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Adapting to Unknown Disturbance Autocorrelation in Regression with Long Memory
Author(s) -
Hidalgo Javier,
Robinson Peter M.
Publication year - 2002
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.1111/1468-0262.00341
Subject(s) - autocorrelation , mathematics , ordinary least squares , nonparametric statistics , autoregressive fractionally integrated moving average , generalized least squares , rate of convergence , statistics , least squares function approximation , monte carlo method , frequency domain , econometrics , long memory , mathematical analysis , computer science , volatility (finance) , computer network , channel (broadcasting) , estimator
We show that it is possible to adapt to nonparametric disturbance autocorrelation in time series regression in the presence of long memory in both regressors and disturbances by using a smoothed nonparametric spectrum estimate in frequency–domain generalized least squares. When the collective memory in regressors and disturbances is sufficiently strong, ordinary least squares is not only asymptotically inefficient but asymptotically non–normal and has a slow rate of convergence, whereas generalized least squares is asymptotically normal and Gauss–Markov efficient with standard convergence rate. Despite the anomalous behavior of nonparametric spectrum estimates near a spectral pole, we are able to justify a standard construction of frequency–domain generalized least squares, earlier considered in case of short memory disturbances. A small Monte Carlo study of finite sample performance is included.