TEL  Vol.2 No.4 , October 2012
Further Results on Convergence for Nonlinear Transformations of Fractionally Integrated Time Series
Author(s) Chien-Ho Wang*
ABSTRACT
This paper presents some new results for the nonlinear transformations of the fractional integration process. Specifically, this paper reviews the weight fractional integration process with the Hurst parameter, 3/2 > d > 5/6 , and investigates the asymptotics of asymptotically homogeneous functional transformations of weight fractional integration process. These new results improve upon the earlier research of Tyurin and Phillips [1].

Cite this paper
C. Wang, "Further Results on Convergence for Nonlinear Transformations of Fractionally Integrated Time Series," Theoretical Economics Letters, Vol. 2 No. 4, 2012, pp. 408-411. doi: 10.4236/tel.2012.24075.
References
[1]   K. Tyurin and P. C. B. Phillips, “The Occupation Density of Fractional Brownian Motion and Some of Its Applications,” Working Paper, Indiana University, Bloomington, 1999.

[2]   J. Y. Park and P. C. B. Phillips, “Asymptotics for Nonlinear Transformations of Integrated Time Series,” Econometric Theory, Vol. 15, No. 3, 1999, pp. 269-298. doi:10.1017/S0266466699153015

[3]   J. Y. Park and P. C. B. Phillips, “Nonlinear Regression with Integrated Time Series,” Econometrica, Vol. 69, No. 1, 2001, pp. 117-161. doi:10.1111/1468-0262.00180

[4]   B. M. P?tscher, “Nonlinear Functions and Convergence to Brownian Motion: Beyond the Continuous Mapping Theorem,” Mimeo, University of Vienna, Vienna, 2001.

[5]   R. de Jong and C.-H. Wang, “Further Results on the Asymptotics for Nonlinear Transformations of Integrated Time Series,” Econometric Theory, Vol. 21, No. 2, 2005, pp. 413-430. doi:10.1017/S026646660505022X

[6]   P. Jeganathan, “Convergence of Functionals of Sums of R.V.S to Local Times of Fractional Stable Motion,” Annals of Probability, Vol. 32, No. 3, 2004, pp. 1771-1795. doi:10.1214/009117904000000658

[7]   J. Akonom and C. Gourieroux, “A Functional Limit Theorem for Fractional Processes,” Working Paper, CEPREMAP, 1987.

[8]   L. Coutin, D. Nualart and C. Tudor, “Tanaka Formula for the Fractional Brownian Motion,” Stochastic Processes and Their Applications, Vol. 94, No. 2, 2001, pp. 301-315. doi:10.1016/S0304-4149(01)00085-0

 
 
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