Hi: I know it's true but I don't know how to prove that exponentially weighted moving average when view ed as a function of $\lambda$, is strictly convex. The exponentially weighted moving average for a time series X_t is defined as $(1-\lambda) \sum_{i=0}^{t} \lambda^{i}X_{t-i}$ for any $t > 0$. Note that $t$ is allowed to go to infinity and $0 < \lambda < 1$. Thanks for the proof or even a reference. I couldn't find much on convexity of the EWMA. Also, my apologies if this is not the correct tag for this question.
Mark