4,080 research outputs found
Adaptive Minnesota Prior for High-Dimensional Vector Autoregressions
We develop a novel, highly scalable estimation method for large Bayesian Vector Autoregressive models (BVARs) and employ it to introduce an "adaptive" version of the Minnesota prior. This flexible prior structure allows each coeffcient of the VAR to have its own shrinkage intensity, which is treated as an additional parameter and estimated from the data. Most importantly, our estimation procedure does not rely on computationally intensive Markov Chain Monte Carlo (MCMC) methods, making it suitable for high-dimensional VARs with more predictors that observations. We use a Monte Carlo study to demonstrate the accuracy and computational gains of our approach. We further illustrate the forecasting performance of our new approach by applying it to a quarterly macroeconomic dataset, and find that it forecasts better than both factor models and other existing BVAR methods
Boosted p-Values for High-Dimensional Vector Autoregression
Assessing the statistical significance of parameter estimates is an important
step in high-dimensional vector autoregression modeling. Using the
least-squares boosting method, we compute the p-value for each selected
parameter at every boosting step in a linear model. The p-values are
asymptotically valid and also adapt to the iterative nature of the boosting
procedure. Our simulation experiment shows that the p-values can keep false
positive rate under control in high-dimensional vector autoregressions. In an
application with more than 100 macroeconomic time series, we further show that
the p-values can not only select a sparser model with good prediction
performance but also help control model stability. A companion R package
boostvar is developed
Dimension Reduction for High Dimensional Vector Autoregressive Models
This paper aims to decompose a large dimensional vector autoregessive (VAR)
model into two components, the first one being generated by a small-scale VAR
and the second one being a white noise sequence. Hence, a reduced number of
common factors generates the entire dynamics of the large system through a VAR
structure. This modelling extends the common feature approach to high
dimensional systems, and it differs from the dynamic factor models in which the
idiosyncratic components can also embed a dynamic pattern. We show the
conditions under which this decomposition exists, and we provide statistical
tools to detect its presence in the data and to estimate the parameters of the
underlying small-scale VAR model. We evaluate the practical value of the
proposed methodology by simulations as well as by empirical applications on
both economic and financial time series.Comment: 21 pages, 6 table
Nonparametric empirical Bayes and compound decision approaches to estimation of a high-dimensional vector of normal means
We consider the classical problem of estimating a vector
\bolds{\mu}=(\mu_1,...,\mu_n) based on independent observations , . Suppose , are independent
realizations from a completely unknown . We suggest an easily computed
estimator \hat{\bolds{\mu}}, such that the ratio of its risk
E(\hat{\bolds{\mu}}-\bolds{\mu})^2 with that of the Bayes procedure
approaches 1. A related compound decision result is also obtained. Our
asymptotics is of a triangular array; that is, we allow the distribution to
depend on . Thus, our theoretical asymptotic results are also meaningful in
situations where the vector \bolds{\mu} is sparse and the proportion of zero
coordinates approaches 1. We demonstrate the performance of our estimator in
simulations, emphasizing sparse setups. In ``moderately-sparse'' situations,
our procedure performs very well compared to known procedures tailored for
sparse setups. It also adapts well to nonsparse situations.Comment: Published in at http://dx.doi.org/10.1214/08-AOS630 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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