ShamanStine.PI {BootPR} R Documentation

## 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

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)

```

[Package BootPR version 0.60 Index]