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 .
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.
 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.
 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.
 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
 B. M. P?tscher, “Nonlinear Functions and Convergence to Brownian Motion: Beyond the Continuous Mapping Theorem,” Mimeo, University of Vienna, Vienna, 2001.
 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
 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.
 J. Akonom and C. Gourieroux, “A Functional Limit Theorem for Fractional Processes,” Working Paper, CEPREMAP, 1987.
 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.