BAYESIAN-APPROACH TO PARAMETER-ESTIMATION AND INTERPOLATION OF TIME-VARYING AUTOREGRESSIVE PROCESSES USING THE GIBBS SAMPLER

A nonstationary time series is one in which the statistics of the proc ess are a function of time; this time dependency makes it impossible t o utilise standard analytically defined statistical estimators to para meterise the process. To overcome this difficulty, the time series is considered within a finite time interval and is modelled as a time-var ying autoregressive (AR) process. The AR coefficients that characteris e this process are functions of time, represented by a family of basis vectors. The corresponding basis coefficients are invariant over the time window and have stationary statistical properties. A method is de scribed for applying a Markov Chain Monte Carlo method known as the Gi bbs sampler to the problem of estimating the parameters of such a time -varying autoregressive (TVAR) model, whose time dependent coefficient s are modelled by basis functions. The Gibbs sampling scheme is then e xtended to include a stage which may be used for interpolation. Result s on synthetic and real audio signals show that the model is flexible, and that a Gibbs sampling framework is a reasonable scheme for estima ting and characterising a time-varying AR process.