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Confidence Intervals for Diffusion Index Forecasts and Inference for Factor‐Augmented Regressions
Author(s) -
Bai Jushan,
Ng Serena
Publication year - 2006
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.1111/j.1468-0262.2006.00696.x
Subject(s) - mathematics , statistics , inference , econometrics , series (stratigraphy) , regression , confidence interval , regression analysis , conditional expectation , factor analysis , index (typography) , standard error , computer science , artificial intelligence , world wide web , paleontology , biology
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 consistent and asymptotically normal if . The conditional mean predicted by the estimated factors is 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.