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A Simple Test for Unit Root Bilinearity


  • Wojciech Charemza
  • Mikhail Lifshits

    (St. Petersburg State University)

  • Svetlana Makarova


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 Ec-01/02, European University at St. Petersburg, Department of Economics, revised 29 Mar 2002.
  • Handle: RePEc:eus:wpaper:ec0102
    Note: Paper submitted to 57th Econometric Society European Meeting, February 2002,

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    References listed on IDEAS

    1. Charemza, Wojciech W. & Lifshits, Mikhail & Makarova, Svetlana, 2005. "Conditional testing for unit-root bilinearity in financial time series: some theoretical and empirical results," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 63-96, January.
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    More about this item


    time-series econometrics; testing; nonstationary bilinear processes;

    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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