Wavelet improvement in turning point detection using a Hidden Markov Model

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.