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How close is a fractional process to a random walk with drift?
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
2015 (English)In: Journal of Time Series Econometrics, ISSN 1941-1928, E-ISSN 1941-1928, Vol. 7, no 2, 217-234 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we investigate how close a fractional process can be to a random walk with drift in terms of the sample path. Given the innovation sequence, we calculate the distance to the closest random walk with drift in the sum of squares sense. We also derive the expected distance between the processes under the assumption of white noise normal innovations. A local approximation formula for this distance is given in terms of the sample size, showing that it increases with the sample size more rapidly than the square of the number of observations. Two empirical examples illustrate the results.

Place, publisher, year, edition, pages
2015. Vol. 7, no 2, 217-234 p.
Keyword [en]
fractional process; random walk; distance
National Category
Natural Sciences Mathematics
URN: urn:nbn:se:uu:diva-242122DOI: 10.1515/jtse-2013-0032ISI: 000364492300004OAI: oai:DiVA.org:uu-242122DiVA: diva2:782387
Available from: 2015-01-21 Created: 2015-01-21 Last updated: 2016-02-17Bibliographically approved

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Larsson, Rolf
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