger Lunde, ESTIMATING THE PERSISTENCE AND THE AUTOCORRELATION FUNCTION OF A TIME SERIES THAT IS MEASURED WITH ERROR, Econometric Theory, Vol. 30, No. 1 (February 2014), pp. 60-93 ...