Package 'BootPR'

Title: Bootstrap Prediction Intervals and Bias-Corrected Forecasting
Description: Contains functions for bias-Corrected Forecasting and Bootstrap Prediction Intervals for Autoregressive Time Series.
Authors: Jae. H. Kim <[email protected]>
Maintainer: Jae H. Kim <[email protected]>
License: GPL-2
Version: 1.0
Built: 2025-02-23 05:16:29 UTC
Source: https://github.com/cran/BootPR

Help Index


Bootstrap Prediction Intervals and Bias-Corrected Forecasting

Description

The package provides alternative bias-correction methods for univariate autoregressive model parameters; and generate point forecats and prediction intervals for economic time series.

A future version will include the case of vector AR models.

Details

Package: BootPR
Type: Package
Version: 1.0
Date: 2023-08-31
License: GPL version 2 or newer

Author(s)

Jae H. Kim

Maintainer: Jae H. Kim <[email protected]>


Andrews-Chen median-unbiased estimation for AR models

Description

This function returns the Andrews-Chen estimates for AR coefficients, residuals, and AR forecasts generated using the Andrews-Chen estimates

Usage

Andrews.Chen(x, p, h, type)

Arguments

x

a time series data set

p

AR order

h

the number of forecast periods

type

"const" for the AR model with intercept only, "const+trend" for the AR model with intercept and trend

Value

coef

Andrews-Chen median-unbiased estimates

ecm.coef

the coefficients in the ADF form

resid

residuals

forecast

point forecasts from Andrews-Chen estimates

Note

The Andrew-Chen estimator may break down when the AR order is very high. I recommend that AR order be kept low

Author(s)

Jae H. Kim

References

Kim, J.H., 2003, Forecasting Autoregressive Time Series with Bias-Corrected Parameter Estimators, International Journal of Forecasting, 19, 493-502.

Andrews, D.W. K. (1993). Exactly median-unbiased estimation of first order autoregressive / unit root models. Econometrica, 61, 139-165.

Andrews, D.W. K., & Chen, H. -Y. (1994). Approximate median unbiased estimation of autoregressive models. Journal of Business & Economic Statistics, 12, 187-204.

Examples

data(IPdata)
BootBC(IPdata,p=1,h=10,nboot=200,type="const+trend")

AR model order selection

Description

AR model selection using AIC, BIC, HQ

Usage

ARorder(x, pmax, type)

Arguments

x

a time series data set

pmax

the maximum AR order

type

"const" for the AR model with intercept only, "const+trend" for the AR model with intercept and trend

Value

ARorder

AR orders selected by AIC, BIC and HQ

Criteria

the values of AIC, BIC and HQ

Author(s)

Jae H. Kim

Examples

data(IPdata)
ARorder(IPdata,pmax=12,type="const+trend")

Bootstrap-after-Bootstrap Prediction

Description

This function calculates bootstrap-after-bootstrap prediction intervals and bootstrap bias-corrected point forecasts

Usage

BootAfterBootPI(x, p, h, nboot, prob, type)

Arguments

x

a time series data set

p

AR order

h

the number of forecast periods

nboot

number of bootstrap iterations

prob

a vector of probabilities

type

"const" for the AR model with intercept only, "const+trend" for the AR model with intercept and trend

Value

PI

prediction intervals

forecast

bias-corrected point forecasts

Author(s)

Jae H. Kim

References

Kim, J.H., 2001, Bootstrap-after-Bootstrap Prediction Intervals for Autoregressive Models, Journal of Business & Economic Statistics 19, 117-128

Kilian, L. (1998). Small sample confidence intervals for impulse response functions. The Review of Economics and Statistics, 80,218-230.

Examples

data(IPdata)
BootAfterBootPI(IPdata,p=1,h=10,nboot=100,prob=c(0.05,0.95),type="const+trend")

Bootstrap bias-corrected estimation and forecasting for AR models

Description

This function returns bias-corrected parameter estimates and forecasts for univariate AR models.

Usage

BootBC(x, p, h, nboot, type)

Arguments

x

a time series data set

p

AR order

h

the number of forecast period

nboot

number of bootstrap iterations

type

"const" for the AR model with intercept only, "const+trend" for the AR model with intercept and trend

Value

coef

Bootstrap bias-corrected parameter estimates

resid

residuals

forecast

point forecasts from bootstrap bias-corrected parameter estimates

Author(s)

Jae H. Kim

References

Kim, J.H., 2003, Forecasting Autoregressive Time Series with Bias-Corrected Parameter Estimators, International Journal of Forecasting, 19, 493-502.

Kilian, L. (1998a). Small sample confidence intervals for impulse response functions. The Review of Economics and Statistics, 80,218-230.

Examples

data(IPdata)
BootBC(IPdata,p=1,h=10,nboot=100,type="const+trend")

Bootstrap prediction intevals and point forecasts with no bias-correction

Description

This function returns bootstrap forecasts and prediction intervals with no bias-correction

Usage

BootPI(x, p, h, nboot, prob, type)

Arguments

x

a time series data set

p

AR order

h

the number of forecast periods

nboot

number of bootstrap iterations

prob

a vector of probabilities

type

"const" for the AR model with intercept only, "const+trend" for the AR model with intercept and trend

Value

PI

prediction intervals

forecast

bias-corrected point forecasts

Author(s)

Jae H. Kim

References

Thombs, L. A., & Schucany, W. R. (1990). Bootstrap prediction intervals for autoregression. Journal of the American Statistical Association, 85, 486-492.

Examples

data(IPdata)
BootPI(IPdata,p=1,h=10,nboot=100,prob=c(0.05,0.95),type="const+trend")

US industrial production data

Description

From Extended Nelson-Plosser data set, annua1, 1860-1988

Usage

data(IPdata)

References

Andrews, D.W. K., & Chen, H. -Y. (1994). Approximate median-unbiased estimation of autoregressive models. Journal of Business & Economic Statistics, 12, 187-204.

Examples

data(IPdata)

OLS parameter estimates and forecasts, no bias-correction

Description

The function returns parameter estimates and forecasts from OLS estimation for AR models

Usage

LS.AR(x, p, h, type, prob)

Arguments

x

a time series data set

p

AR order

h

the number of forecast period

prob

a vector of probabilities

type

"const" for the AR model with intercept only, "const+trend" for the AR model with intercept and trend

Value

coef

OLS parameter estimates

resid

OLS residuals

forecast

point forecasts from OLS parameter estimates

PI

Prediction Intervals based on OLS parameter estimates based on normal approximation

Author(s)

Jae H. Kim

Examples

data(IPdata)
LS.AR(IPdata,p=6,h=10,type="const+trend", prob=c(0.05,0.95))

Plotting point forecasts

Description

The function returns plots the point forecasts

Usage

Plot.Fore(x, fore, start, end, frequency)

Arguments

x

a time series data set

fore

point forecasts

start

starting date

end

ending date

frequency

data frequency

Details

frequency=1 for annual data, 4 for quarterly data, 12 for monthly data

start=c(1980,4) indicates April 1980 if frequency=12

end = c(2000,1) indicates 1st quarter of 2000 if freqeuncy = 4

Value

plot

Author(s)

Jae H. Kim

Examples

data(IPdata)
BootF <- BootBC(IPdata,p=1,h=10,nboot=100,type="const+trend")
Plot.Fore(IPdata,BootF$forecast,start=1860,end=1988,frequency=1)

Plotting prediction intervals and point forecasts

Description

The function returns plots the point forecasts and prediction intervals

Usage

Plot.PI(x, fore, Interval, start, end, frequency)

Arguments

x

a time series data set

fore

point forecasts

Interval

Prediction Intervals

start

starting date

end

ending date

frequency

data frequency

Details

frequency=1 for annual data, 4 for quarterly data, 12 for monthly data

start=c(1980,4) indicates April 1980 if frequency=12

end = c(2000,1) indicates 1st quarter of 2000 if freqeuncy = 4

Value

plot

Author(s)

Jae H. Kim

Examples

data(IPdata)
PI <- ShamanStine.PI(IPdata,p=1,h=10,nboot=100,prob=c(0.025,0.05,0.95,0.975),type="const+trend",0)
Plot.PI(IPdata,PI$forecast,PI$PI,start=1860,end=1988,frequency=1)

Roy-Fuller median-unbiased estimation

Description

This function returns parameter estimates and forecasts based on Roy-Fuller medin-unbiased estimator for AR models

Usage

Roy.Fuller(x, p, h, type)

Arguments

x

a time series data set

p

AR order

h

the number of forecast period

type

"const" for the AR model with intercept only, "const+trend" for the AR model with intercept and trend

Value

coef

Roy-Fuller parameter estimates

resid

residuals

forecast

point forecasts from Roy-Fuller parameter estimates

Author(s)

Jae H. Kim

References

Kim, J.H., 2003, Forecasting Autoregressive Time Series with Bias-Corrected Parameter Estimators, International Journal of Forecasting, 19, 493-502.

Roy, A., & Fuller, W. A. (2001). Estimation for autoregressive time series with a root near one. Journal of Business & Economic Statistics, 19(4), 482-493.

Examples

data(IPdata)
Roy.Fuller(IPdata,p=6,h=10,type="const+trend")

Bootstrap prediction interval using Shaman and Stine bias formula

Description

The function returns bias-corrected forecasts and bootstrap prediction intervals using Shaman and Stine bias formula for univariate AR models

Usage

ShamanStine.PI(x, p, h, nboot, prob, type, pmax)

Arguments

x

a time series data set

p

AR order

h

the number of forecast periods

nboot

number of bootstrap iterations

prob

a vector of probability values

type

"const" for the AR model with intercept only, "const+trend" for the AR model with intercept and trend

pmax

for exogenous lag order algorithm, pmax = 0, for endogenous lag order algorithm, pmax is an integer greater than 0

Value

PI

prediction intervals

forecast

bias-corrected point forecasts

Author(s)

Jae H. Kim

References

Kim, J.H., 2004, Bootstrap Prediction Intervals for Autoregression using Asymptotically Mean-Unbiased Parameter Estimators, International Journal of Forecasting, 20, 85-97.

Kim, J.H., 2003, Forecasting Autoregressive Time Series with Bias-Corrected Parameter Estimators, International Journal of Forecasting, 19, 493-502.

Shaman, P., & Stine, R. A. (1988). The bias of autoregressive coefficient estimators. Journal of the American Statistical Association, 83, 842-848.

Stine, R. A., & Shaman, P. (1989). A fixed point characterization for bias of autoregressive estimators. The Annals of Statistics,17, 1275-1284.

Kilian, L. (1998a). Small sample confidence intervals for impulse response functions. The Review of Economics and Statistics, 80,218-230.

Examples

data(IPdata)
ShamanStine.PI(IPdata,p=1,h=10,nboot=100,prob=c(0.05,0.95),type="const+trend",pmax=0)

bias-corrected estimation based on Shaman-Stine formula

Description

The function returns parameter estimates and bias-corrected forecasts using Shaman and Stine bias formula for univariate AR models

Usage

Stine.Shaman(x, p, h, type)

Arguments

x

a time series data set

p

AR order

h

the number of forecast period

type

"const" for the AR model with intercept only, "const+trend" for the AR model with intercept and trend

Value

coef

Bias-corrected parameter estimates using Shama-Stine formula

resid

residuals

forecast

point forecasts from bias-corrected parameter estimates

Author(s)

Jae H. Kim

References

Kim, J.H., 2003, Forecasting Autoregressive Time Series with Bias-Corrected Parameter Estimators, International Journal of Forecasting, 19, 493-502.

Shaman, P., & Stine, R. A. (1988). The bias of autoregressive coefficient estimators. Journal of the American Statistical Association, 83, 842-848.

Stine, R. A., & Shaman, P. (1989). A fixed point characterization for bias of autoregressive estimators. The Annals of Statistics,17, 1275-1284.

Kilian, L. (1998a). Small sample confidence intervals for impulse response functions. The Review of Economics and Statistics, 80,218-230.

Examples

data(IPdata)
Stine.Shaman(IPdata,p=6,h=10,type="const+trend")