sufficientForecasting: Sufficient Forecasting using Factor Models

Description

The sufficient forecasting (SF) method is implemented by this package for a single time series forecasting using many predictors and a possibly nonlinear forecasting function. Assuming that the predictors are driven by some latent factors, the SF first conducts factor analysis and then performs sufficient dimension reduction on the estimated factors to derive predictive indices for forecasting. The package implements several dimension reduction approaches, including principal components (PC), sliced inverse regression (SIR), and directional regression (DR). Methods for dimension reduction are as described in: Fan, J., Xue, L. and Yao, J. (2017) doi:10.1016/j.jeconom.2017.08.009, Luo, W., Xue, L., Yao, J. and Yu, X. (2022) doi:10.1093/biomet/asab037 and Yu, X., Yao, J. and Xue, L. (2022) doi:10.1080/07350015.2020.1813589.

Author(s)

Maintainer: Jing Fu jingfu991224@outlook.com

Authors:

• Jianqing Fan

• Wei Luo

• Lingzhou Xue

• Jiawei Yao

• Xiufan Yu

See Also

Useful links:

• https://github.com/JingFu1224/sufficientForecasting

• Report bugs at https://github.com/JingFu1224/sufficientForecasting/issues

Select a method from PC, SIR and DR to do point prediction

Description

Select a method from PC, SIR and DR to do point prediction

Usage

SF(
  y,
  X,
  newX = NULL,
  K = "default",
  L = 1,
  method = "SIR.LM",
  hyperparameter = list()
)

Arguments

Value

Out-of-sample forecast for newX; or in-sample forecast for the last observed data point if newX is NULL

References

Fan, J., Xue, L. and Yao, J. (2017), Sufficient forecasting using factor models, Journal of econometrics 201(2), 292–306

Luo, W., Xue, L., Yao, J. and Yu, X. (2022), Inverse moment methods for sufficient forecasting using high-dimensional predictors, Biometrika 109(2), 473–487.

Yu, X., Yao, J. and Xue, L. (2022), Nonparametric estimation and conformal inference of the sufficient forecasting with a diverging number of factors, Journal of Business & Economic Statistics 40(1), 342–354.

Examples

utils::data(dataExample,package = "sufficientForecasting")
SF(dataExample$y,dataExample$X,method = "SIR.LLM",
hyperparameter = list(nslices = 5,discretization = TRUE))
SF(dataExample$y,dataExample$X,dataExample$newX,method = "DR")
SF(dataExample$y,dataExample$X,dataExample$newX,method = "PC")

Conformal inference of the sufficient forecasting

Description

Conformal inference of the sufficient forecasting

Usage

SF.CI(
  y,
  X,
  newX = NULL,
  type = "LM",
  K = "default",
  L = 1,
  alpha = 0.1,
  discretization = TRUE,
  nslices = 10
)

Arguments

Value

A list with components

yhat

Out-of-sample forecast for newX; or in-sample forecast for the last observed data point if newX is NULL

ci_lower

Lower bound of conformal interval

ci_upper

Upper bound of conformal interval

References

Yu, X., Yao, J. and Xue, L. (2022), Nonparametric estimation and conformal inference of the sufficient forecasting with a diverging number of factors, Journal of Business & Economic Statistics 40(1), 342–354.

Examples

utils::data(dataExample,package = "sufficientForecasting")
SF.CI(dataExample$y,dataExample$X,type = "LM",alpha = 0.05)

Directional regression for sufficient forecasting

Description

Directional regression for sufficient forecasting

Usage

SF.DR(y, X, newX = NULL, K = "default", L = 1, etaopg = "default", nslices = 3)

Arguments

Value

Out-of-sample forecast for newX; or in-sample forecast for the last observed data point if newX is NULL

References

Luo, W., Xue, L., Yao, J. and Yu, X. (2022), Inverse moment methods for sufficient forecasting using high-dimensional predictors, Biometrika 109(2), 473–487.

Examples

utils::data(dataExample,package = "sufficientForecasting")
SF.DR(dataExample$y,dataExample$X,dataExample$newX)

Principal component regression for sufficient forecasting

Description

Principal component regression for sufficient forecasting

Usage

SF.PC(y, X, newX = NULL, K = "default", L = "default")

Arguments

Value

Out-of-sample forecast for newX; or in-sample forecast for the last observed data point if newX is NULL

Examples

utils::data(dataExample,package = "sufficientForecasting")
SF.PC(dataExample$y,dataExample$X)

Sliced inverse regression for sufficient forecasting

Description

Sliced inverse regression for sufficient forecasting

Usage

SF.SIR(
  y,
  X,
  newX = NULL,
  type = "LM",
  K = "default",
  L = 1,
  discretization = TRUE,
  nslices = 10
)

Arguments

Value

Out-of-sample forecast for newX; or in-sample forecast for the last observed data point if newX is NULL

References

Fan, J., Xue, L. and Yao, J. (2017), Sufficient forecasting using factor models, Journal of econometrics 201(2), 292–306.

Yu, X., Yao, J. and Xue, L. (2022), Nonparametric estimation and conformal inference of the sufficient forecasting with a diverging number of factors, Journal of Business & Economic Statistics 40(1), 342–354.

Examples

utils::data(dataExample,package = "sufficientForecasting")
SF.SIR(dataExample$y,dataExample$X,type = "LLM")

A simulated dataset

Description

This is a simulated dataset consisting of predictors, responses, and additional predictors to make forecasting at a future time. In this example, the dimension of predictors is p=100, and the number of observed time periods is T=100.

Usage

dataExample

Format

• dataExample$X simulated predictors; a p by T matrix

• dataExample$y simulated responses; a T by 1 vector

• dataExample$newX simulated new predictors for forecasting; a p by 1 vector

Estimate the number of common factors K

Description

Estimate the number of common factors K

Usage

getK(y, X, Kmax = 12)

Arguments

Value

Estimate of K

References

Bai, J., and Ng, S. (2002), Determining the number of factors in approximate factor models, Econometrica 70(1), 191-221.

Li, H., Li, Q. and Shi, Y. (2017), Determining the number of factors when the number of factors can increase with sample size, Journal of Econometrics 197(1), 76–86.