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Bayesian time series regression with nonparametric modeling of autocorrelation

Title
Bayesian time series regression with nonparametric modeling of autocorrelation
Author
김건호
Keywords
Autocorrelation function; Whittle likelihood; Bayesian framework; Gaussian process prior
Issue Date
2018-11
Publisher
SPRINGER HEIDELBERG
Citation
COMPUTATIONAL STATISTICS, v. 33, no. 4, page. 1715-1731
Abstract
Series models have several functions: comprehending the functional dependence of variable of interest on covariates, forecasting the dependent variable for future values of covariates and estimating variance disintegration, co-integration and steady-state relations. Although the regression function in a time series model has been extensively modeled both parametrically and nonparametrically, modeling of the error autocorrelation is mainly restricted to the parametric setup. A proper modeling of autocorrelation not only helps to reduce the bias in regression function estimate, but also enriches forecasting via a better forecast of the error term. In this article, we present a nonparametric modeling of autocorrelation function under a Bayesian framework. Moving into the frequency domain from the time domain, we introduce a Gaussian process prior to the log of the spectral density, which is then updated by using a Whittle approximation for the likelihood function (Whittle likelihood). The posterior computation is simplified due to the fact that Whittle likelihood is approximated by the likelihood of a normal mixture distribution with log-spectral density as a location shift parameter, where the mixture is of only five components with known means, variances, and mixture probabilities. The problem then becomes conjugate conditional on the mixture components, and a Gibbs sampler is used to initiate the unknown mixture components as latent variables. We present a simulation study for performance comparison, and apply our method to the two real data examples.
URI
https://link.springer.com/article/10.1007%2Fs00180-018-0796-9https://repository.hanyang.ac.kr/handle/20.500.11754/120755
ISSN
0943-4062; 1613-9658
DOI
10.1007/s00180-018-0796-9
Appears in Collections:
COLLEGE OF ECONOMICS AND FINANCE[S](경제금융대학) > ECONOMICS & FINANCE(경제금융학부) > Articles
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