Moving Average Processes with Infinite Variance

The sample autocorrelation function (acf) of a stationary process has played a central statistical role in traditional time series analysis, where the assumption is made that the marginal distribution has a second moment. Now, the classical methods based on acf are not applicable in heavy tailed modeling. Using the codifference function as dependence measure for such processes be shown it be as a new tool for order identification of stable moving average processes. Based on the empirical characteristic function, we propose a consistent estimator of the codifference function. In addition, we derive the limiting distribution. Finally, simulation study shows the method is good.