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Level Shifts and the Illusion of Long Memory in Economic Time Series

  • Smith, Aaron D.

When applied to time series processes containing occasional level shifts, the logperiodogram (GPH) estimator often erroneously finds long memory. For a stationary short-memory process with a slowly varying level, I show that the GPH estimator is substantially biased, and I derive an approximation to this bias. The asymptotic bias lies on the (0,1) interval, and its exact value depends on the ratio of the expected number of level shifts to a user-defined bandwidth parameter. Using this result, I formulate the Modified GPH estimator, which has a markedly lower bias. I illustrate this new estimator via applications to soybean prices and stock market volatility.

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File URL: http://purl.umn.edu/11974
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Paper provided by University of California, Davis, Department of Agricultural and Resource Economics in its series Working Papers with number 11974.

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Date of creation: 2004
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Handle: RePEc:ags:ucdavw:11974
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Web page: http://www.agecon.ucdavis.edu/

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  1. Allan Timmermann, 1998. "Structural Breaks, Incomplete Information and Stock Prices," FMG Discussion Papers dp311, Financial Markets Group.
  2. Hidalgo, Javier & Robinson, Peter M., 1996. "Testing for structural change in a long-memory environment," Journal of Econometrics, Elsevier, vol. 70(1), pages 159-174, January.
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  4. Francis X. Diebold & Atsushi Inoue, 2000. "Long Memory and Regime Switching," NBER Technical Working Papers 0264, National Bureau of Economic Research, Inc.
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  6. Deo, Rohit S. & Hurvich, Clifford M., 2001. "On The Log Periodogram Regression Estimator Of The Memory Parameter In Long Memory Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 17(04), pages 686-710, August.
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  8. Robert F. Engle & Aaron D. Smith, 1999. "Stochastic Permanent Breaks," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 553-574, November.
  9. Granger, Clive W.J. & Hyung, Namwon, 1999. "Occasional Structural Breaks and Long Memory," University of California at San Diego, Economics Working Paper Series qt4d60t4jh, Department of Economics, UC San Diego.
  10. Andrew J. Filardo & Stephen F. Gordon, 1993. "Business cycle durations," Research Working Paper 93-11, Federal Reserve Bank of Kansas City.
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  12. Liu, Ming, 2000. "Modeling long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 99(1), pages 139-171, November.
  13. Chen, Chung & Tiao, George C, 1990. "Random Level-Shift Time Series Models, ARIMA Approximations, and Level-Shift Detection," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 83-97, January.
  14. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
  15. 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 357-84, March.
  16. Chib, Siddhartha, 1998. "Estimation and comparison of multiple change-point models," Journal of Econometrics, Elsevier, vol. 86(2), pages 221-241, June.
  17. Cavanagh, Christopher L. & Elliott, Graham & Stock, James H., 1995. "Inference in Models with Nearly Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1131-1147, October.
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