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A Simple Test for Unit Root Bilinearity

Author

Listed:
  • Wojciech Charemza
  • Mikhail Lifshits

    (St. Petersburg State University)

  • Svetlana Makarova

Abstract

The paper introduces a t-ratio type test for detecting bilinearity in a stochastic unit root process. It appears that such process is a realistic approximation for many economic and financial time series. It is shown that, under the null of no bilinearity, the tests statistics are asymptotically normally distributed. Proofs of this asymptotic normality requires the Gihman and Skorohod theory for multivariate diffusion processes. Finite sample results describe speed of convergence, power of the tests and possible distortions to unit root testing which might appear due to the presence of bilinearity. It is concluded that the two-step testing procedure suggested here (the first step for the linear unit root and the second step for its bilinearity) is consistent in the sense that the size of step one test is not affected by the possible detection of bilinearity at step two.

Suggested Citation

  • Wojciech Charemza & Mikhail Lifshits & Svetlana Makarova, 2002. "A Simple Test for Unit Root Bilinearity," EUSP Department of Economics Working Paper Series 2002/01, European University at St. Petersburg, Department of Economics, revised 29 Mar 2002.
    • Handle: RePEc:eus:wpaper:ec2002_01
    Note: Paper submitted to 57th Econometric Society European Meeting, February 2002, http://www.eea-esem.com/papers/eea-esem/esem2002/617/Bilinear.pdf
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    References listed on IDEAS

    as
    1. Peel, David & Davidson, James, 1998. "A non-linear error correction mechanism based on the bilinear model1," Economics Letters, Elsevier, vol. 58(2), pages 165-170, February.
    2. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    3. T. Grahn, 1995. "A Conditional Least Squares Approach To Bilinear Time Series Estimation," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(5), pages 509-529, September.
    4. Ikeda, Shinsuke & Shibata, Akihisa, 1992. "Fundamentals-dependent bubbles in stock prices," Journal of Monetary Economics, Elsevier, vol. 30(1), pages 143-168, October.
    5. Granger, Clive W. J. & Swanson, Norman R., 1997. "An introduction to stochastic unit-root processes," Journal of Econometrics, Elsevier, vol. 80(1), pages 35-62, September.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    time-series econometrics; testing; nonstationary bilinear processes;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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