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Wavelet Improvement in Turning Point Detection using a Hidden Markov Model

Author

Listed:
  • Li, Yushu

    () (Department of Business and Management Science, Norwegian School of Economics)

  • Reese, Simon

    () (Department of Economics, Lund University)

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 (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.

Suggested Citation

  • Li, Yushu & Reese, Simon, 2012. "Wavelet Improvement in Turning Point Detection using a Hidden Markov Model," Working Papers 2012:14, Lund University, Department of Economics, revised 05 Apr 2014.
    • Handle: RePEc:hhs:lunewp:2012_014
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    References listed on IDEAS

    as
    1. Arthur F. Burns & Wesley C. Mitchell, 1946. "Measuring Business Cycles," NBER Books, National Bureau of Economic Research, Inc, number burn46-1, January.
    2. 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.
    3. 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.
    4. Benoit Bellone & David Saint-Martin, 2004. "Detecting Turning Points with Many Predictors through Hidden Markov Models," Econometrics 0407001, EconWPA.
    5. Grané, Aurea & Veiga, Helena, 2009. "Wavelet-based detection of outliers in volatility models," DES - Working Papers. Statistics and Econometrics. WS ws090403, Universidad Carlos III de Madrid. Departamento de Estadística.
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    More about this item

    Keywords

    HMM; turning point; wavelet; outlier;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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