Fractional Gaussian Noise and hyperbolic decay time series model fitting

Description

Exact and Whittle MLE for time series models with hyperbolic decay. Simulation and regression supported for FGN.

Details

Author(s)

A. I. McLeod and Justin Veenstra

Maintainer: aimcleod@uwo.ca

References

Hipel, K.W. and McLeod, A.I., (2005). Time Series Modelling of Water Resources and Environmental Systems. Electronic reprint of our book orginally published in 1994. http://www.stats.uwo.ca/faculty/aim/1994Book/.

McLeod, A.I., Yu, Hao, Krougly, Zinovi L. (2007). Algorithms for Linear Time Series Analysis, Journal of Statistical Software.

McLeod, A.I. and Veenstra, Justin (2012). Hyperbolic Decay Time Series Models (in press).

See Also

HurstK, FitFGN, FitRegressionFGN, SimulateFGN, print.FitFGN, summary.FitFGN, predict.FitFGN, plot.FitFGN, residuals.FitFGN, GetFitFGN, GetFitFD, GetFitPLS, GetFitPLA

Examples

#Example 1
#Compare HurstK and MLE for H
#Hurst K for Nile Minima
data(NileMin)
HurstK(NileMin)
out<-FitFGN(NileMin)
summary(out)
plot(out)
coef(out)
#
#Example 2.
#Compare models
## Not run: 
   T1 <- proc.time()[3]
   ansFD <- GetFitFD(NileMin)
   T2 <- proc.time()[3]
   ansFGN <- GetFitFGN(NileMin)
   T3 <- proc.time()[3]
   ansPLS <- GetFitPLS(NileMin)
   T4 <- proc.time()[3]
   ansPLA <- GetFitPLA(NileMin)
   T5 <- proc.time()[3]
   tbLLE <- c(ansFD[[2]],ansFGN[[2]],ansPLS[[2]],ansPLA[[2]])
   est <-  c(ansFD[[3]],ansFGN[[3]],ansPLS[[3]],ansPLA[[3]])
   tbLL <- round(tbLLE, 2)
   est <- round(est, 3)
   T<-c(T2-T1,T3-T2,T4-T3,T5-T4)
   m<-matrix(c(est,tbLL, T),nrow=4, ncol=3)
   dimnames(m)<-list(list("FD","FGN","PLS","PLA"), list("alpha","logL", "time"))
   mE <- m
   mE
   #
   T1 <- proc.time()[3]
   ansFD <- GetFitFD(NileMin, algorithm="wmle")
   T2 <- proc.time()[3]
   ansFGN <- GetFitFGN(NileMin, algorithm="wmle")
   T3 <- proc.time()[3]
   ansPLA <- GetFitPLS(NileMin, algorithm="wmle")
   T4 <- proc.time()[3]
   ansPLS <- GetFitPLA(NileMin, algorithm="wmle")
   T5 <- proc.time()[3]
   #tbLL <- c(ansFD[[2]],ansFGN[[2]],ansPLS[[2]],ansPLA[[2]])
   z <- NileMin-mean(NileMin)
   tbLLW <- c(LLFD(ansFD[[1]],z), LLFGN(ansFGN[[1]],z), LLPLS(ansPLS[[1]],z), LLPLA(ansPLA[[1]],z))
   est <-  c(ansFD[[3]],ansFGN[[3]],ansPLS[[3]],ansPLA[[3]])
   tbLL <- round(tbLLW, 2)
   est <- round(est, 3)
   T<-c(T2-T1,T3-T2,T4-T3,T5-T4)
   m<-matrix(c(est,tbLL, T),nrow=4, ncol=3)
   dimnames(m)<-list(list("FD","FGN","PLS","PLA"), list("alpha","logL", "time"))
   mW<-m
   mW
   m<-cbind(mE,mW)
   m
   
## 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.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

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/FGN-package.Rd_%03d_medium.png", width=480, height=480)
> ### Name: FGN-package
> ### Title: Fractional Gaussian Noise and hyperbolic decay time series model
> ###   fitting
> ### Aliases: FGN-package
> ### Keywords: ts package
> 
> ### ** Examples
> 
> #Example 1
> #Compare HurstK and MLE for H
> #Hurst K for Nile Minima
> data(NileMin)
> HurstK(NileMin)
[1] 0.8249975
> out<-FitFGN(NileMin)
> summary(out)
#Nile River minima series
H = 0.831,  R-sq = 38.46%
length of series = 663 ,  number of parameters = 2
mean =  11.4812518853695 RMSE =  0.696191503559154
loglikelihood = 236.52 ,  AIC = -469 ,  BIC =  -460
100 98.73 0.4887911
> plot(out)
> coef(out)
          MLE         sd Z-ratio
H   0.8314766 0.02662516  12.450
mu 11.4812519 0.29693674  38.666
> #
> #Example 2.
> #Compare models
> ## Not run: 
> ##D    T1 <- proc.time()[3]
> ##D    ansFD <- GetFitFD(NileMin)
> ##D    T2 <- proc.time()[3]
> ##D    ansFGN <- GetFitFGN(NileMin)
> ##D    T3 <- proc.time()[3]
> ##D    ansPLS <- GetFitPLS(NileMin)
> ##D    T4 <- proc.time()[3]
> ##D    ansPLA <- GetFitPLA(NileMin)
> ##D    T5 <- proc.time()[3]
> ##D    tbLLE <- c(ansFD[[2]],ansFGN[[2]],ansPLS[[2]],ansPLA[[2]])
> ##D    est <-  c(ansFD[[3]],ansFGN[[3]],ansPLS[[3]],ansPLA[[3]])
> ##D    tbLL <- round(tbLLE, 2)
> ##D    est <- round(est, 3)
> ##D    T<-c(T2-T1,T3-T2,T4-T3,T5-T4)
> ##D    m<-matrix(c(est,tbLL, T),nrow=4, ncol=3)
> ##D    dimnames(m)<-list(list("FD","FGN","PLS","PLA"), list("alpha","logL", "time"))
> ##D    mE <- m
> ##D    mE
> ##D    #
> ##D    T1 <- proc.time()[3]
> ##D    ansFD <- GetFitFD(NileMin, algorithm="wmle")
> ##D    T2 <- proc.time()[3]
> ##D    ansFGN <- GetFitFGN(NileMin, algorithm="wmle")
> ##D    T3 <- proc.time()[3]
> ##D    ansPLA <- GetFitPLS(NileMin, algorithm="wmle")
> ##D    T4 <- proc.time()[3]
> ##D    ansPLS <- GetFitPLA(NileMin, algorithm="wmle")
> ##D    T5 <- proc.time()[3]
> ##D    #tbLL <- c(ansFD[[2]],ansFGN[[2]],ansPLS[[2]],ansPLA[[2]])
> ##D    z <- NileMin-mean(NileMin)
> ##D    tbLLW <- c(LLFD(ansFD[[1]],z), LLFGN(ansFGN[[1]],z), LLPLS(ansPLS[[1]],z), LLPLA(ansPLA[[1]],z))
> ##D    est <-  c(ansFD[[3]],ansFGN[[3]],ansPLS[[3]],ansPLA[[3]])
> ##D    tbLL <- round(tbLLW, 2)
> ##D    est <- round(est, 3)
> ##D    T<-c(T2-T1,T3-T2,T4-T3,T5-T4)
> ##D    m<-matrix(c(est,tbLL, T),nrow=4, ncol=3)
> ##D    dimnames(m)<-list(list("FD","FGN","PLS","PLA"), list("alpha","logL", "time"))
> ##D    mW<-m
> ##D    mW
> ##D    m<-cbind(mE,mW)
> ##D    m
> ##D    
> ## End(Not run)
>   
> 
> 
> 
> 
> dev.off()
null device 
          1 
>