第6回思考院セミナー / The 6th Seminar of the School of Statistical Thinking

Prediction is a key issue in time series analysis. Just as classical mean regression models, classical autoregressive ones, yielding L$^2$ point-predictions, provide rather poor predictive summaries; a much more informative approach is based on quantile (auto)regression, where the whole distribution of future observations conditional on the past is consistently recovered. Since their introduction by Koenker and Xiao in 2006, quantile autoregression (QAR) methods have emerged as a successful and widely adopted alternative to the traditional L$^2$ ones and their point-predictors. Due to the lack of a well-accepted concept of multivariate quantiles, however, QAR methods so far have been limited to univariate time series. Building upon recent measure-transportation-based concepts of multivariate quantiles, we develop here a nonparametric vector quantile autoregressive approach (QVAR) to the %analysis and prediction of (nonlinear as well as linear) multivariate time series.

Based on joint work with Alberto Gonz\'alez-Sanz and Yisha Yao (Department of Statistics, Columbia University, New York, USA).