BootPR (version 0.60)

ShamanStine.PI: 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

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)

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