Simple (but effective) tests of long memory versus structural breaks

This paper proposes two simple tests that are based on certain time domain properties of I(d) processes. First, if a time series follows an I(d) process, then each subsample of the time series also follows an I(d) process with the same value of d. Second, if a time series follows an I(d) process, then its dth differenced series follows an I(0) process. Simple as they may sound, these properties provide useful tools to distinguish between true and spurious I(d) processes. In the first test, we split the sample into b subsamples, estimate d for each subsample, and compare them with the estimate of d from the full sample. In the second test, we estimate d, use the estimate to take the dth difference of the sample, and apply the KPSS test and Phillips-Perron test to the differenced data and its partial sum. Both tests are applicable to both stationary and nonstationary I(d) processes. Simulations show that the proposed tests have good power against the spurious long memory models considered in the literature. The tests are applied to the daily realized volatility of the S&P 500 index.