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Testing for co-non-linearity

This article introduces the concept of co-non-linearity. Co-non-linearity is an example of a common feature in time series (Engle and Koziciki, 1993, J. Bus. Econ. Statist.) and an extension of the concept of common nonlinear components (Anderson and Vahid, 1998, J. Econometrics). If some time series follow a non-linear process but there exists a linear relationship between the levels of these series that removes the non-linearity, then this relationship is said to be a co-non-linear relationship. In this article I show how to determine the number of such co-non-linear relationships. Furthermore, I show how to formulate hypothesis tests on the co-non-linear relationships in a full maximum likelihood framework.

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Paper provided by Statistics Norway, Research Department in its series Discussion Papers with number 699.

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Date of creation: Jul 2012
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Handle: RePEc:ssb:dispap:699
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  1. H. Peter Boswijk & Jurgen Doornik, 2003. "Identifying, Estimating and Testing Restricted Cointegrated Systems: An Overview," Economics Papers 2003-W10, Economics Group, Nuffield College, University of Oxford.
  2. González, Andrés & Teräsvirta, Timo, 2006. "Modelling autoregressive processes with a shifting mean," SSE/EFI Working Paper Series in Economics and Finance 637, Stockholm School of Economics, revised 22 May 2007.
  3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  4. Vahid, F & Engle, Robert F, 1993. "Common Trends and Common Cycles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(4), pages 341-60, Oct.-Dec..
  5. 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.
  6. Doornik, Jurgen A, 1999. " Erratum [Approximations to the Asymptotic Distribution of Cointegration Tests]," Journal of Economic Surveys, Wiley Blackwell, vol. 13(2), pages i, April.
  7. Anderson, Heather M. & Victor Issler, Joao & Vahid, Farshid, 2006. "Common features," Journal of Econometrics, Elsevier, vol. 132(1), pages 1-5, May.
  8. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543, March.
  9. Ericsson, Neil R, 1993. "Testing for Common Features: Comment," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 380-83, October.
  10. Terasvirta, Timo & Tjostheim, Dag & Granger, Clive W. J., 2010. "Modelling Nonlinear Economic Time Series," OUP Catalogue, Oxford University Press, number 9780199587155, March.
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