Sufficient Forecasting Using Factor Models
Sufficient Forecasting Using Factor Models
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DOI：
10.2139/ssrn.2607666
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发表时间：
2014-12
期刊：
影响因子：
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通讯作者：
Jianqing Fan;Lingzhou Xue;Jiawei Yao
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文献类型：
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作者：
Jianqing Fan;Lingzhou Xue;Jiawei Yao
我们考虑预测一个单一的时间序列时，有大量的预测和可能的非线性效应。首先通过主成分分析实现的高维（近似）因子模型降维。使用提取的因素，我们开发了一种新的预测方法，称为充分的预测，它提供了一组足够的预测指标，从高维预测推断，提供额外的预测能力。在假定采用半参数（近似）因子模型时，将采用预测主成分分析来提高推断因子的准确性。我们的方法也适用于横截面充分回归提取的因素。充分预测和深度学习架构之间的联系被明确地阐述。充分的预测正确估计投影指数的基本因素，即使在存在的非参数预测功能。所提出的方法扩展了足够的降维到高维制度凝聚的横截面信息，通过因子模型。我们得到的估计的中心子空间，这些投影方向以及足够的预测指标的估计的渐近性质。我们进一步表明，自然的方法运行的目标对估计因子的多元回归产生的线性估计，实际上福尔斯落入这个中心子空间。我们的方法和理论允许预测因子的数量大于观测值的数量。最后，我们证明了充分的预测改善了线性预测在模拟研究和预测宏观经济变量的实证研究。
We consider forecasting a single time series when there is a large number of predictors and a possible nonlinear effect. The dimensionality was first reduced via a high-dimensional (approximate) factor model implemented by the principal component analysis. Using the extracted factors, we develop a novel forecasting method called the sufficient forecasting, which provides a set of sufficient predictive indices, inferred from high-dimensional predictors, to deliver additional predictive power. The projected principal component analysis will be employed to enhance the accuracy of inferred factors when a semi-parametric (approximate) factor model is assumed. Our method is also applicable to cross-sectional sufficient regression using extracted factors. The connection between the sufficient forecasting and the deep learning architecture is explicitly stated. The sufficient forecasting correctly estimates projection indices of the underlying factors even in the presence of a nonparametric forecasting function. The proposed method extends the sufficient dimension reduction to high-dimensional regimes by condensing the cross-sectional information through factor models. We derive asymptotic properties for the estimate of the central subspace spanned by these projection directions as well as the estimates of the sufficient predictive indices. We further show that the natural method of running multiple regression of target on estimated factors yields a linear estimate that actually falls into this central subspace. Our method and theory allow the number of predictors to be larger than the number of observations. We finally demonstrate that the sufficient forecasting improves upon the linear forecasting in both simulation studies and an empirical study of forecasting macroeconomic variables.