66,655 research outputs found
Sparse cointegration
Cointegration analysis is used to estimate the long-run equilibrium relations
between several time series. The coefficients of these long-run equilibrium
relations are the cointegrating vectors. In this paper, we provide a sparse
estimator of the cointegrating vectors. The estimation technique is sparse in
the sense that some elements of the cointegrating vectors will be estimated as
zero. For this purpose, we combine a penalized estimation procedure for vector
autoregressive models with sparse reduced rank regression. The sparse
cointegration procedure achieves a higher estimation accuracy than the
traditional Johansen cointegration approach in settings where the true
cointegrating vectors have a sparse structure, and/or when the sample size is
low compared to the number of time series. We also discuss a criterion to
determine the cointegration rank and we illustrate its good performance in
several simulation settings. In a first empirical application we investigate
whether the expectations hypothesis of the term structure of interest rates,
implying sparse cointegrating vectors, holds in practice. In a second empirical
application we show that forecast performance in high-dimensional systems can
be improved by sparsely estimating the cointegration relations
Combining predictions from linear models when training and test inputs differ
Methods for combining predictions from different models in a supervised
learning setting must somehow estimate/predict the quality of a model's
predictions at unknown future inputs. Many of these methods (often implicitly)
make the assumption that the test inputs are identical to the training inputs,
which is seldom reasonable. By failing to take into account that prediction
will generally be harder for test inputs that did not occur in the training
set, this leads to the selection of too complex models. Based on a novel,
unbiased expression for KL divergence, we propose XAIC and its special case
FAIC as versions of AIC intended for prediction that use different degrees of
knowledge of the test inputs. Both methods substantially differ from and may
outperform all the known versions of AIC even when the training and test inputs
are iid, and are especially useful for deterministic inputs and under covariate
shift. Our experiments on linear models suggest that if the test and training
inputs differ substantially, then XAIC and FAIC predictively outperform AIC,
BIC and several other methods including Bayesian model averaging.Comment: 12 pages, 2 figures. To appear in Proceedings of the 30th Conference
on Uncertainty in Artificial Intelligence (UAI2014). This version includes
the supplementary material (regularity assumptions, proofs
Fitting Prediction Rule Ensembles with R Package pre
Prediction rule ensembles (PREs) are sparse collections of rules, offering
highly interpretable regression and classification models. This paper presents
the R package pre, which derives PREs through the methodology of Friedman and
Popescu (2008). The implementation and functionality of package pre is
described and illustrated through application on a dataset on the prediction of
depression. Furthermore, accuracy and sparsity of PREs is compared with that of
single trees, random forest and lasso regression in four benchmark datasets.
Results indicate that pre derives ensembles with predictive accuracy comparable
to that of random forests, while using a smaller number of variables for
prediction
Forecasting with many predictors - Is boosting a viable alternative?
This paper evaluates the forecast performance of boosting, a variable selection device, and compares it with the forecast combination schemes and dynamic factor models presented in Stock and Watson (2006). Using the same data set and comparison methodology, we find that boosting is a serious competitor for forecasting US industrial production growth in the short run and that it performs best in the longer run
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