`library(sufficientForecasting)`

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.

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.

We can use SF.SIR to forecast.

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

Also, We can use SF.DR.

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

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.

Stock, J. H. , and Watson, M. W. (2002b), Macroeconomic forecasting
using diffusion indexes, *Journal of Business & Economic
Statistics* 20, 147–162.