The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals Ii

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The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals Ii

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Davidson, James
de Jong, Robert M.

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James E. H. Davidson

Abstract

This paper derives a functional central limit theorem for the partial sums of fractionally integrated processes, otherwise known as I(d) processes for d 1/2. Such processes have long memory, and the limit distribution is the so-called fractional Brownian motion, having correlated increments even asymptotically. The underlying shock variables may themselves exhibit quite general weak dependence by being near-epoch-dependent functions of mixing processes. Several weak convergence results for stochastic integrals having fractional integrands and weakly dependent integrators are also obtained. Taken together, these results permit I(p + d) integrands for any integer p 1.

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Publisher Info
Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 16 (2000)
Issue (Month): 05 (October)
Pages: 643-666
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Handle: RePEc:cup:etheor:v:16:y:2000:i:05:p:643-666_16

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Article
- de Jong, Robert M. & Davidson, James, 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals I," Econometric Theory, Cambridge University Press, vol. 16(05), pages 621-642, October. [Downloadable!]

Cited by:
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Morten Ørregaard Nielsen, 2008. "A Powerful Tuning Parameter Free Test of the Autoregressive Unit Root Hypothesis," Working Papers 1175, Queen's University, Department of Economics. [Downloadable!]
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Jonathan Hill, 2006. "On Functional Central Limit Theorems for Dependent, Heterogeneous Tail Arrays with Applications to Tail Index and Tail Dependence Estimators," Working Papers 0607, Florida International University, Department of Economics. [Downloadable!]
Kapetanios, G. & Pesaran, M.H. & Yamagata, T., 2006. "Panels with Nonstationary Multifactor Error Structures," Cambridge Working Papers in Economics 0651, Faculty of Economics, University of Cambridge. [Downloadable!]
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- George Kapetanios & M. Hashem Pesaran & Takashi Yamagata, 2006. "Panels with Nonstationary Multifactor Error Structures," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
Uwe Hassler & Francesc Marmol & Carlos Velasco, 2002. "Residual Log-Periodogram Inference for Long-Run Relationships," Darmstadt Discussion Papers in Economics 115, Institut für Volkswirtschaftslehre (Department of Economics), Technische Universität Darmstadt (Darmstadt University of Technology). [Downloadable!]
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James Davidson & Nigar Hashimzade, 2007. "Representation and Weak Convergence of Stochastic Integrals with Fractional Integrator Processes," CREATES Research Papers 2007-45, School of Economics and Management, University of Aarhus. [Downloadable!]
Morten Ørregaard Nielsen, 2008. "A Powerful Test of the Autoregressive Unit Root Hypothesis Based on a Tuning Parameter Free Statistic," Working Papers 1185, Queen's University, Department of Economics. [Downloadable!]
Other versions:
- Morten Ørregaard Nielsen, 2008. "A Powerful Test of the Autoregressive Unit Root Hypothesis Based on a Tuning Parameter Free Statistic," CREATES Research Papers 2008-36, School of Economics and Management, University of Aarhus. [Downloadable!]
- Nielsen, Morten ?rregaard, 2009. "A Powerful Test Of The Autoregressive Unit Root Hypothesis Based On A Tuning Parameter Free Statistic," Econometric Theory, Cambridge University Press, vol. 25(06), pages 1515-1544, December. [Downloadable!]
Todd E. Clark & Michael W. McCracken, 2008. "Combining forecasts from nested models," Working Papers 2008-037, Federal Reserve Bank of St. Louis. [Downloadable!]
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- Todd E. Clark & Michael W. McCracken, 2007. "Combining forecasts from nested models," Finance and Economics Discussion Series 2007-43, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
- Todd E. Clark & Michael W. McCracken, 2009. "Combining Forecasts from Nested Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(3), pages 303-329, 06. [Downloadable!] (restricted)
Robert de Jong, 2004. "Nonlinear estimators with integrated regressors but without exogeneity," Econometric Society 2004 North American Winter Meetings 324, Econometric Society. [Downloadable!]
Gengenbach,Christian & Palm,Franz C. & Urbain,Jean-Pierre, 2005. "Panel Cointegration Testing in the Presence of Common Factors," Research Memoranda 050, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
Donald W.K. Andrews & Patrik Guggenberger, 2007. "Hybrid and Size-Corrected Subsample Methods," Cowles Foundation Discussion Papers 1606, Cowles Foundation, Yale University. [Downloadable!]
Jen-Je Su, 2003. "On the power of the multivariate KPSS test of stationarity against fractionally integrated alternatives," Applied Economics Letters, Taylor and Francis Journals, vol. 10(10), pages 637-641, August. [Downloadable!] (restricted)
Chi-Young Choi & Ling Hu & Masao Ogaki, 2005. "Structural Spurious Regressions and A Hausman-type Cointegration Test," RCER Working Papers 517, University of Rochester - Center for Economic Research (RCER). [Downloadable!]

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