Strong Orthogonal Decompositions and Nonlinear Impulse Response Functions for Infinite-Variance Processes
AbstractIn this paper we prove Wold-type decompositions with strongorthogonal prediction innovations exist in smooth, re‡exive Banach spaces of discrete time processes if and only if the projection operator generating the innovations satisfies the property of iterations. Our theory includes as special cases all previous Wold-type decompositions of discrete time processes; completely characterizes when nonlinear heavy-tailed processes obtain a strong-orthogonal moving average representation; and easily promotes a theory of nonlinear impulse response functions for infinite variance processes. We exemplify our theory by developing a nonlinear impulse response func tion for smooth transition threshold processes, we discuss how to test de composition innovations for strong orthogonality and whether the proposed model represents the best predictor, and we apply the methodology to currency exchange rates.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Florida International University, Department of Economics in its series Working Papers with number 0408.
Length: 37 pages
Date of creation: May 2004
Date of revision:
Orthogonal decompositions; Banach spaces; projection iterations; infinite variance; moving average; nonlinear impulse response function; smooth transition autoregression; Lp-metric projection; Lp-GMM.;
Other versions of this item:
- Jonathan B. Hill, 2004. "Strong Orthogonal Decompositions and Non-Linear Impulse Response Functions for Infinite Variance Processes," Econometrics 0401001, EconWPA, revised 22 Apr 2004.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C29 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Other
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-08-13 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Dufour, J.M. & Renault, E., 1995.
"Short-Run and Long-Rub Causality in Time Series: Theory,"
Cahiers de recherche
9538, Universite de Montreal, Departement de sciences economiques.
- Jean-Marie Dufour & Eric Renault, 1998. "Short Run and Long Run Causality in Time Series: Theory," Econometrica, Econometric Society, vol. 66(5), pages 1099-1126, September.
- Dufour, J.M. & Renault, E., 1995. "Short-Run and Long-Rub Causality in Time Series: Theory," Cahiers de recherche 9538, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Lin, Wen-Ling, 1997. "Impulse Response Function for Conditional Volatility in GARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 15-25, January.
- Koop, Gary & Pesaran, M. Hashem & Potter, Simon M., 1996. "Impulse response analysis in nonlinear multivariate models," Journal of Econometrics, Elsevier, vol. 74(1), pages 119-147, September.
- Christian Gourieroux & Joanna Jasiak, 1999.
"Nonlinear Innovations and Impulse Response,"
99-44, Centre de Recherche en Economie et Statistique.
- Davis, Richard & Resnick, Sidney, 1985. "More limit theory for the sample correlation function of moving averages," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 257-279, September.
- Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1993. "Nonlinear Dynamic Structures," Econometrica, Econometric Society, vol. 61(4), pages 871-907, July.
- Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-38, July.
- Barry Falk & Chun-Hsuan Wang, 2003.
"Testing long-run PPP with infinite-variance returns,"
Journal of Applied Econometrics,
John Wiley & Sons, Ltd., vol. 18(4), pages 471-484.
- Falk, Barry L. & Wang, Chun-Hsuan, 2003. "Testing Long-Run Ppp with Infinite-Variance Returns," Staff General Research Papers 10323, Iowa State University, Department of Economics.
- Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
- Cheung, Yin-Wong, 1993. "Long Memory in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 93-101, January.
- Simon M. Potter, 1999.
"Nonlinear impulse response functions,"
65, Federal Reserve Bank of New York.
- Jonathan Hill, 2006. "Asymptotically Nuisance-Parameter-Free Consistent Tests of Lp-Functional Form," Working Papers 0608, Florida International University, Department of Economics.
- Greg Hannsgen, 2011. "Infinite-variance, Alpha-stable Shocks in Monetary SVAR: Final Working Paper Version," Economics Working Paper Archive wp_682, Levy Economics Institute.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sheng Guo).
If references are entirely missing, you can add them using this form.