1. Motivation

Forecasting a single time series using high dimensional predictors has received a lot of interests in macroeconomics, finance, business and many other research fields. It is usually reasonable to assume that a few underlying common factors drive the forecasting target and the high-dimensional predictors. The use of principal components effectively reduces the dimensionality and more importantly provides a useful characterization of predictors.

By assuming the linear forecasting function, Stock and Watson (1989, 2002a, 2002b) demonstrated the validity of the estimated principal components in forecasting. Bai and Ng (2006) conducted inferences on factor-augmented regressions to enable the forecast. Bair et al. (2006) applied the correlation screening to obtain relevant predictors, and Bai and Ng (2008) established the thresholding criteria to rule out predictors not informative for the target.

However, all of the aforementioned works may not perform well when the target and the latent factors have possibly nonlinear relationship. The possibly nonlinear and nonseparable forecasting function poses a significant challenge when extracting the information relevant to the target. The package provides sufficient forecasting (SF) procedure to make predictions. SF procedure obtains sufficient predictive indices with provable theoretical guarantees, allowing for an unknown nonlinear forecasting function.

2. Examples

2.1 Data

The package contains existing datasets: dataExample$y, dataExample$X, and dataExample$newX. y is a 100 by 1 matrix, X is a 100 by 100 matrix. X and y are our training sets. Our goal is to predict what the value of y is when we know next predictors are newX.

2.2 SF.SIR

We can use SF.SIR to forecast.

SF.SIR(y=dataExample$y,X=dataExample$X,newX=dataExample$newX)
#> [1] -0.2051

2.3 SF.DR

Also, We can use SF.DR.

SF.DR(y=dataExample$y,X=dataExample$X,newX=dataExample$newX)
#> [1] -0.1283

References

Bai, J. , and Ng, S. (2006), Confidence intervals for diffusion index forecasts and inference for factor-augmented regressions, Econometrica 74(4), 1133–1150.

Bai, J. , and Ng, S. (2008), Forecasting economic time series using targeted predictors, Journal of Econometrics 146, 304–317.

Bair, E. , Hastie, T. , Paul, D. , and Tibshirani, R. (2006), Prediction by supervised principal components, Journal of the American Statistical Association 101, 119–137.

Stock, J. H. , and Watson, M. W. (1989), New indexes of coincident and leading economic indicators, NBER Macroeconomics Annual 4, 351–409.

Stock, J. H. , and Watson, M. W. (2002a), Forecasting using principal components from a large number of predictors, Journal of the American Statistical Association 97, 1167–1179.