Model selection criteria are used in many contexts in economics. The issue of determining an appropriate criterion, or alternative method, for model selection is a topic of much interest for applied econometricians. These criteria are used when formal testing methods are difficult due to a large number of models being compared, or when a sequential modelling strategy is being used. In econometrics, we are familiar with the use of model selection criteria for determining the order of an ARMA process and the number of dependent variable lags in Augmented Dickey-Fuller equations. The latter application is examined as an interesting example of the sensitivity of results to the choice of criterion. An application of model selection criteria to spline fitting is also considered, introducing a new, flexible, modelling strategy for technical progress in a production economy and for returns to scale in a resource economics context. In this latter context we have a system of estimating equations. Two of the criteria which are compared are the Cross-Validation score (CV) and the Generalized Cross- Validation Criterion (GCV), which until now have only had single equation context expressions. Multiple equation expressions for these criteria are introduced, and are used in the two applications. Comparison of the models selected by the different criteria in each context reveals that results can differ greatly with the choice of criterion. In the unit root test application, the choice of criterion influences the number of times the false hypothesis is not rejected. In the production economy and resource applications, measures of technical progress and returns to scale differ greatly, as do own and cross price elasticities, depending on which criterion is used for selecting the appropriate spline structure. An overview of the literature on model selection is given, with new expressions and interpretations for some model selection criteria, and historical notes.

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This thesis is concerned with forecasting key floating exchange rates. The first half is based on the predictions of almost two hundred forecasters, working in banks, industrial companies, chambers of commerce and specialist forecasting agencies. It demonstrates that individual forecasters interpret commonly available information differently, and that these differences of opinion translate into economically meaningful heterogeneity in forecast performance - some forecasters are significantly more accurate than others. It also shows that the dispersion of forecasts helps to explain turnover in the foreign exchange futures market. The notion that the best predictive model of the exchange rate is a random walk has stood the test of time. In chapter three we evaluate the forecasts of our panellists based on a variety of metrics, using the random walk as a benchmark. Over short horizons (three months) the random walk remains preeminent, but over a one year horizon several forecasters demonstrate an ability to outperform. In an attempt to overturn the short horizon results we combine forecasts using several techniques in chapter four, but to no avail. It would appear that we are unable to find any information that is not discounted into the current spot rate but which is relevant over short forecast intervals. The second half of the thesis builds three exchange rate models based on an augmented theory of purchasing power parity, with which we forecast key rates. The five variable, simultaneous equation models each incorporate long-run equilibria characterised by economically meaningful restrictions, and complex short term dynamics. The thesis demonstrates that these models are capable of generating fully dynamic forecasts which rank very favourably when compared to our panellists. More tellingly, it also shows that the forecasts are significantly better than a random walk over all but the shortest of horizons.

Markov distributions describe multivariate data with conditional independence structures. Dawid and Lauritzen (1993) extended this idea to hyper Markov laws for prior distributions. A hyper Markov law is a distribution over Markov distributions whose marginals satisfy the same conditional independence constraints. These laws have been used for Gaussian mixtures (Escobar, 1994; Escobar and West, 1995) and contingency tables (Liu and Massam, 2006; Dobra and Massam, 2009). In this paper, we develop a family of non-parametric hyper Markov laws that we call hyper Dirichlet processes, combining the ideas of hyper Markov laws and non-parametric processes. Hyper Dirichlet processes are joint laws with Dirichlet process laws for particular marginals. We also describe a more general class of Dirichlet processes that are not hyper Markov, but still contain useful properties for describing graphical data. The graphical Dirichlet processes are simple Dirichlet processes with a hyper Markov base measure. This class allows an extremely straight-forward application of existing Dirichlet knowledge and technology to graphical settings. Given the wide-spread use of Dirichlet processes, there are many applications of this framework waiting to be explored. One broad class of applications, known as Dirichlet process mixtures, has been used for constructing mixture densities such that the underlying number of components may be determined by the data (Lo, 1984; Escobar, 1994; Escobar and West, 1995). I consider the use of the new graphical Dirichlet process in this setting, which imparts a conditional independence structure inside each component. In other words, given the component or cluster membership, the data exhibit the desired independence structure. We discuss two applications. Expanding on the work of Escobar and West (1995), we estimate a non-parametric mixture of Markov Gaussians using a Gibbs sampler. Secondly, we employ the Mode-Oriented Stochastic Search of Dobra and Massam (2009) for determining a suitable conditional independence model, focusing on contingency tables. In general, the mixing induced by a Dirichlet process does not drastically increase the complexity beyond that of a simpler Bayesian hierarchical models sans mixture components. We provide a specific representation for decomposable graphs with useful algorithms for local updates.

In this thesis, I derive generalization error bounds — bounds on the expected inaccuracy of the predictions — for time series forecasting models. These bounds allow forecasters to select among competing models, and to declare that, with high probability, their chosen model will perform well — without making strong assumptions about the data generating process or appealing to asymptotic theory. Expanding upon results from statistical learning theory, I demonstrate how these techniques can help time series forecasters to choose models which behave well under uncertainty. I also show how to estimate the β-mixing coefficients for dependent data so that my results can be used empirically. I use the bound explicitly to evaluate different predictive models for the volatility of IBM stock and for a standard set of macroeconomic variables. Taken together my results show how to control the generalization error of time series models with fixed or growing memory.

Diss. (sammanfattning) Stockholm : Karol. inst. / Härtill 7 uppsatser.

Thesis (M.S.)--Oregon State University, 2009. / Printout. Includes bibliographical references (leaves 60-61). Also available on the World Wide Web.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1994. / Vita. Abstract. Includes bibliographical references (leaves 152-163). Also available via the Internet.