The Bayesian linear model framework has become increasingly popular building block in regression problems. It has been shown to produce models with good predictive power and can be used with basis functions that are nonlinear in the data to provide exible estimated regression functions. Further, model uncertainty can be accounted for by Bayesian model averaging. We propose a more simple way to account for model uncertainty that is based on generalized ridge regression estimators. This is shown to predict well and to be much more computationally ecient than standard model averaging methods. Further, we demonstrate how to eciently mix over dierent sets of basis functions, letting the data determine which are most appropriate for the problem at hand. Keywords: Bayesian model averaging, generalized ridge regression, prediction, regression splines, shrinkage. 1

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Expressions are derived for generalized ridge (GR), ordinary ridge (OR) and shrunken least squares (SLS) predictors that are optimal for predicting the response at a single or at multiple future observations. As in the case of biased estimation, these predictors depend on the true (population) regression coefficient values and the true variance of the underlying linear regression model. Hence, we propose operational predictors where the unknown parameters in the biased predictors are estimated from the data. Using the Mean Squared Error of Prediction (MSEP) criterion, we compare the proposed predictors with the OLS predictor. Several traditional biased predictors, including the predictors based on the

Volatility modeling is the lifeline of the derivative- and asset-pricing evaluation process. As such, it is understandable that a voluminous literature has evolved to discuss the temporal dependencies in financial market volatility. Much of this literature has been directed at daily and lower frequencies using ARCH and stochastic volatility type models. With access to high frequency and ultra high-frequency databases, more recent research has been able to explain about fifty percent of the interdaily forecasts of latent volatility. Relying upon hourly intervals, the GARCH(1,1) results presented here are consistent with prior studies. However, this paper adds to the tools available for conducting volatility exploration by introducing an adaptive radial basis function neural network that significantly lowers overall prediction error while maintaining a high explanatory ratio. The newly formulated RBF implements a closed-form regularization parameter with Bayesian prior information. It is an algorithmic extension that will permit more accurate and insightful analyses to be performed on high frequency financial time series. Over the past decade, research efforts increased significantly in the area of modeling volatility behavior in capital market high frequency data. Obtaining accurate

Over the recent past, stylized facts have not yielded a synthesis regarding the predictability of returns for alternative investment assets such as hedge funds. Recent studies on alternative asset return predictability have added to the ambiguity. These studies suggest that classification prediction methods may dominate more traditional return-level prediction methodology. This paper examines the predictive accuracy of three alternate radial basis function neural networks when applied to the returns of thirteen Credit Swiss First Boston/Tremont (CSFB) hedge fund indices. We provide evidence that the Kajiji-4 RBF neural network dominates within the RBF topology in the prediction of hedge fund returns by both level and classification. The results also show that the Kajiji-4 method is capable of near perfect directional prediction.

Abstract. In this paper we propose and analyse a choice of parameters in the multi-penalty regularization. A modified discrepancy principle is presented within the multi-parameter regularization framework. An order optimal error bound is obtained under standard smoothness assumptions. We also propose a numerical realization of the multi-parameter discrepancy principle based on the model function approximation. Numerical experiments on a series of test problems support theoretical results. Finally we show how proposed approach can be successfully implemented in Laplacian Regularized Least Squares for learning from labeled and unlabeled examples. 1.