This paper investigates Hidden Markov Models (HMMs) in which the observations are generated from an autoregressive (AR) model. The overall model performs nonstationary spectral analysis and automatically segments a time series into discrete dynamic regimes. Because learning in HMMs is sensitive to initial conditions, we initialize the HMM model with parameters derived from a cluster analysis of Kalman filter coefficients. An important aspect of the Kalman filter implementation is that the state noise is estimated on-line. This allows for an initial estimation of AR parameters for each of the different dynamic regimes. These estimates are then fine-tuned with the HMM model. The method is demonstrated on a number of synthetic problems and on electroencephalogram data.
- Markov Chains
- Statistical Models
- Computer-Assisted Signal Processing