邹国华研究员学术报告：Model averaging prediction for time series models with a diverging number of parameters
报告题目：Modelaveraging prediction for time series models with a diverging number ofparameters
报 告 人：邹国华研究员（中科院数学与系统科学研究院）
An importantproblem with model averaging approach is the choice of weights. In this paper,a generalized Mallows model averaging (GMMA) criterion for choosing weights isdeveloped in the context of an infinite order autoregressive (AR(infinity))process. The GMMA method adapts to the circumstances in which the dimensions ofcandidate models can be large and increase with the sample size. The GMMAmethod is shown to be asymptotically optimal in the sense of obtaining the bestout-of-sample mean-squared prediction error (MSPE) for both theindependent-realization and the same-realization predictions, which, as abyproduct, solves a conjecture put forward by Hansen (2008) that the well-knownMallows model averaging (MMA) criterion from Hansen (2007) is asymptoticallyoptimal for predicting the future of a times series. The rate of the GMMA basedweight estimator tending to the optimal weight vector minimizing theindependent-realization MSPE is derived as well. Both simulation experiment andreal data analysis illustrate the merits of GMMA method in the prediction ofAR(infinity) process.