A tutorial will take place in a hybrid mode on Tuesday the 16th of July 2024 in the Teaching Building No. 4, Room 108.

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Prediction-based statistical inference for multiple time series

Prof. Yan Liu, Waseda University, Japan.
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Description:

The aim is to discuss the prediction, interpolation and estimation problems in time series analysis. We deal with these problems in the same framework, i.e., we consider the parameter estimation for time series from the perspective of the prediction and interpolation problem. The prediction error and the interpolation error are regarded as contrast functions, and the parameters are estimated by the minimum contrast estimation. The new contrast functions are not contained in the class of either location or scale disparities. The consistency and the asymptotic distributions of the estimator are elucidated for finite-variance and infinite-variance time series. Also, it is shown in the case of finite-variance time series that the estimator is robust against the fourth-order cumulants. Also, as an extension of our previous work based on the prediction problem for the scalar-valued time series, we propose a minimum contrast estimator for multivariate time series in the frequency domain. This extension has not been thoroughly investigated, although the minimum contrast estimator for univariate time series has been studied for a long time. The proposal is based on the prediction errors of parametric time series models. The properties of the proposed contrast estimation function are explained in detail. We also derive the asymptotic normality of the proposed estimator, and compare the asymptotic variance with the existing results. The asymptotic efficiency of the proposed minimum contrast estimation is also considered. Some numerical simulations illustrate the theoretical results. Some applications and discussions will be provided.