FGN (version 2.0-12)

NileMin: Nile Annual Minima, 622 AD to 1284 AD

Description

Annual Minimum flow of Nile River. See below for details.

Usage

data(NileMin)

Format

The format is: Time-Series [1:663] from 622 to 1284: 11.57 10.88 11.69 11.69 9.84 ... - attr(*, "title")= "Nile River minima series"

Source

Toussoun, O. (1925). Memoire sur l'Histoire du Nil. In Memoires a l'Institut d'Egypte, 18, 366-404.

Details

The minimum annual level of the Nile has been recorded over many centuries and was given by Toussoun (1925). The data over the period 622 AD to 1284 AD is considered more homogenous and reliable than the full dataset and has been analyzed by Beran (1994) and Percival and Walden (2000). The full dataset is available StatLib Datasets hipel-mcleod archive -- file: Minimum.

References

Beran, J. (1994). Statistics for Long-Memory Processes. Chapman and Hall, New York.

Percival, D.B. and Walden, A.T. (2000) Wavelet Methods for Time Series Analysis. Cambridge University Press.

Examples

#Example 1
#Compute Hurst's K estimate of H
data(NileMin)
HurstK(NileMin)
GetFitFGN(NileMin)

#Example 2
#Script for comparing FGN/ARMA forecast performance
#
## Not run: 
# data(NileMin)
# outNileMin<-FitFGN(NileMin)
# set.seed(12177)
# z<-Boot(outNileMin)
# n<-length(z)
# K<-100 #number of out-of-sample data values
# z1<-z[1:(length(z)-K)] #training data
# z2<-z[-(1:(length(z)-K))] #testing data
# #
# #FGN fit to z1 and forecast using z2
# maxLead<-3
# n1<-length(z1)
# outz1<-FitFGN(z1)
# H<-outz1$H
# mu<-outz1$muHat
# rFGN<-var(z1)*acvfFGN(H, n + maxLead -1)
# F<-TrenchForecast(c(z1,z2), rFGN, mu, n1, maxLead=maxLead)$Forecasts
# nF<-nrow(F)
# err1<-z2-F[,1][-nF]
# err2<-z2[-1]-F[,2][-c(nF,(nF-1))]
# err3<-z2[-c(1,2)]-F[,3][-c(nF,(nF-1),(nF-2))]
# rmse1<-sqrt(mean(err1^2))
# rmse2<-sqrt(mean(err2^2))
# rmse3<-sqrt(mean(err3^2))
# FGNrmse<-c(rmse1,rmse2,rmse3)
# #
# #ARMA(p,q) fit to z1 and forecast using z2
# p<-2
# q<-1
# ansz1<-arima(z1, c(p,0,q))
# phi<-theta<-numeric(0)
# if (p>0) phi<-coef(ansz1)[1:p]
# if (q>0) theta<-coef(ansz1)[(p+1):(p+q)]
# zm<-coef(ansz1)[p+q+1]
# sigma2<-ansz1$sigma2
# vz<-tacvfARMA(phi=phi, theta=theta, sigma2=sigma2, maxLag=0)
# r<-vz*ARMAacf(ar=phi, ma=theta, lag.max=n + maxLead -1)
# F<-TrenchForecast(c(z1,z2), r, zm, n1, maxLead=3)$Forecasts
# err1<-z2-F[,1][-nF]
# err2<-z2[-1]-F[,2][-c(nF,(nF-1))]
# err3<-z2[-c(1,2)]-F[,3][-c(nF,(nF-1),(nF-2))]
# rmse1<-sqrt(mean(err1^2))
# rmse2<-sqrt(mean(err2^2))
# rmse3<-sqrt(mean(err3^2))
# ARMArmse<-c(rmse1,rmse2,rmse3)
# #
# #tabulate result
# tb<-matrix(c(FGNrmse,ARMArmse),ncol=2)
# dimnames(tb)<-list(c("lead1","lead2","lead3"),c("FGN","ARMA"))
# ## End(Not run)