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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

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Paper provided by Econometric Society in its series Econometric Society 2004 North American Winter Meetings with number 145.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nawm04:145
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  1. Olivier Jean Blanchard & Danny Quah, 1988. "The Dynamic Effects of Aggregate Demand and Supply Disturbances," NBER Working Papers 2737, National Bureau of Economic Research, Inc.
  2. 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.).
  3. 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.
  4. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037, June.
  5. 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.
  6. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, vol. 18(1), pages 49-75, July.
  7. Bruce E. Hansen, 1996. "Sample Splitting and Threshold Estimation," Boston College Working Papers in Economics 319., Boston College Department of Economics, revised 12 May 1998.
  8. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-30, March.
  9. Potter, Simon M., 2000. "Nonlinear impulse response functions," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1425-1446, September.
  10. Elwood, S. Kirk, 1998. "Is the persistence of shocks to output asymmetric?," Journal of Monetary Economics, Elsevier, vol. 41(2), pages 411-426, April.
  11. Marc Hallin, 1980. "Invertibility and generalized invertibility of time-series models," ULB Institutional Repository 2013/1991, ULB -- Universite Libre de Bruxelles.
  12. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation for Research in Economics, Yale University.
  13. 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.
  14. Granger, C. W. J. & Andersen, Allan, 1978. "On the invertibility of time series models," Stochastic Processes and their Applications, Elsevier, vol. 8(1), pages 87-92, November.
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