Distribution Theory for the Studentized Mean for Long, Short, and Negative Memory Time Series

Tucker McElroy () and D N Politis

University of California at San Diego, Economics Working Paper Series from Department of Economics, UC San Diego

Abstract: We consider the problem of estimating the variance of the partial sums of a stationary time series that has either long memory, short memory, negative/intermediate memory, or is the ¯rst- di®erence of such a process. The rate of growth of this variance depends crucially on the type of memory, and we present results on the behavior of tapered sums of sample autocovariances in this context when the bandwidth vanishes asymptotically. We also present asymptotic results for the case that the bandwidth is a ¯xed proportion of sample size, extending known results to the case of °at-top tapers. We adopt the ¯xed proportion bandwidth perspective in our empirical section, presenting two methods for estimating the limiting critical values { both the subsampling method and a plug-in approach. Extensive simulation studies compare the size and power of both approaches as applied to hypothesis testing for the mean. Both methods perform well { although the subsampling method appears to be better sized { and provide a viable framework for conducting inference for the mean. In summary, we supply a uni¯ed asymptotic theory that covers all di®erent types of memory under a single umbrella.

Keywords: kernel; lag-windows; overdifferencing; spectral estimation; subsampling; tapers; unit-root problem; Social and Behavioral Sciences (search for similar items in EconPapers)
Date: 2011-09-01
New Economics Papers: this item is included in nep-ecm and nep-ets
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Citations: View citations in EconPapers (1)

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Related works:
Journal Article: Distribution theory for the studentized mean for long, short, and negative memory time series (2013)
Working Paper: Distribution Theory for the Studentized Mean for Long, Short, and Negative Memory Time Series (2012)
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