Parameter estimation for non-Gaussian autoregressive processes
نویسندگان
چکیده
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 results indicate that using the Gibbs sampler to approximate the vector MAP estimator provides estimates with precision that compares favorably with the CRLBs. Also briefly discussed are issues regarding the implementation of the Gibbs sampler for AR mixture models.
منابع مشابه
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...
متن کاملNon-Gaussian Autoregressive Processes with Tukey g-and-h Transformations
When performing a time series analysis of continuous data, for example from climate or environmental problems, the assumption that the process is Gaussian is often violated. Therefore, we introduce two non-Gaussian autoregressive time series models that are able to fit skewed and heavy-tailed time series data. Our two models are based on the Tukey g-and-h transformation. We discuss parameter es...
متن کاملSingular 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...
متن کاملParameter estimation for autoregressive Gaussian-mixture processes: the EMAX algorithm
The problem of estimating parameters of discrete-time non-Gaussian autoregressive (AR) processes is addressed. The subclass of such processes considered is restricted to those whose driving noise samples are statistically independent and identically distributed according to a Gaussian-mixture probability density function (pdf). Because the likelihood function for this problem is typically unbou...
متن کاملModified 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...
متن کامل