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Wavelet improvement in turning point detection using a hidden Markov model: from the aspects of cyclical identification and outlier correction

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  • Yushu Li
  • Simon Reese

Abstract

The hidden Markov model (HMM) has been widely used in regime classification and turning point detection for econometric series after the decisive paper by Hamilton (Econometrica 57(2):357–384, 1989 ). The present paper will show that when using HMM to detect the turning point in cyclical series, the accuracy of the detection will be influenced when the data are exposed to high volatilities or combine multiple types of cycles that have different frequency bands. Moreover, outliers will be frequently misidentified as turning points. The present paper shows that these issues can be resolved by wavelet multi-resolution analysis based methods. By providing both frequency and time resolutions, the wavelet power spectrum can identify the process dynamics at various resolution levels. We apply a Monte Carlo experiment to show that the detection accuracy of HMMs is highly improved when combined with the wavelet approach. Further simulations demonstrate the excellent accuracy of this improved HMM method relative to another two change point detection algorithms. Two empirical examples illustrate how the wavelet method can be applied to improve turning point detection in practice. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Yushu Li & Simon Reese, 2014. "Wavelet improvement in turning point detection using a hidden Markov model: from the aspects of cyclical identification and outlier correction," Computational Statistics, Springer, vol. 29(6), pages 1481-1496, December.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:6:p:1481-1496
    DOI: 10.1007/s00180-014-0502-5
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    References listed on IDEAS

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    1. 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.
    2. Hamilton, James D & Perez-Quiros, Gabriel, 1996. "What Do the Leading Indicators Lead?," The Journal of Business, University of Chicago Press, vol. 69(1), pages 27-49, January.
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    5. James H. Stock & Mark W. Watson, 1989. "New Indexes of Coincident and Leading Economic Indicators," NBER Chapters, in: NBER Macroeconomics Annual 1989, Volume 4, pages 351-409, National Bureau of Economic Research, Inc.
    6. Leroux, Brian G., 1992. "Maximum-likelihood estimation for hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 127-143, February.
    7. Arthur F. Burns & Wesley C. Mitchell, 1946. "Measuring Business Cycles," NBER Books, National Bureau of Economic Research, Inc, number burn46-1.
    8. Benoit Bellone & David Saint-Martin, 2004. "Detecting Turning Points with Many Predictors through Hidden Markov Models," Econometrics 0407001, University Library of Munich, Germany.
    9. Layton, Allan P., 1996. "Dating and predicting phase changes in the U.S. business cycle," International Journal of Forecasting, Elsevier, vol. 12(3), pages 417-428, September.
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    1. Bjørn Gunnar Hansen & Yushu Li, 2017. "An Analysis of Past World Market Prices of Feed and Milk and Predictions for the Future," Agribusiness, John Wiley & Sons, Ltd., vol. 33(2), pages 175-193, April.

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