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Nonstationary Nonlinearity: An Outlook for New Opportunities

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  • Park, Joon

    (Rice U)

Abstract

In this paper, we look for new opportunities that can be exploited using some of the recent developments on the theory of nonlinear models with integrated time series. Heuristic introductions on the basic tools and asymptotics are followed by the opportunities in three different directions: in data generation, in mean and in volatility. In the direction of data generation, we investigate the nonlinear transformations of random walks. It is shown in particular that they can generate stationary long memory as well as bounded nonstationarity and leptokurticity, which we commonly observe in many of economic and financial data. We then discuss how the nonlinear mean relationships between integrated processes can be appropriately formulated, interpreted and estimated within the regression framework. Both the nonlinear least squares regression and the nonparametric kernel regression are considered. Such formulations allow us to explore the nonlinear and nonparametric cointegration, which may be used in modelling the nonlinear and nonparametric longrun relationships among various economic and financial time series. Finally, a stochastic volatility model with the conditional variance specified as a nonlnear function of a random walk is examined. Established are various time series properties of the model, which are shown to be largely consistent with the observed characteristics of many time series data.

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Bibliographic Info

Paper provided by Rice University, Department of Economics in its series Working Papers with number 2003-05.

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Date of creation: Mar 2003
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Handle: RePEc:ecl:riceco:2003-05

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  1. Peter C.B. Phillips & Joon Y. Park, 1999. "Nonstationary Binary Choice," Cowles Foundation Discussion Papers 1223, Cowles Foundation for Research in Economics, Yale University.
  2. Yoosoon Chang, 2000. "Nonlinear IV Unit Root Tests in Panels with Cross-Sectional Dependency," CIRJE F-Series CIRJE-F-85, CIRJE, Faculty of Economics, University of Tokyo.
  3. Chang, Yoosoon & Park, Joon Y., 2003. "Index models with integrated time series," Journal of Econometrics, Elsevier, vol. 114(1), pages 73-106, May.
  4. Park, Joon, 2003. "Strong Approximations for Nonlinear Transformations of Integrated Time Series," Working Papers 2003-18, Rice University, Department of Economics.
  5. Joon Y. Park & Peter C.B. Phillips, 1998. "Nonlinear Regressions with Integrated Time Series," Cowles Foundation Discussion Papers 1190, Cowles Foundation for Research in Economics, Yale University.
  6. Park, Joon Y., 2002. "Nonstationary nonlinear heteroskedasticity," Journal of Econometrics, Elsevier, vol. 110(2), pages 383-415, October.
  7. Yoosoon Chang & Joon Y. Park & Peter C. B. Phillips, 2001. "Nonlinear econometric models with cointegrated and deterministically trending regressors," Econometrics Journal, Royal Economic Society, vol. 4(1), pages 1-36.
  8. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(03), pages 269-298, June.
  9. Phillips, Peter C. B. & Park, Joon Y. & Chang, Yoosoon, 2004. "Nonlinear instrumental variable estimation of an autoregression," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 219-246.
  10. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation for Research in Economics, Yale University.
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Cited by:
  1. Miller, J. Isaac & Park, Joon Y., 2005. "How They Interact to Generate Persistency in Memory," Working Papers 2005-01, Rice University, Department of Economics.
  2. Joon Y. Park & J. Isaac Miller, 2004. "Nonlinearity, Nonstationarity, and Thick Tails: How They Interact to Generate Persistency in Memory," Econometric Society 2004 North American Summer Meetings 597, Econometric Society.
  3. Chang, Yoosoon, 2003. "Nonlinear IV Panel Unit Root Tests," Working Papers 2003-06, Rice University, Department of Economics.

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