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Conditional heteroskedasticity in qualitative response models of time series: a Gibbs sampling approach to the bank prime rate

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  • Michael J. Dueker

Abstract

Previous time series applications of qualitative response models have ignored features of the data, such as conditional heteroskedasticity, that are routinely addressed in time-series econometrics of financial data. This article addresses this issue by adding Markov-switching heteroskedasticity to a dynamic ordered probit model of discrete changes in the bank prime lending rate and estimation via the Gibbs sampler. The dynamic ordered probit model of Eichengreen, Watson and Grossman (1995) allows for serial autocorrelation in probit analysis of a time series, and the present article demonstrates the relative simplicity of estimating a dynamic ordered probit using the Gibbs sampler instead of the Eichengreen et al. maximum-likelihood procedure. In addition, the extension to regime-switching parameters and conditional heteroskedasticity is easy to implement under Gibbs sampling. The article compares tests of goodness of fit between dynamic ordered probit models of the prime rate that have constant variance and conditional heteroskedasticity.

Suggested Citation

  • Michael J. Dueker, 1998. "Conditional heteroskedasticity in qualitative response models of time series: a Gibbs sampling approach to the bank prime rate," Working Papers 1998-011, Federal Reserve Bank of St. Louis.
  • Handle: RePEc:fip:fedlwp:1998-011
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    1. Bernard, Henri & Gerlach, Stefan, 1998. "Does the Term Structure Predict Recessions? The International Evidence," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 3(3), pages 195-215, July.
    2. Hausman, Jerry A. & Lo, Andrew W. & MacKinlay, A. Craig, 1992. "An ordered probit analysis of transaction stock prices," Journal of Financial Economics, Elsevier, vol. 31(3), pages 319-379, June.
    3. James D. Hamilton & Oscar Jorda, 2002. "A Model of the Federal Funds Rate Target," Journal of Political Economy, University of Chicago Press, vol. 110(5), pages 1135-1167, October.
    4. Estrella, Arturo & Mishkin, Frederic S., 1997. "The predictive power of the term structure of interest rates in Europe and the United States: Implications for the European Central Bank," European Economic Review, Elsevier, vol. 41(7), pages 1375-1401, July.
    5. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
    6. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    7. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    8. Eichengreen, Barry & Watson, Mark W & Grossman, Richard S, 1985. "Bank Rate Policy under the Interwar Gold Standard: A Dynamic Probit Model," Economic Journal, Royal Economic Society, vol. 95(379), pages 725-745, September.
    9. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Keywords

    Prime rate ; Econometric models;

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