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.
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This paper was revised while the first author visited Texas A&M University. An earlier version was presented at the Econometric Society European Meeting in Milano, August 27–31, 2008.
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Hassler, U., Scheithauer, J. Detecting changes from short to long memory. Stat Papers 52, 847–870 (2011). https://doi.org/10.1007/s00362-009-0292-y
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DOI: https://doi.org/10.1007/s00362-009-0292-y