10,883 research outputs found
High-dimensional Linear Regression for Dependent Data with Applications to Nowcasting
Recent research has focused on penalized least squares (Lasso)
estimators for high-dimensional linear regressions in which the number of
covariates is considerably larger than the sample size . However, few
studies have examined the properties of the estimators when the errors and/or
the covariates are serially dependent. In this study, we investigate the
theoretical properties of the Lasso estimator for a linear regression with a
random design and weak sparsity under serially dependent and/or nonsubGaussian
errors and covariates. In contrast to the traditional case, in which the errors
are independent and identically distributed and have finite exponential
moments, we show that can be at most a power of if the errors have only
finite polynomial moments. In addition, the rate of convergence becomes slower
owing to the serial dependence in the errors and the covariates. We also
consider the sign consistency of the model selection using the Lasso estimator
when there are serial correlations in the errors or the covariates, or both.
Adopting the framework of a functional dependence measure, we describe how the
rates of convergence and the selection consistency of the estimators depend on
the dependence measures and moment conditions of the errors and the covariates.
Simulation results show that a Lasso regression can be significantly more
powerful than a mixed-frequency data sampling regression (MIDAS) and a Dantzig
selector in the presence of irrelevant variables. We apply the results obtained
for the Lasso method to nowcasting with mixed-frequency data, in which serially
correlated errors and a large number of covariates are common. The empirical
results show that the Lasso procedure outperforms the MIDAS regression and the
autoregressive model with exogenous variables in terms of both forecasting and
nowcasting
Nonparametric estimation for Levy processes with a view towards mathematical finance
Nonparametric methods for the estimation of the Levy density of a Levy
process are developed. Estimators that can be written in terms of the ``jumps''
of the process are introduced, and so are discrete-data based approximations. A
model selection approach made up of two steps is investigated. The first step
consists in the selection of a good estimator from a linear model of proposed
Levy densities, while the second is a data-driven selection of a linear model
among a given collection of linear models. By providing lower bounds for the
minimax risk of estimation over Besov Levy densities, our estimators are shown
to achieve the ``best'' rate of convergence. A numerical study for the case of
histogram estimators and for variance Gamma processes, models of key importance
in risky asset price modeling driven by Levy processes, is presented.Comment: 68 pages, 19 figures, submitted to Annals of Statistic
COUNTS WITH AN ENDOGENOUS BINARY REGRESSOR: A SERIES EXPANSION APPROACH
We propose an estimator for count data regression models where a binary regressor is endogenously determined. This estimator departs from previous approaches by using a flexible form for the conditional probability function of the counts. Using a Monte Carlo experiment we show that our estimator improves the fit and provides a more reliable estimate of the impact of regressors on the count when compared to alternatives which do restrict the mean to be linear-exponential. In an application to the number of trips by households in the US, we find that the estimate of the treatment effect obtained is considerably different from the one obtained under a linear-exponential mean specification.Count data, Polynominal Poisson Expansions, Flexible Functional Form.
Intermittent process analysis with scattering moments
Scattering moments provide nonparametric models of random processes with
stationary increments. They are expected values of random variables computed
with a nonexpansive operator, obtained by iteratively applying wavelet
transforms and modulus nonlinearities, which preserves the variance. First- and
second-order scattering moments are shown to characterize intermittency and
self-similarity properties of multiscale processes. Scattering moments of
Poisson processes, fractional Brownian motions, L\'{e}vy processes and
multifractal random walks are shown to have characteristic decay. The
Generalized Method of Simulated Moments is applied to scattering moments to
estimate data generating models. Numerical applications are shown on financial
time-series and on energy dissipation of turbulent flows.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1276 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Moments of spectral functions: Monte Carlo evaluation and verification
The subject of the present study is the Monte Carlo path-integral evaluation
of the moments of spectral functions. Such moments can be computed by formal
differentiation of certain estimating functionals that are
infinitely-differentiable against time whenever the potential function is
arbitrarily smooth. Here, I demonstrate that the numerical differentiation of
the estimating functionals can be more successfully implemented by means of
pseudospectral methods (e.g., exact differentiation of a Chebyshev polynomial
interpolant), which utilize information from the entire interval . The algorithmic detail that leads to robust numerical
approximations is the fact that the path integral action and not the actual
estimating functional are interpolated. Although the resulting approximation to
the estimating functional is non-linear, the derivatives can be computed from
it in a fast and stable way by contour integration in the complex plane, with
the help of the Cauchy integral formula (e.g., by Lyness' method). An
interesting aspect of the present development is that Hamburger's conditions
for a finite sequence of numbers to be a moment sequence provide the necessary
and sufficient criteria for the computed data to be compatible with the
existence of an inversion algorithm. Finally, the issue of appearance of the
sign problem in the computation of moments, albeit in a milder form than for
other quantities, is addressed.Comment: 13 pages, 2 figure
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