Package BootPR. February 19, 2015
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1 Tye Package Package BootPR February 19, 2015 Title Bootstra Prediction Intervals and Bias-Corrected Forecasting Version 0.60 Date Autor Jae. H. Kim Maintainer Bias-Corrected Forecasting and Bootstra Prediction Intervals for Autoregressive Time Series License GPL-2 NeedsComilation no Reository CRAN Date/Publication :08:50 R toics documented: BootPR-ackage Andrews.Cen ARorder BootAfterBootPI BootBC BootPI IPdata LS.AR Plot.Fore Plot.PI Roy.Fuller SamanStine.PI Stine.Saman Inde 14 1
2 2 Andrews.Cen BootPR-ackage Bootstra Prediction Intervals and Bias-Corrected Forecasting Details Te ackage rovides alternative bias-correction metods for univariate autoregressive model arameters; and generate oint forecats and rediction intervals for economic time series. A future version will include te case of vector AR models. Package: BootPR Tye: Package Version: 0.59 Date: License: GPL version 2 or newer Maintainer: <J.Kim@latrobe.edu.au> Andrews.Cen Andrews-Cen median-unbiased estimation for AR models Tis function returns te Andrews-Cen estimates for AR coefficients, residuals, and AR s generated using te Andrews-Cen estimates Andrews.Cen(,,, ) te number of eriods
3 ARorder 3 coef ecm.coef resid Andrews-Cen median-unbiased estimates te coefficients in te ADF form residuals oint s from Andrews-Cen estimates Note Te Andrew-Cen estimator may break down wen te is very ig. I recommend tat be ket low Kim, J.H., 2003, Forecasting Autoregressive Time Series wit Bias-Corrected Parameter Estimators, International Journal of Forecasting, 19, Andrews, D.W. K. (1993). Eactly median-unbiased estimation of first order autoregressive / unit root models. Econometrica, 61, Andrews, D.W. K., & Cen, H. -Y. (1994). Aroimate median unbiased estimation of autoregressive models. Journal of Business & Economic Statistics, 12, BootBC(IPdata,=1,=10,nboot=200,="const+trend") ARorder AR model order selection AR model selection using AIC, BIC, HQ ARorder(, ma, ) ma te maimum
4 4 BootAfterBootPI ARorder Criteria s selected by AIC, BIC and HQ te values of AIC, BIC and HQ ARorder(IPdata,ma=12,="const+trend") BootAfterBootPI Bootstra-after-Bootstra Prediction Tis function calculates bootstra-after-bootstra rediction intervals and bootstra bias-corrected oint s BootAfterBootPI(,,, nboot, rob, ) nboot rob te number of eriods number of bootstra iterations a vector of robabilities PI rediction intervals bias-corrected oint s
5 BootBC 5 Kim, J.H., 2001, Bootstra-after-Bootstra Prediction Intervals for Autoregressive Models, Journal of Business & Economic Statistics 19, Kilian, L. (1998). Small samle confidence intervals for imulse resonse functions. Te Review of Economics and Statistics, 80, BootAfterBootPI(IPdata,=1,=10,nboot=100,rob=c(0.05,0.95),="const+trend") BootBC Bootstra bias-corrected estimation and ing for AR models Tis function returns bias-corrected arameter estimates and s for univariate AR models. BootBC(,,, nboot, ) nboot te number of eriod number of bootstra iterations coef resid Bootstra bias-corrected arameter estimates residuals oint s from bootstra bias-corrected arameter estimates Kim, J.H., 2003, Forecasting Autoregressive Time Series wit Bias-Corrected Parameter Estimators, International Journal of Forecasting, 19, Kilian, L. (1998a). Small samle confidence intervals for imulse resonse functions. Te Review of Economics and Statistics, 80,
6 6 BootPI BootBC(IPdata,=1,=10,nboot=100,="const+trend") BootPI Bootstra rediction intevals and oint s wit no biascorrection Tis function returns bootstra s and rediction intervals wit no bias-correction BootPI(,,, nboot, rob, ) nboot rob te number of eriods number of bootstra iterations a vector of robabilities PI rediction intervals bias-corrected oint s Tombs, L. A., & Scucany, W. R. (1990). Bootstra rediction intervals for autoregression. Journal of te American Statistical Association, 85, BootPI(IPdata,=1,=10,nboot=100,rob=c(0.05,0.95),="const+trend")
7 IPdata 7 IPdata US industrial roduction data From Etended Nelson-Plosser data set, annua1, Andrews, D.W. K., & Cen, H. -Y. (1994). Aroimate median-unbiased estimation of autoregressive models. Journal of Business & Economic Statistics, 12, LS.AR OLS arameter estimates and s, no bias-correction Te function returns arameter estimates and s from OLS estimation for AR models LS.AR(,,,, rob) rob te number of eriod a vector of robabilities
8 8 Plot.Fore coef resid PI OLS arameter estimates OLS residuals oint s from OLS arameter estimates Prediction Intervals based on OLS arameter estimates based on normal aroimation LS.AR(IPdata,=6,=10,="const+trend", rob=c(0.05,0.95)) Plot.Fore Plotting oint s Te function returns lots te oint s Plot.Fore(, fore, start, end, frequency) fore start end frequency oint s starting date ending date data frequency Details frequency=1 for annual data, 4 for quarterly data, 12 for montly data start=c(1980,4) indicates Aril 1980 if frequency=12 end = c(2000,1) indicates 1st quarter of 2000 if freqeuncy = 4 lot
9 Plot.PI 9 BootF <- BootBC(IPdata,=1,=10,nboot=100,="const+trend") Plot.Fore(IPdata,BootF$,start=1860,end=1988,frequency=1) Plot.PI Plotting rediction intervals and oint s Te function returns lots te oint s and rediction intervals Plot.PI(, fore, Interval, start, end, frequency) fore Interval start end frequency oint s Prediction Intervals starting date ending date data frequency Details frequency=1 for annual data, 4 for quarterly data, 12 for montly data start=c(1980,4) indicates Aril 1980 if frequency=12 end = c(2000,1) indicates 1st quarter of 2000 if freqeuncy = 4 lot PI <- SamanStine.PI(IPdata,=1,=10,nboot=100,rob=c(0.025,0.05,0.95,0.975),="const+trend",0) Plot.PI(IPdata,PI$,PI$PI,start=1860,end=1988,frequency=1)
10 10 Roy.Fuller Roy.Fuller Roy-Fuller median-unbiased estimation Tis function returns arameter estimates and s based on Roy-Fuller medin-unbiased estimator for AR models Roy.Fuller(,,, ) te number of eriod coef resid Roy-Fuller arameter estimates residuals oint s from Roy-Fuller arameter estimates Kim, J.H., 2003, Forecasting Autoregressive Time Series wit Bias-Corrected Parameter Estimators, International Journal of Forecasting, 19, Roy, A., & Fuller, W. A. (2001). Estimation for autoregressive time series wit a root near one. Journal of Business & Economic Statistics, 19(4), Roy.Fuller(IPdata,=6,=10,="const+trend")
11 SamanStine.PI 11 SamanStine.PI Bootstra rediction interval using Saman and Stine bias formula Te function returns bias-corrected s and bootstra rediction intervals using Saman and Stine bias formula for univariate AR models SamanStine.PI(,,, nboot, rob,, ma) nboot rob ma te number of eriods number of bootstra iterations a vector of robability values for eogenous lag order algoritm, ma = 0, for endogenous lag order algoritm, ma is an integer greater tan 0 PI rediction intervals bias-corrected oint s Kim, J.H., 2004, Bootstra Prediction Intervals for Autoregression using Asymtotically Mean- Unbiased Parameter Estimators, International Journal of Forecasting, 20, Kim, J.H., 2003, Forecasting Autoregressive Time Series wit Bias-Corrected Parameter Estimators, International Journal of Forecasting, 19, Saman, P., & Stine, R. A. (1988). Te bias of autoregressive coefficient estimators. Journal of te American Statistical Association, 83, Stine, R. A., & Saman, P. (1989). A fied oint caracterization for bias of autoregressive estimators. Te Annals of Statistics,17, Kilian, L. (1998a). Small samle confidence intervals for imulse resonse functions. Te Review of Economics and Statistics, 80,
12 12 Stine.Saman SamanStine.PI(IPdata,=1,=10,nboot=100,rob=c(0.05,0.95),="const+trend",ma=0) Stine.Saman bias-corrected estimation based on Saman-Stine formula Te function returns arameter estimates and bias-corrected s using Saman and Stine bias formula for univariate AR models Stine.Saman(,,, ) te number of eriod coef resid Bias-corrected arameter estimates using Sama-Stine formula residuals oint s from bias-corrected arameter estimates Kim, J.H., 2003, Forecasting Autoregressive Time Series wit Bias-Corrected Parameter Estimators, International Journal of Forecasting, 19, Saman, P., & Stine, R. A. (1988). Te bias of autoregressive coefficient estimators. Journal of te American Statistical Association, 83, Stine, R. A., & Saman, P. (1989). A fied oint caracterization for bias of autoregressive estimators. Te Annals of Statistics,17, Kilian, L. (1998a). Small samle confidence intervals for imulse resonse functions. Te Review of Economics and Statistics, 80,
13 Stine.Saman 13 Stine.Saman(IPdata,=6,=10,="const+trend")
14 Inde Toic ts Andrews.Cen, 2 ARorder, 3 BootAfterBootPI, 4 BootBC, 5 BootPI, 6 BootPR-ackage, 2 IPdata, 7 LS.AR, 7 Plot.Fore, 8 Plot.PI, 9 Roy.Fuller, 10 SamanStine.PI, 11 Stine.Saman, 12 Andrews.Cen, 2 ARorder, 3 BootAfterBootPI, 4 BootBC, 5 BootPI, 6 BootPR (BootPR-ackage), 2 BootPR-ackage, 2 IPdata, 7 LS.AR, 7 Plot.Fore, 8 Plot.PI, 9 Roy.Fuller, 10 SamanStine.PI, 11 Stine.Saman, 12 14
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