Structural breaks versus long memory, a simulation study

In the last decade lot of interest, both in the econometric and statistical literature, has been paid to the issue of confusing long memory and structural breaks in level. Indeed, there is evidence that a stationary short memory process that encounters occasional level shifts can show a slow rate of decay in the autocorrelation function and other properties of I(d) processes, where d can be a fraction. On the other hand, when the data generating process is an integrated or fractionally integrated process (with no breaks), several breaks can be detected spuriously. Thus, testing procedures that allow a distinction between long memory and level shifts are currently a popular subject of research. Here we show the results of a simulation study on a simple empirical strategy that can be applied as a first check, to assess "what is what". This strategy consists in fitting long memory and structural break models separately; in case both provide plausible explanation of the DGP of the data at hand, the long memory and structural break analysis are repeated on the series break-free and on the filtered series, respectively. Then, the presence of breaks in the filtered series and/or of long memory behavior in the break-free series indicate whether the series shows real or spurious breaks and long memory.