We characterize the finite variation property for stationary increment mixed moving averages driven by infinitely divisible random measures. Such processes include fractional and moving average processes driven by Levy processes, and also their mixtures. We establish two types of zero-one laws for the finite variation property. We also consider some examples to illustrate our results.
Stochastic Processes and Their Applications, 2013, Vol 123, Issue 6, p. 1871-1890