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Testing Common Nonlinear Features in Nonlinear Vector Autoregressive Models

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  • Li, Dao

    ()
    (School of Technology and Business Studies)

  • He, Changli

    ()
    (School of Technology and Business Studies)

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    Abstract

    This paper studies a special class of vector smooth-transition autoregressive (VS- TAR) models containing common nonlinear features (CNFs). To test the existence of CNFs in a VSTAR model, a triangular representation for such a system containing CNFs is proposed. A procedure of testing CNFs in a VSTAR model is consisting of two steps: rst, test unit root in a STAR model against a stable STAR process for each individual time series; secondly, examine if nonlinear features are common in the system by a La- grange Multiplier (LM) test when the null of unit root is rejected in the rst step. The asymptotic distribution of the LM test is derived. Simulation studies of both unit root test and LM test have been carried out to investigate the nite sample properties. In the empirical application, the procedure of testing CNFs is illustrated by analyzing the monthly growth of consumption and income data of United States (1985:1 to 2011:11). The consumption and income system contains CNFs, and an estimated common nonlin- ear factor in VSTAR model is suggested.

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    Bibliographic Info

    Paper provided by Örebro University, School of Business in its series Working Papers with number 2012:7.

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    Length: 39 pages
    Date of creation: 13 Feb 2012
    Date of revision:
    Handle: RePEc:hhs:oruesi:2012_007

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    Postal: Örebro University School of Business, SE - 701 82 ÖREBRO, Sweden
    Phone: 019-30 30 00
    Fax: 019-33 25 46
    Web page: http://www.oru.se/Institutioner/Handelshogskolan-vid-Orebro-universitet/
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    Keywords: Vector STAR models; Common features; Lagrange Multiplier test;

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    1. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 393-95, October.
    2. Changli He & Rickard Sandberg, 2006. "Dickey-Fuller Type of Tests against Nonlinear Dynamic Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 835-861, December.
    3. Changli He & Timo Terasvirta & Andres Gonzalez, 2009. "Testing Parameter Constancy in Stationary Vector Autoregressive Models Against Continuous Change," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 225-245.
    4. 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.
    5. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, September.
    6. James H. Stock & Mark W. Watson, 1991. "A simple estimator of cointegrating vectors in higher order integrated systems," Working Paper Series, Macroeconomic Issues 91-3, Federal Reserve Bank of Chicago.
    7. Eitrheim, Øyvind & Teräsvirta, Timo, 1995. "Testing the Adequacy of Smooth Transition Autoregressive Models," Working Paper Series in Economics and Finance 56, Stockholm School of Economics.
    8. Lin, Chien-Fu Jeff & Terasvirta, Timo, 1994. "Testing the constancy of regression parameters against continuous structural change," Journal of Econometrics, Elsevier, vol. 62(2), pages 211-228, June.
    9. Granger, C W J & Swanson, Norman, 1996. "Future Developments in the Study of Cointegrated Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(3), pages 537-53, August.
    10. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 369-80, October.
    11. Perron, P., 1989. "Testing For A Unit Root In A Time Series With A Changing Mean," Papers 347, Princeton, Department of Economics - Econometric Research Program.
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