Detecting changes from short to long memory

Abstract

This paper studies well-known tests by Kim et al. (J Econom 109:389–392, 2002) and Busetti and Taylor (J Econom 123:33–66, 2004) for the null hypothesis of short memory against a change to nonstationarity, I (1). The potential break point is not assumed to be known but estimated from the data. First, we show that the tests are also applicable for a change from I (0) to a fractional order of integration I (d) with d > 0 (long memory) in that the tests are consistent. The rates of divergence of the test statistics are derived as functions of the sample size T and d. Second, we compare their finite sample power experimentally. Third, we consider break point estimation for a change from I (0) to I (d) for finite samples in computer simulations. It turns out that the estimators proposed for the integer case (d = 1) are practically reliable only if d is close enough to 1.