Efficient estimation of parameters for non-Gaussian autoregressive processes

Modified Maximum Likelihood Estimation in First-Order Autoregressive Moving Average Models with some Non-Normal Residuals

When modeling time series data using autoregressive-moving average processes, it is a common practice to presume that the residuals are normally distributed. However, sometimes we encounter non-normal residuals and asymmetry of data marginal distribution. Despite widespread use of pure autoregressive processes for modeling non-normal time series, the autoregressive-moving average models have le...

Sequential Parameter Estimation of Time-Varying Non-Gaussian Autoregressive Processes

Parameter estimation of time-varying non-Gaussian autoregressive processes can be a highly nonlinear problem. The problem gets even more difficult if the functional form of the time variation of the process parameters is unknown. In this paper, we address parameter estimation of such processes by particle filtering, where posterior densities are approximated by sets of samples (particles) and p...

Singular Value Decomposition-Based ARMA Model Parameter Estimation of Non-Gaussian Processes

Autoregressive moving average (ARMA) modeling has been used in many fields. This paper presents an approach to time series analysis of a general ARMA model parameters estimation. The proposed technique is based on the singular value decomposition (SVD) of a covariance matrix of a third order cumulants from only the output sequence. The observed data sequence is corrupted by additive Gaussian no...

Autoregressive Gaussian Random Vectors of First Order

Parameter estimation for non-Gaussian autoregressive processes

It is proposed to jointly estimate the parameters of nonGaussian autoregressive (AR) processes in a Bayesian context using the Gibbs sampler. Using the Markov chains produced by the sampler an approximation to the vector MAP estimator is implemented. The results reported here used AR(4) models driven by noise sequences where each sample is iid as a two component Gaussian sum mixture. The result...