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Abstract:
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The sufficient forecasting (Fan et al., 2017) provides an effective nonparametric forecasting procedure to estimate sufficient indices from high-dimensional predictors in the presence of a possible nonlinear forecast function. In this paper, we first revisit the sufficient forecasting, and explore its underlying connections to Fama-Macbeth regression and partial least squares. Then, we develop a unified nonparametric estimation procedure for sufficient forecasting under the high-dimensional framework with large cross sections, a large time dimension and a diverging number of factors. We derive the rate of convergence of the estimated factors and loadings, and characterize the asymptotic behavior of the estimated sufficient forecasting directions. We obtain the predictive inference for the estimated nonparametric forecast function with nonparametrically estimated sufficient indices. We further demonstrate the power of the sufficient forecasting in an empirical study of financial markets.
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