Nonlinear persistence and copersistence
In a nonlinear framework, temporal dependence of time series is sensitive to transformations. The aim of this paper is to examine in detail the relationships between various forms of persistence and nonlinear transformations of stationary and nonstationary processes. We introduce the concept of persistence space and use it to define the degrees of persistence of univariate or multivariate processes. For illustration, we examine and compare the persistence structure of a fractionally integrated process and a beta mixture of AR(1) processes. The study of multivariate processes is focused on nonlinear comovements between the components, called the copersistence directions, or cointegration directions in the nonstationary case. We find that, in general, there is multiplicity of such directions, causing an identification problem in the analysis of nonlinear cointegration.
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- Vahid, F & Engle, Robert F, 1993. "Common Trends and Common Cycles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(4), pages 341-360, Oct.-Dec..
- Engle, Robert & Granger, Clive, 2015.
"Co-integration and error correction: Representation, estimation, and testing,"
Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
- Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-276, March.
- Granger, Clive W J, 1993. "Strategies for Modelling Nonlinear Time-Series Relationships," The Economic Record, The Economic Society of Australia, vol. 69(206), pages 233-238, September.
- Hansen, Lars Peter & Alexandre Scheinkman, Jose & Touzi, Nizar, 1998. "Spectral methods for identifying scalar diffusions," Journal of Econometrics, Elsevier, vol. 86(1), pages 1-32, June.
- 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.
- Peter C.B. Phillips & Joon Y. Park, 1998. "Asymptotics for Nonlinear Transformations of Integrated Time Series," Cowles Foundation Discussion Papers 1182, Cowles Foundation for Research in Economics, Yale University.
- Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
- Ermini, Luigi & Granger, Clive W. J., 1993. "Some generalizations on the algebra of I(1) processes," Journal of Econometrics, Elsevier, vol. 58(3), pages 369-384, August.
- Luigi Ermini & Clive W.J. Granger, 1991. "Some Generalizations on the Algebra of I(1) Processes," Working Papers 199113, University of Hawaii at Manoa, Department of Economics.
- Corradi, Valentina & Swanson, Norman R. & White, Halbert, 2000. "Testing for stationarity-ergodicity and for comovements between nonlinear discrete time Markov processes," Journal of Econometrics, Elsevier, vol. 96(1), pages 39-73, May.
- Corradi, V. & Swanson, N. & White, H., 1996. "Testing for Stationarity-Ergodicity and for Comovements Between Nonlinear Discrete Time Markov Processes," Papers 4-96-6, Pennsylvania State - Department of Economics.
- Christian Gourieroux & Joanna Jasiak, 1998. "Nonlinear Autocorrelograms : An Application to Intra-Trade Durations," Working Papers 98-41, Center for Research in Economics and Statistics.
- 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.
- Yoosoon Chang & Joon Y. Park & Peter C.B. Phillips, 1999. "Nonlinear Econometric Models with Cointegrated and Deterministically Trending Regressors," Cowles Foundation Discussion Papers 1245, Cowles Foundation for Research in Economics, Yale University.
- Vahid, Farshid & Engle, Robert F., 1997. "Codependent cycles," Journal of Econometrics, Elsevier, vol. 80(2), pages 199-221, October.
- He, Changli & Teräsvirta, Timo, 1997. "Statistical Properties of the Asymmetric Power ARCH Process," SSE/EFI Working Paper Series in Economics and Finance 199, Stockholm School of Economics, revised 30 Sep 1997.
- Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 369-380, October.
- Robert F. Engle & Sharon Kozicki, 1990. "Testing For Common Features," NBER Technical Working Papers 0091, National Bureau of Economic Research, Inc.
- Granger, Clive W J, 1986. "Developments in the Study of Cointegrated Economic Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 213-228, August.
- Anderson, Heather M. & Vahid, Farshid, 1998. "Testing multiple equation systems for common nonlinear components," Journal of Econometrics, Elsevier, vol. 84(1), pages 1-36, May.
- Deo, Rohit S. & Hurvich, Clifford M., 2001. "On The Log Periodogram Regression Estimator Of The Memory Parameter In Long Memory Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 17(04), pages 686-710, August.
- Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
- Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 393-395, October. Full references (including those not matched with items on IDEAS)
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