Nonparametric regression under dependent errors with infinite variance |
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Authors: | Peng Liang Yao Qiwei |
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Institution: | (1) School of Mathematics, Georgia Institute of Technology, 30332-0160 Atlanta, GA, USA;(2) Department of Statistics, London School of Economics, WC2A 2AE London, UK |
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Abstract: | We consider local least absolute deviation (LLAD) estimation for trend functions of time series with heavy tails which are
characterised via a symmetric stable law distribution. The setting includes both causal stable ARMA model and fractional stable
ARIMA model as special cases. The asymptotic limit of the estimator is established under the assumption that the process has
either short or long memory autocorrelation. For a short memory process, the estimator admits the same convergence rate as
if the process has the finite variance. The optimal rate of convergencen
−2/5 is obtainable by using appropriate bandwidths. This is distinctly different from local least squares estimation, of which
the convergence is slowed down due to the existence of heavy tails. On the other hand, the rate of convergence of the LLAD
estimator for a long memory process is always slower thann
−2/5 and the limit is no longer normal. |
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Keywords: | ARMA fractional ARIMA heavy tail least absolute deviation estimation long memory median stable distribution time series |
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