Confidence intervals for diffusion index forecasts and inference for factor-augmented regressions

• 成果类型: Article; Proceedings Paper
• 署名作者: Bai, Jushan; Ng, Serena
• 署名单位: New York University; Tsinghua University; University of Michigan System; University of Michigan
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.1111/j.1468-0262.2006.00696.x
• 发表日期: 2006
• 页码: 1133-1150
• 关键词: monetary-policy; principal components; heteroskedasticity

摘要

We consider the situation when there is a large number of series, N, each with T observations, and each series has some predictive ability for some variable of interest. A methodology of growing interest is first to estimate common factors from the panel of data by the method of principal components and then to augment an otherwise standard regression with the estimated factors. In this paper, we show that the least squares estimates obtained from these factor-augmented regressions are root T consistent and asymptotically normal if root T/N -> 0. The conditional mean predicted by the estimated factors is min[root T, root N] consistent and asymptotically normal. Except when T/N goes to zero, inference should take into account the effect of estimated regressors on the estimated conditional mean. We present analytical formulas for prediction intervals that are valid regardless of the magnitude of N/T and that can also be used when the factors are nonstationary.