Highly Robust Estimation of the Autocorrelation Coefficient

0431671 - ÚI 2015 RIV CZ eng C - Konferenční příspěvek (zahraniční konf.)
Kalina, Jan - Vlčková, Katarína
Highly Robust Estimation of the Autocorrelation Coefficient.
The 8th International Days of Statistics and Economics. Slaný: Melandrium, 2014 - (Löster, T.; Pavelka, T.), s. 588-597. ISBN 978-80-87990-02-5.
[International Days of Statistics and Economics /8./. Prague (CZ), 11.09.2014-13.09.2014]
Grant ostatní: Nadační fond na opdporu vědy(CZ) Neuron
Institucionální podpora: RVO:67985807
Klíčová slova: time series * autoregressive process * linear regression * robust econometrics
Kód oboru RIV: BB - Aplikovaná statistika, operační výzkum

The classical autocorrelation coefficient estimator in the time series context is very sensitive to the presence of outlying measurements in the data. This paper proposes several new robust estimators of the autocorrelation coefficient. First, we consider an autoregressive process of the first order AR(1) to be observed. Robust estimators of the autocorrelation coefficient are proposed in a straightforward way based on robust regression. Further, we consider the task of robust estimation of the autocorrelation coefficient of residuals of linear regression. The task is connected to verifying the assumption of independence of residuals and robust estimators of the autocorrelation coefficient are defined based on the Durbin-Watson test statistic for robust regression. The main result is obtained for the implicitly weighted autocorrelation coefficient with small weights assigned to outlying measurements. This estimator is based on the least weighted squares regression and we exploit its asymptotic properties to derive an asymptotic test that the autocorrelation coefficient is equal to 0. Finally, we illustrate different estimators on real economic data, which reveal the advantage of the approach based on the least weighted squares regression. The estimator turns out to be resistant against the presence of outlying measurements.
Trvalý link: http://hdl.handle.net/11104/0236256