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"

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.

Source

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

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)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
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Type 'license()' or 'licence()' for distribution details.

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Type 'contributors()' for more information and
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Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(FGN)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/FGN/NileMin.Rd_%03d_medium.png", width=480, height=480)
> ### Name: NileMin
> ### Title: Nile Annual Minima, 622 AD to 1284 AD
> ### Aliases: NileMin
> ### Keywords: datasets
> 
> ### ** Examples
> 
> #Example 1
> #Compute Hurst's K estimate of H
> data(NileMin)
> HurstK(NileMin)
[1] 0.8249975
> GetFitFGN(NileMin)
$H
[1] 0.8314766

$loglikelihood
[1] 236.5197

$alpha
[1] 0.3370469

$algorithm
[1] "emle"

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