Bayesian Lattice Filters for Time-Varying Autoregression and Time–Frequency Analysis

Monitoring Time-Varying Parameters in an Autoregression

On Bayesian analysis of non-linear continuous-time autoregression models

This paper introduces a method for performing fully Bayesian inference for non-linear conditional autoregressive continuous-time models, based on a finite skeleton of observations. Our approach uses MCMC and involves imputing data from times at which observations are not made. It uses a reparameterisation technique for the missing data, and due to the non-Markovian nature of the models, it is n...

Robust relative stability of time-invariant and time-varying lattice filters

We consider the relative stability of time-invariant and time-varying unnormalized lattice filters. First, we consider a set of lattice filters whose reflection parameters i obey j ij i and provide necessary and sufficient conditions on the i that guarantee that each time-invariant lattice in the set has poles inside a circle of prescribed radius 1= < 1, i.e., is relatively stable with degree o...

Time-Varying Filters for Musical Applications

A variety of methods are available for implementing time-varying digital filters for musical applications. The considerations for musical applications differ from those of other applications, such as speech coding. This domain requires realtime parametric control of a filter such as an equalizer, allowing parameters to vary each sample, e.g. by user interaction, a low-frequency oscillator (LFO)...

Mode Identification of Volatility in Time-varying Autoregression

In many applications, time series exhibit non-stationary behavior that might reasonably be modeled as a time-varying autoregressive process. In the context of such a model, we discuss the problem of testing for modality of the variance function. We propose a test of modality which is local, and which when used iteratively, can be used to identify the total number of modes in a given series. Thi...