True or spurious long memory? A new test

It is well known that long memory characteristics observed in data can be generated by nonstationary structural-break or slow regime switching models. We propose a statistical test to distinguish between true long memory and spurious long memory based on invariance of the long memory parameter for temporal aggregates of the process under the null of true long memory. Geweke Porter-Hudak estimates of the long memory parameter obtained from different temporal aggregates of the underlying time series are shown to be asymptotically jointly normal, leading to a test statistic that is constructed as the quadratic form of a demeaned vector of the estimates. The result is a test statistic that is very simple to implement. Simulations show the test to have good size and power properties for the classic alternatives to true long memory that have been suggested in the literature. The asymptotic distribution of the test statistic is also valid for a stochastic volatility with Gaussian long memory model. The test is applied to foreign exchange rate data. Based on all the models considered in this article, we conclude that the long memory property in exchange rate volatility is generated by a true long memory process.