Generating schemes for long memory processes: regimes, aggregation and linearity
AbstractThis paper analyses a class of nonlinear time series models exhibiting long memory. These processes exhibit short memory fluctuations around a local mean (regime) which switches randomly such that the durations of the regimes follow a power law. We show that if a large number of independent copies of such a process are aggregated, the resulting processes are Gaussian, have a linear representation, and converge after normalisation to fractional Brownian motion. Two cases arise, a stationary case in which the partial sums of the process converge, and a nonstationary case in which the process itself converges, the Hurst coefficient falling in the ranges ( 1 2 , 1) and (0, 1 2 ) respectively. However, a non-aggregated regime process is shown to converge to a Levy motion with infinite variance, suitably normalised, emphasising the fact that time aggregation alone fails to yield a FCLT. We comment on the relevance of our results to the interpretation of the long memory phenomenon, and also report some simulations aimed to throw light on the problem of discriminating between the models in practice. --
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 128 (2005)
Issue (Month): 2 (October)
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Web page: http://www.elsevier.com/locate/jeconom
Other versions of this item:
- Davidson, James & Sibbertsen, Philipp, 2002. "Generating schemes for long memory processes: Regimes, aggregation and linearity," Technical Reports 2002,46, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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