60 research outputs found
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Universality of Bayesian Predictions
Given the sequential update nature of Bayes rule, Bayesian methods find natural application to prediction problems. Advances in computational methods allow to routinely use Bayesian methods in econometrics. Hence, there is a strong case for feasible predictions in a Bayesian framework. This paper studies the theoretical properties of Bayesian predictions and shows that under minimal conditions we can derive finite sample bounds for the loss incurred using
Bayesian predictions under the Kullback-Leibler divergence. In particular, the concept of universality of predictions is discussed and universality is established for Bayesian predictions in a variety of settings. These include predictions under almost arbitrary loss functions, model
averaging, predictions in a non stationary environment and under model miss-specification.
Given the possibility of regime switches and multiple breaks in economic series, as well as the
need to choose among different forecasting models, which may inevitably be miss-specified, the
finite sample results derived here are of interest to economic and financial forecasting
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Forecasting Distributions with Experts Advice
This paper considers forecasts of the distribution of data whose distribution function is possibly time varying. The forecast is achieved via time varying combinations of experts’ forecasts. We derive theoretical worse case bounds for general algorithms based on multiplicative updates of the combination weights. The bounds are useful to study the properties of forecast combinations when data are nonstationary and there is no unique best model. An application with an empirical study is used to highlight the results in practice
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Online Forecast Combination for Dependent Heterogeneous Data
This paper studies a procedure to combine individual forecasts that achieve theoretical optimal performance. The results apply to a wide variety of loss functions and no conditions are imposed on the data sequences and the individual forecasts apart from a tail condition. The theoretical results show that the bounds are also valid in the case of time varying combination weights, under specific conditions on the nature of time variation. Some experimental evidence to confirm the results is provided
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Nearest Neighbor Conditional Estimation for Harris Recurrent Markov Chains
This paper is concerned with consistent nearest neighbor time series estimation for data generated by a Harris recurrent Markov chain. The goal is to validate nearest neighbor estimation in this general time series context, using simple and weak conditions. The framework considered covers, in a unified manner, a wide variety of statistical quantities, e.g. autoregression function, conditional quantiles, conditional tail estimators and, more generally, extremum estimators. The focus is theoretical, but examples are given to highlight applications
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Forecasting Using Time Varying Meta-Elliptical Distributions with a Study of Commodity Futures Prices
We propose a methodological approach to the forecast and evaluation of multivariate distributions with time varying parameters. For reasons related to feasible inference attention is restricted to meta-elliptical distributions. We use our approach for the study of a large data set of 16 commodity prices. Our approach leads to a theory for model validation avoiding common problems caused by discontinuities, time variation of parameters and nuisance parameters
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Copula Based Monte Carlo Integration in Financial Problems
A computational technique that transform integrals over RK, or some of its subsets, into the hypercube [0, 1]K can be exploited in order to solve integrals via Monte Carlo integration without the need to simulate from the original distribution; all that is needed is to simulate iid uniform [0, 1] pseudo random variables. In particular the technique arises from the copula representation of multivariate distributions and the use of the marginal quantile function of the data. The procedure is further simplified if the quantile function has closed form. Several financial applications are considered in order to highlight the scope of this numerical technique for financial problem
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