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Large Vector Auto Regressions
One popular approach for nonstructural economic and financial forecasting is
to include a large number of economic and financial variables, which has been
shown to lead to significant improvements for forecasting, for example, by the
dynamic factor models. A challenging issue is to determine which variables and
(their) lags are relevant, especially when there is a mixture of serial
correlation (temporal dynamics), high dimensional (spatial) dependence
structure and moderate sample size (relative to dimensionality and lags). To
this end, an \textit{integrated} solution that addresses these three challenges
simultaneously is appealing. We study the large vector auto regressions here
with three types of estimates. We treat each variable's own lags different from
other variables' lags, distinguish various lags over time, and is able to
select the variables and lags simultaneously. We first show the consequences of
using Lasso type estimate directly for time series without considering the
temporal dependence. In contrast, our proposed method can still produce an
estimate as efficient as an \textit{oracle} under such scenarios. The tuning
parameters are chosen via a data driven "rolling scheme" method to optimize the
forecasting performance. A macroeconomic and financial forecasting problem is
considered to illustrate its superiority over existing estimators
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