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Stochastic and deterministic unit root models: problem of dominance


  • Svetlana Makarova
  • Wojciech Charemza


The paper considers the question of dominance, in the context of financial markets, of the deterministic unit root processes with a structural break by the bilinear unit root model without such break or vice versa. In the deterministic unit root process breaks are usually interpreted as exogenous, while the unit root bilinearity is mostly attributed to speculation. A series of Monte Carlo experiments show substantial size distortions in testing for the deterministic unit root process in the presence of unit root bilinearity and vice versa. To eliminate this problem, two additional tests are proposed here: one for the joint testing of the process with a structural break and unit root bilinearity, and the other for testing the unit root bilinearity conditional on the break. The asymptotic properties of these tests have been analysed. The tests are applied for the daily stock price indices for 63 countries, for the period 1992-2005. It has been found out that in 34 cases the bilinearity is present in the series, and in only two cases a structural break was discovered without the presence of bilinearity. Since for most of the series a possible break occurs either in 2000 or 2001, it sheds some new light on the reasons for the stock market breakdown at the beginning of the 21st century.

Suggested Citation

  • Svetlana Makarova & Wojciech Charemza, 2005. "Stochastic and deterministic unit root models: problem of dominance," Computing in Economics and Finance 2005 190, Society for Computational Economics.
  • Handle: RePEc:sce:scecf5:190

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    References listed on IDEAS

    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    4. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    5. Geske, Robert & Johnson, Herb E, 1984. " The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-1524, December.
    6. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
    7. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-1250.
    8. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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    Blog mentions

    As found by, the blog aggregator for Economics research:
    1. Wojciech Charemza
      by Metablog Obserwatora Finansowego in Obserwator Finansowy on 2009-12-10 17:59:58

    More about this item


    REGULAR Unit root bilinearity; nonlinear time series models; structural breaks;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets


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