Abstract
We discuss the robust estimation of a linear trend if the noise follows an autoregressive process of first order. We find the ordinary repeated median to perform well except for negative correlations. In this case it can be improved by a Prais-Winsten transformation using a robust autocorrelation estimator.
Highlights
We discuss the robust estimation of a linear trend from a noisy time series Y1, . . . , Yn of moderate size n in the presence of autoregressive disturbances of first order, AR(1), and irrelevant measurement artifacts
A number of papers compares the efficiencies of the ordinary least squares (OLS), the generalized least squares (GLS), the first differences (FD), the Cochrane-Orcutt (CO) and the Prais-Winsten (PW) estimators among others for estimation of the slope β, often under the idealized assumption that φ is known
We note that the resulting estimates μSCLS and βSCLS correspond to the CO approach based on φSCLS
Summary
We discuss the robust estimation of a linear trend from a noisy time series Y1, . . . , Yn of moderate size n in the presence of autoregressive disturbances of first order, AR(1), and irrelevant measurement artifacts (outliers). Robust fitting of linear trends to data within a moving time window of length n has been investigated recently by Davies, Fried and Gather (2004). In this context, the central level μ and the case of moderate n are of primary interest. Based on a comparison of robust regression techniques, they find Siegel’s (1982) repeated median (RM) to be very suitable for automatic estimation of trends because of its robustness, stability and computational tractability. We compare repeated median approaches for robust estimation of linear trends.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
