Summary
The paper analyses univariate autoregressive AR(p) models with tightness prior. The framework of the model is the conjugate normal linear model where the prior distribution is assumed to be a random walk process. The deviation from the prior distribution is measured by the tightness (hyper-) parameter λ. It is shown how the estimation of the starting values can be incorporated into the Gibbs sampling scheme. We demonstrate this approach with simulated and economic time series. It is found that for typical economic sample size the sampling fluctuations influence the posterior distribution considerably and informative prior distributions seem to be useful, especially for prediction.
Keywords
- Posterior Distribution
- Prior Distribution
- Gibbs Sampler
- Random Walk Process
- Full Conditional Distribution
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Chib S. (1993): Bayes regression with autoregressive errors: A Gibbs sampling approach. Journal of Econometrics, 58, 275–294.
Gelfand A.E., Smith A.F.M. (1990): Sampling based approaches to calculating marginal densities. Journal of American Statistcal Association, 85, 398–409.
Littermann R.B. (1986): A statistical approach to economic forecasting. Journal of Business and Economic Statistics, 4, 1–24..
Marriott J., Ravishanker N., Gelfand A.E., Pai J. (1992): Bayesian analysis of ARMA processes: Complete sampling based inference under full likelihood, mimeo, University of Connecticut.
Polasek W. (1993): Gibbs sampling in VAR models with tightness priors, mimeo, University of Basel.
Polasek W. (1994): Gibbs sampling in B-VAR models with latent variables. WWZ-discussion papers Nr. 9415, University of Basel.
Shiller R.J. (1973): A distributed lag estimator derived from smoothness priors. Econometrica, 41, 775–788
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin · Heidelberg
About this paper
Cite this paper
Polasek, W., Jin, S. (1996). Gibbs Sampling in AR Models with Random Walk Priors. In: Gaul, W., Pfeifer, D. (eds) From Data to Knowledge. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79999-0_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-79999-0_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60354-2
Online ISBN: 978-3-642-79999-0
eBook Packages: Springer Book Archive