Speaker: Haihan Yu, PhD Candidate, Department of Statistics, Iowa State University

Title: A Composite Empirical Likelihood Method for Time Series in Frequency Domain Inference

Abstract: Frequency domain analysis of time series is often complicated by periodogram-based statistics having complex variances, so that approximations from resampling or empirical likelihood (EL) can be helpful. Existing versions of periodogram-based EL for time series, though, are restricted to linear processes and special spectral parameters. This talk introduces a new spectral EL (SEL) method by merging two different EL frameworks for time series, namely, block-based and periodogram-based EL. The resulting SEL statistics have some nice features for inference: these admit chi-square limits under mild conditions and can be coupled to an effective bootstrap procedure. The scope of EL for time series inference is then greatly expanded as SEL: can handle any spectral parameters; is valid for general processes (including nonlinear); and has a provable bootstrap that provides a novel alternative to other resampling plans in the frequency domain. Numerical studies suggest that the method has good performance, which is also demonstrated with real examples.