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Asymptotic inference for monstationary fractionally integrated processes

Listed author(s):
  • Mármol, Francesc
  • Dolado, Juan José

This paper studies the asymptotic of nonstationary fractionally integrated (NFI) multivariate processes with memory parameter d> 112. We provide conditions to establish a functional central limit theorem and weak convergence of stochastic integrals for NFI processes under the assumptions of these results are given. More specifically, we obtain the rates of convergence and limiting distributions of the OLS estimators of cointegrating vectors in triangular representations. Further, we extend Sims, Stock and Watson's (1990) analysis on estimation and hypothesis testing in vector autoregressions with integrated processes and deterministic components to the more general fractional framework. We show how their main conclusions remain valid when dealing with NFI processes. That is, whenever a block of coefficients can be written as coefficients on zero mean 1(0) regressors in a model that includes a constant term, they will have a joint asymptotic normal distribution, so that the corresponding restrictions can be tested using standard asymptotic chi-square distribution theory. Otherwise, in general, the associated statistics will have nonstandard limiting distributions.

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File URL: http://e-archivo.uc3m.es/bitstream/handle/10016/6350/ws996823.PDF?sequence=1
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Paper provided by Universidad Carlos III de Madrid. Departamento de Estadística in its series DES - Working Papers. Statistics and Econometrics. WS with number 6350.

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Date of creation: Oct 1999
Handle: RePEc:cte:wsrepe:6350
Contact details of provider: Web page: http://portal.uc3m.es/portal/page/portal/dpto_estadistica

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  1. Toda, Hiro Y & Phillips, Peter C B, 1993. "Vector Autoregressions and Causality," Econometrica, Econometric Society, vol. 61(6), pages 1367-1393, November.
  2. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Oxford University Press, vol. 53(4), pages 473-495.
  3. Park, Joon Y. & Phillips, Peter C.B., 1989. "Statistical Inference in Regressions with Integrated Processes: Part 2," Econometric Theory, Cambridge University Press, vol. 5(01), pages 95-131, April.
  4. D Marinucci & Peter M. Robinson, 1998. "Semiparametric frequency domain analysis of fractional cointegration," LSE Research Online Documents on Economics 2258, London School of Economics and Political Science, LSE Library.
  5. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
  6. D. Marinucci, 1998. "Band spectrum regression for cointegrated time series with long memory innovations," LSE Research Online Documents on Economics 6871, London School of Economics and Political Science, LSE Library.
  7. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(03), pages 468-497, December.
  8. Phillips, P.C.B., 1988. "Weak Convergence of Sample Covariance Matrices to Stochastic Integrals Via Martingale Approximations," Econometric Theory, Cambridge University Press, vol. 4(03), pages 528-533, December.
  9. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
  10. Liu, Ming, 1998. "Asymptotics Of Nonstationary Fractional Integrated Series," Econometric Theory, Cambridge University Press, vol. 14(05), pages 641-662, October.
  11. D Marinucci, 1998. "Band Spectrum Regression for Cointegrated Time Series with Long Memory Innovations," STICERD - Econometrics Paper Series 353, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  12. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, vol. 61(4), pages 783-820, July.
  13. Jeganathan, P., 1999. "On Asymptotic Inference In Cointegrated Time Series With Fractionally Integrated Errors," Econometric Theory, Cambridge University Press, vol. 15(04), pages 583-621, August.
  14. Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, vol. 55(5), pages 1035-1056, September.
  15. D Marinucci & Peter M. Robinson, 1998. "Weak convergence of multivariate fractional processes," LSE Research Online Documents on Economics 2322, London School of Economics and Political Science, LSE Library.
  16. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-144, January.
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