Resource title

Prediction and nonparametric estimation for time series with heavy tails

Resource image

image for OpenScout resource :: Prediction and nonparametric estimation for time series with heavy tails

Resource description

Motivated by prediction problems for time series with heavy-tailed marginal distributions, we consider methods based on `local least absolute deviations' for estimating a regression median from dependent data. Unlike more conventional `local median' methods, which are in effect based on locally fitting a polynomial of degree 0, techniques founded on local least absolute deviations have quadratic bias right up to the boundary of the design interval. Also in contrast to local least-squares methods based on linear fits, the order of magnitude of variance does not depend on tail-weight of the error distribution. To make these points clear, we develop theory describing local applications to time series of both least-squares and least-absolute-deviations methods, showing for example that, in the case of heavy-tailed data, the conventional local-linear least-squares estimator suffers from an additional bias term as well as increased variance.

Resource author

Resource publisher

Resource publish date

Resource language

en

Resource content type

application/pdf

Resource resource URL

http://eprints.lse.ac.uk/6086/1/Prediction_and_nonparametric_estimation_for_time_series_with_heavy_tails%28LSERO%29.pdf

Resource license