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Threshold Integrated Moving Average Models (Does Size Matter? Maybe So)


  • Oscar Martin
  • Jesus Gonzalo


The aim of this paper is to identify permanent and transitory shocks. This identification is done according to the size of the shocks or the size of some other important economic variable. In order to be able to carry this identification scheme on, we introduce a new class of threshold models: threshold integrated moving average models (TIMA). These are integrated models with a threshold structure in the moving average part. In one of the regimes the moving average has a unit root and in the other an invertible one. The former regime corresponds to transitory shocks, while the latter corresponds to permanent shocks. The paper analyzes the impulse response function generated by TIMA models and their invertibility. Consistency and asymptotic normality of least squares estimators are established and hypothesis tests for TIMA models are developed. The paper concludes with an application to exchange rates and stock market prices

Suggested Citation

  • Oscar Martin & Jesus Gonzalo, 2004. "Threshold Integrated Moving Average Models (Does Size Matter? Maybe So)," Econometric Society 2004 North American Winter Meetings 145, Econometric Society.
  • Handle: RePEc:ecm:nawm04:145

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    References listed on IDEAS

    1. Blanchard, Olivier Jean & Quah, Danny, 1989. "The Dynamic Effects of Aggregate Demand and Supply Disturbances," American Economic Review, American Economic Association, vol. 79(4), pages 655-673, September.
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    3. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    4. Elwood, S. Kirk, 1998. "Is the persistence of shocks to output asymmetric?," Journal of Monetary Economics, Elsevier, vol. 41(2), pages 411-426, April.
    5. Jon Faust, 1998. "The robustness of identified VAR conclusions about money," International Finance Discussion Papers 610, Board of Governors of the Federal Reserve System (U.S.).
    6. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    7. Koop, Gary & Pesaran, M. Hashem & Potter, Simon M., 1996. "Impulse response analysis in nonlinear multivariate models," Journal of Econometrics, Elsevier, vol. 74(1), pages 119-147, September.
    8. Potter, Simon M., 2000. "Nonlinear impulse response functions," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1425-1446, September.
    9. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
    10. Faust, Jon, 1998. "The robustness of identified VAR conclusions about money," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 49(1), pages 207-244, December.
    11. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    12. Marc Hallin, 1980. "Invertibility and generalized invertibility of time-series models," ULB Institutional Repository 2013/1991, ULB -- Universite Libre de Bruxelles.
    13. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    14. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, vol. 18(1), pages 49-75, July.
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    Cited by:

    1. Gonzalo, Jesus & Martinez, Oscar, 2006. "Large shocks vs. small shocks. (Or does size matter? May be so.)," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 311-347.
    2. Catherine Bruneau & Amine Lahiani, 2006. "Estimation d'un modèle TIMA avec asymétrie contemporaine par inférence indirecte," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 142(IV), pages 479-500, December.
    3. González Gómez, Andrés, 2004. "A smooth permanent surge process," SSE/EFI Working Paper Series in Economics and Finance 572, Stockholm School of Economics.

    More about this item


    Asymmetries; Movong Average Models; Permanent Shock; Persistence; Threshold Models; Transitory Shock.;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation


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