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Introduction to M-M Processes

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  • Granger, Clive W.J.
  • Hyung, Namwon

Abstract

This paper introduces a new type of nonlinear model, the min-max model, and analyzes the properties for a pair of series. Stability conditions of this system are given for the nonlinearly integrated bivariate series. Under these stability conditions, the difference of the two series has a threshold-type nonlinearity. One can construct a threshold error correction model from min-max processes. Neglected nonlinearity tests are applied, to the univariate series and to the system, to detect nonlinearity, and it turns out that the tests using the system have better power. We apply the min-max model to U.S. Treasury bill and commercial paper interest rates. The spread of these interest rates shows a threshold-type nonlinearity, and this model outperforms a linear model in terms of its predictability out-of-sample

Suggested Citation

  • Granger, Clive W.J. & Hyung, Namwon, 1998. "Introduction to M-M Processes," University of California at San Diego, Economics Working Paper Series qt9pk546xs, Department of Economics, UC San Diego.
    • Handle: RePEc:cdl:ucsdec:qt9pk546xs
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    References listed on IDEAS

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    1. Balke, Nathan S & Fomby, Thomas B, 1997. "Threshold Cointegration," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(3), pages 627-645, August.
    2. Corradi, Valentina & Swanson, Norman R. & White, Halbert, 2000. "Testing for stationarity-ergodicity and for comovements between nonlinear discrete time Markov processes," Journal of Econometrics, Elsevier, vol. 96(1), pages 39-73, May.
    3. Benjamin M. Friedman & Kenneth Kuttner, 1993. "Why Does the Paper-Bill Spread Predict Real Economic Activity?," NBER Chapters, in: Business Cycles, Indicators, and Forecasting, pages 213-254, National Bureau of Economic Research, Inc.
    4. Granger, C. W. J. & Newbold, Paul, 1986. "Forecasting Economic Time Series," Elsevier Monographs, Elsevier, edition 2, number 9780122951831 edited by Shell, Karl.
    5. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    6. Christina D. Romer & David H. Romer, 1990. "New Evidence on the Monetary Transmission Mechanism," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 21(1), pages 149-214.
    7. Lee, Tae-Hwy & White, Halbert & Granger, Clive W. J., 1993. "Testing for neglected nonlinearity in time series models : A comparison of neural network methods and alternative tests," Journal of Econometrics, Elsevier, vol. 56(3), pages 269-290, April.
    8. James H. Stock & Mark W. Watson, 1993. "Business Cycles, Indicators, and Forecasting," NBER Books, National Bureau of Economic Research, Inc, number stoc93-1.
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    Cited by:

    1. Granger Clive W.J., 2008. "Non-Linear Models: Where Do We Go Next - Time Varying Parameter Models?," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(3), pages 1-11, September.
    2. Lee, O. & Shin, D.W., 2007. "A note on geometric ergodicity of a multiple threshold AR(1) processes on the boundary region with application to integrated m-m processes," Economics Letters, Elsevier, vol. 96(2), pages 226-231, August.

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