2,951 research outputs found
Uniformly root- consistent density estimators for weakly dependent invertible linear processes
Convergence rates of kernel density estimators for stationary time series are
well studied. For invertible linear processes, we construct a new density
estimator that converges, in the supremum norm, at the better, parametric, rate
. Our estimator is a convolution of two different residual-based
kernel estimators. We obtain in particular convergence rates for such
residual-based kernel estimators; these results are of independent interest.Comment: Published at http://dx.doi.org/10.1214/009053606000001352 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Efficient prediction for linear and nonlinear autoregressive models
Conditional expectations given past observations in stationary time series
are usually estimated directly by kernel estimators, or by plugging in kernel
estimators for transition densities. We show that, for linear and nonlinear
autoregressive models driven by independent innovations, appropriate smoothed
and weighted von Mises statistics of residuals estimate conditional
expectations at better parametric rates and are asymptotically efficient. The
proof is based on a uniform stochastic expansion for smoothed and weighted von
Mises processes of residuals. We consider, in particular, estimation of
conditional distribution functions and of conditional quantile functions.Comment: Published at http://dx.doi.org/10.1214/009053606000000812 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Graphical modelling of multivariate time series
We introduce graphical time series models for the analysis of dynamic
relationships among variables in multivariate time series. The modelling
approach is based on the notion of strong Granger causality and can be applied
to time series with non-linear dependencies. The models are derived from
ordinary time series models by imposing constraints that are encoded by mixed
graphs. In these graphs each component series is represented by a single vertex
and directed edges indicate possible Granger-causal relationships between
variables while undirected edges are used to map the contemporaneous dependence
structure. We introduce various notions of Granger-causal Markov properties and
discuss the relationships among them and to other Markov properties that can be
applied in this context.Comment: 33 pages, 7 figures, to appear in Probability Theory and Related
Field
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