Properties of Nonlinear Transformations of Non-Gaussian Linear Processes

• Activity Number: 396
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Yongli Sang*+ and Hailin Sang
• Companies: and University of Mississippi
• Keywords: long memory ; memory estimation ; non-Gaussian linear process ; nonlinear transformation ; non-stationary process ; short memory

Abstract

In this paper, we study the memory properties of nonlinear transformations of non-Gaussian linear processes. Dittmann and Granger (2002) studied the Hermite transformations of Gaussian I(d) processes by applying the orthonormality of the Hermite polynomials under the measure for the standard normal distribution. Nevertheless, the orthogonality does not hold for transformation of non-Gaussian linear processes. We make use of the martingale decomposition method developed by Ho and Hsing (1996, 1997) to study the memory properties of nonlinear transformations of non-Gaussian linear processes and obtain consistent results as in the Gaussian case. In particular, the transformation of short-memory time series still has short-memory and the transformation of long-memory time series may have a different memory parameter. Furthermore, we study the memory properties of nonlinear transformations of general non-stationary type I and type II time series and obtain promising results. This study has application in financial market data analysis and econometrics when the time series observations have non-Gaussian heavy tails.