Oracally Efficient Estimation of Autoregressive Error Distribution with Simultaneous Confidence Band

Abstract

[evdate 2013-12-19] HKUST International Forum on Probability and Statistics. Talk no. 16. Title from slide title.

The Second HKUST International Forum on Probability and Statistics (2013), held 19 December, 2013, at the Hong Kong University of Science and Technology. Co-sponsored by the HKUST Jockey Club Institute for Advanced Study and the Center for Statistical Science.

Abstract: The talk propose kernel estimator for the distribution function of unobserved errors in autoregressive time series, based on residuals computed by estimating the autoregressive coefficients with Yule-Walker method. Under mild assumptions, the speaker establish oracle efficiency of the proposed estimator, i.e., it is asymptotically as efficient as the kernel estimator of the distribution function based on the unobserved error sequence itself. Applying result of \cite{WCY13}, the proposed estimator is also asymptotically indistinguishable from the empirical distribution function based on the unobserved errors. A smooth simultaneous confidence band (SCB) is then constructed based on the proposed smooth distribution estimator and Kolmogorov distribution. Simulation examples support the asymptotic theory.

Duration: 31 min.