On the convexity of the autocorrelation function of an AR(p) process (Q1113246)

It is known that stationarity for an autoregressive process of order p requires that the absolute value of the roots of the corresponding characteristic equation be less than 1. It is shown here that if those roots are real, distinct and lie between 0 and 1, then the autocorrelation function is positive and convex. Further, an asymptotic test is given for testing convexity of the autocorrelation function.