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In this paper, we propose a test for a break in the level of a fractionally integrated process when the timing of the putative break is not known. This testing problem has received considerable attention in the literature in the case where the time series is weakly autocorrelated. Less attention has been given to the case where the underlying time series is allowed to be fractionally integrated. Here, valid testing can only be performed if the limiting null distribution of the level break test statistic is well defined for all values of the fractional integration exponent considered. However, conventional sup-Wald type tests diverge when the data are strongly autocorrelated. We show that a sup-Wald statistic, which is standardized using a non-parametric kernel-based long-run variance estimator, does possess a well-defined limit distribution, depending only on the fractional integration parameter, provided the recently developed fixed- b asymptotic framework is applied. We give the appropriate asymptotic critical values for this sup-Wald statistic and show that it has good finite sample size and power properties. [ABSTRACT FROM AUTHOR]

We have developed a new test against spurious long memory based on the invariance of long memory parameter to aggregation. By using the local Whittle estimator, the statistic takes the supremum among combinations of paired aggregated series. Simulations show that the test performs good in finite sample sizes, and is able to distinguish long memory from spurious processes with excellent power. Moreover, the empirical application gives further evidence that the observed long memory in German stock returns is spurious. [ABSTRACT FROM PUBLISHER]

Abstract: The principal objective of this study is to determine whether the long-memory property is real or a spurious result caused by contemporaneous aggregation. In order to assess the presence of long memory in returns and volatility, two different long-memory detection techniques (modified R/S analysis and the GPH test) were applied to the KOSPI 50 index and its 50 constituent individual stock prices. According to the empirical evidence gleaned from the two long-memory tests, we conclude that there exists significant evidence for the long-memory property in volatility in both the market index and in a majority of individual stocks. These findings indicate that the observed evidence of the long-memory feature in volatility of index series is not spurious, and that we can reject the hypothesis that spurious long-memory evidence in the volatility of index series is the consequence of contemporaneous aggregation. However, this conclusion should be considered cautiously, given that a considerable number of the individual stock volatilities in square returns strongly show a short-memory property, as the level of significance in statistical decisions is lowered to the 1% level. [ABSTRACT FROM AUTHOR]