498,887 research outputs found
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
The Stochastic Fluctuation of the Quantile Regression Curve
Let (X1, Y1), . . ., (Xn, Yn) be i.i.d. rvs and let l(x) be the unknown p-quantile regression curve of Y on X. A quantile-smoother ln(x) is a localised, nonlinear estimator of l(x). The strong uniform consistency rate is established under general conditions. In many applications it is necessary to know the stochastic fluctuation of the process {ln(x) - l(x)}. Using strong approximations of the empirical process and extreme value theory allows us to consider the asymptotic maximal deviation sup06x61 |ln(x)-l(x)|. The derived result helps in the construction of a uniform confidence band for the quantile curve l(x). This confidence band can be applied as a model check, e.g. in econometrics. An application considers a labour market discrimination effect.Quantile Regression, Consistency Rate, Confidence Band, Check Function, Kernel Smoothing, Nonparametric Fitting
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