MARKOV CHAINMONTE CARLO ESTIMATION FOR THE SEASONAL AUTOREGRESSIVE PROCESS WITH APPLICATION TO PITCHMODELLING
Many time series exhibit long term dependencies that cannot accurately be accounted for by standard autoregressive (AR) type models, unless the model order is chosen to match the frequency of these correlations. One such example is the glottal excita-tion waveform, which comprises of highly correlated pulses, separated by the pitch period. Increasing the AR order leads to models that are less parsimonious than required by the data, and subsequent poor generalisation. Often improved modelling accuracy can be achieved by altering the structure of the model to better account for the longer term effects. The seasonal AR process is one such model, and results from a simple extension to the standard AR process. This report considers the application of the seasonal AR process to modelling the glottal waveform. The parameter estimation problem is stated within a Bayesian framework, leading to analytically intractable in-tegrals. These integrals are elegantly approximated by Markov chain Monte Carlo (MCMC) sampling strategies. Results are presented for both synthetic and real data sets.