# John Geweke

- 30 November 2007
- WORKING PAPER SERIES - No. 831Details
- Abstract
- With the aim of constructing predictive distributions for daily returns, we introduce a new Markov normal mixture model in which the components are themselves normal mixtures. We derive the restrictions on the autocovariances and linear representation of integer powers of the time series in terms of the number of components in the mixture and the roots of the Markov process. We use the model prior predictive distribution to study its implications for some interesting functions of returns. We apply the model to construct predictive distributions of daily S&P500; returns, dollarpound returns, and one- and ten-year bonds. We compare the performance of the model with ARCH and stochastic volatility models using predictive likelihoods. The model's performance is about the same as its competitors for the bond returns, better than its competitors for the S&P 500 returns, and much better for the dollar-pound returns. Validation exercises identify some potential improvements.
- JEL Code
**C53**: Mathematical and Quantitative Methods→Econometric Modeling→Forecasting and Prediction Methods, Simulation Methods**G12**: Financial Economics→General Financial Markets→Asset Pricing, Trading Volume, Bond Interest Rates**C11**: Mathematical and Quantitative Methods→Econometric and Statistical Methods and Methodology: General→Bayesian Analysis: General**C14**: Mathematical and Quantitative Methods→Econometric and Statistical Methods and Methodology: General→Semiparametric and Nonparametric Methods: General

- 26 November 2008
- WORKING PAPER SERIES - No. 969Details
- Abstract
- Bayesian inference in a time series model provides exact, out-of-sample predictive distributions that fully and coherently incorporate parameter uncertainty. This study compares and evaluates Bayesian predictive distributions from alternative models, using as an illustration five alternative models of asset returns applied to daily S&P 500 returns from 1976 through 2005. The comparison exercise uses predictive likelihoods and is inherently Bayesian. The evaluation exercise uses the probability integral transform and is inherently frequentist. The illustration shows that the two approaches can be complementary, each identifying strengths and weaknesses in models that are not evident using the other.
- JEL Code
**C11**: Mathematical and Quantitative Methods→Econometric and Statistical Methods and Methodology: General→Bayesian Analysis: General**C53**: Mathematical and Quantitative Methods→Econometric Modeling→Forecasting and Prediction Methods, Simulation Methods

- 3 March 2009
- WORKING PAPER SERIES - No. 1017Details
- Abstract
- A prediction model is any statement of a probability distribution for an outcome not yet observed. This study considers the properties of weighted linear combinations of n prediction models, or linear pools, evaluated using the conventional log predictive scoring rule. The log score is a concave function of the weights and, in general, an optimal linear combination will include several models with positive weights despite the fact that exactly one model has limiting posterior probability one. The paper derives several interesting formal results: for example, a prediction model with positive weight in a pool may have zero weight if some other models are deleted from that pool. The results are illustrated using S&P 500 returns with prediction models from the ARCH, stochastic volatility and Markov mixture families. In this example models that are clearly inferior by the usual scoring criteria have positive weights in optimal linear pools, and these pools substantially outperform their best components.
- JEL Code
**C11**: Mathematical and Quantitative Methods→Econometric and Statistical Methods and Methodology: General→Bayesian Analysis: General**C53**: Mathematical and Quantitative Methods→Econometric Modeling→Forecasting and Prediction Methods, Simulation Methods

- 20 December 2011
- WORKING PAPER SERIES - No. 1409Details
- Abstract
- This paper develops a multi-way analysis of variance for non-Gaussian multivariate distributions and provides a practical simulation algorithm to estimate the corresponding components of variance. It specifically addresses variance in Bayesian predictive distributions, showing that it may be decomposed into the sum of extrinsic variance, arising from posterior uncertainty about parameters, and intrinsic variance, which would exist even if parameters were known. Depending on the application at hand, further decomposition of extrinsic or intrinsic variance (or both) may be useful. The paper shows how to produce simulation-consistent estimates of all of these components, and the method demands little additional effort or computing time beyond that already invested in the posterior simulator. It illustrates the methods using a dynamic stochastic general equilibrium model of the US economy, both before and during the global financial crisis.
- JEL Code
**C11**: Mathematical and Quantitative Methods→Econometric and Statistical Methods and Methodology: General→Bayesian Analysis: General**C53**: Mathematical and Quantitative Methods→Econometric Modeling→Forecasting and Prediction Methods, Simulation Methods

- 23 April 2013
- WORKING PAPER SERIES - No. 1537Details
- Abstract
- Prediction of macroeconomic aggregates is one of the primary functions of macroeconometric models, including dynamic factor models, dynamic stochastic general equilibrium models, and vector autoregressions. This study establishes methods that improve the predictions of these models, using a representative model from each class and a canonical 7-variable postwar US data set. It focuses on prediction over the period 1966 through 2011. It measures the quality of prediction by the probability densities assigned to the actual values of these variables, one quarter ahead, by the predictive distributions of the models in real time. Two steps lead to substantial improvement. The first is to use full Bayesian predictive distributions rather than substitute a "plug-in" posterior mode for parameters. Across models and quarters, this leads to a mean improvement in probability of 50.4%. The second is to use an equally-weighted pool of predictive densities from the three models, which leads to a mean improvement in probability of 41.9% over the full Bayesian predictive distributions of the individual models. This improvement is much better than that a
- JEL Code
**C11**: Mathematical and Quantitative Methods→Econometric and Statistical Methods and Methodology: General→Bayesian Analysis: General**C51**: Mathematical and Quantitative Methods→Econometric Modeling→Model Construction and Estimation**C53**: Mathematical and Quantitative Methods→Econometric Modeling→Forecasting and Prediction Methods, Simulation Methods