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Nonstationary Discrete Choice

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Abstract

This paper develops an asymptotic theory for time series discrete choice models with explanatory variables generated as integrated processes and with multiple choices and threshold parameters determining the choices. The theory extends recent work by Park and Phillips (2000) on binary choice models. As in this earlier work, the maximum likelihood (ML) estimator is consistent and has a limit theory with multiple rates of convergence (n^{3/4} and n^{1/4}) and mixture normal distributions where the mixing variates depend on Brownian local time as well as Brownian motion. An extended arc sine limit law is given for the sample proportions of the various choices. The new limit law exhibits a wider range of potential behavior that depends on the values taken by the threshold parameters.

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File URL: http://cowles.econ.yale.edu/P/cd/d13b/d1364.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1364.

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Length: 37 pages
Date of creation: May 2002
Date of revision:
Publication status: Published in Journal of Econometrics (2004), 120(1): 103-138
Handle: RePEc:cwl:cwldpp:1364

Note: CFP 1103.
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Brownian motion; Brownian local time; Discrete choice model; Dual convergence rates; Extended arc sine laws; Integrated time series; Maximum likelihood estimation; Threshold parameters;

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References

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  1. Peter C.B. Phillips, 1998. "Econometric Analysis of Fisher's Equation," Cowles Foundation Discussion Papers 1180, Cowles Foundation for Research in Economics, Yale University.
  2. Joon Y. Park & Peter C. B. Phillips, 1999. "Nonstationary Binary Choice," Working Paper Series no5, Institute of Economic Research, Seoul National University.
  3. Ling Hu & Peter C.B. Phillips, 2002. "Nonstationary Discrete Choice," Cowles Foundation Discussion Papers 1364, Cowles Foundation for Research in Economics, Yale University.
  4. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-61, January.
  5. Graciela Kaminsky & Saul Lizondo & Carmen M. Reinhart, 1998. "Leading Indicators of Currency Crises," IMF Staff Papers, Palgrave Macmillan, vol. 45(1), pages 1-48, March.
  6. Ling Hu & Peter C.B. Phillips, 2002. "Dynamics of the Federal Funds Target Rate: A Nonstationary Discrete Choice Approach," Cowles Foundation Discussion Papers 1365, Cowles Foundation for Research in Economics, Yale University.
  7. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation for Research in Economics, Yale University.
  8. Peter C.B. Phillips & Joon Y. Park, 1998. "Asymptotics for Nonlinear Transformations of Integrated Time Series," Cowles Foundation Discussion Papers 1182, Cowles Foundation for Research in Economics, Yale University.
  9. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
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Citations

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Cited by:
  1. Peter C.B.Phillips & Yangru Wu & Jun Yu, 2009. "Explosive Behavior in the 1990s Nasdaq: When Did Exuberance Escalate Asset Values?," Working Papers CoFie-03-2008, Sim Kee Boon Institute for Financial Economics.
  2. Peter C.B. Phillips & Sainan Jin & Ling Hu, 2005. "Nonstationary Discrete Choice: A Corrigendum and Addendum," Cowles Foundation Discussion Papers 1516, Cowles Foundation for Research in Economics, Yale University.
  3. David-Jan Jansen & Jakob de Haan, 2006. "Does ECB Communication Help in Predicting its Interest Rate Decisions?," CESifo Working Paper Series 1804, CESifo Group Munich.
  4. Dong He & Laurent L. Pauwels, 2008. "What Prompts the People's Bank of China to Change Its Monetary Policy Stance? Evidence from a Discrete Choice Model," China & World Economy, Institute of World Economics and Politics, Chinese Academy of Social Sciences, vol. 16(6), pages 1-21.
  5. Ling Hu & Peter C.B. Phillips, 2002. "Nonstationary Discrete Choice," Cowles Foundation Discussion Papers 1364, Cowles Foundation for Research in Economics, Yale University.
  6. John B. Carlson & Ben R. Craig & William R. Melick, 2005. "Recovering market expectations of FOMC rate changes with options on federal funds futures," Working Paper 0507, Federal Reserve Bank of Cleveland.
  7. Vadim Marmer, 2005. "Nonlinearity, Nonstationarity and Spurious Forecasts," Econometrics 0503002, EconWPA, revised 15 Dec 2005.
  8. Hyeongwoo Kim, 2014. "Estimating Interest Rate Setting Behavior in Korea: An Ordered Probit Model Approach," Auburn Economics Working Paper Series auwp2014-02, Department of Economics, Auburn University.
  9. Helmut Herwartz & Konstantin A. Kholodilin, 2011. "In-Sample and Out-of-Sample Prediction of Stock Market Bubbles: Cross-Sectional Evidence," Discussion Papers of DIW Berlin 1173, DIW Berlin, German Institute for Economic Research.
  10. Wang, Qiying & Phillips, Peter C.B., 2009. "Asymptotic Theory For Local Time Density Estimation And Nonparametric Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 25(03), pages 710-738, June.
  11. de Jong, Robert & Hu, Ling, 2011. "A note on nonlinear models with integrated regressors and convergence order results," Economics Letters, Elsevier, vol. 111(1), pages 23-25, April.
  12. Ling Hu & Peter C.B. Phillips, 2002. "Dynamics of the Federal Funds Target Rate: A Nonstationary Discrete Choice Approach," Cowles Foundation Discussion Papers 1365, Cowles Foundation for Research in Economics, Yale University.
  13. Chiara Scotti, 2006. "A bivariate model of Fed and ECB main policy rates," International Finance Discussion Papers 875, Board of Governors of the Federal Reserve System (U.S.).

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