R version 3.2.5 (2016-04-14) -- "Very, Very Secure Dishes"
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.

> x <- c(250785
+ ,250140
+ ,255755
+ ,254671
+ ,253919
+ ,253741
+ ,252729
+ ,253810
+ ,256653
+ ,255231
+ ,258405
+ ,251061
+ ,254811
+ ,254895
+ ,258325
+ ,257608
+ ,258759
+ ,258621
+ ,257852
+ ,260560
+ ,262358
+ ,260812
+ ,261165
+ ,257164
+ ,260720
+ ,259581
+ ,264743
+ ,261845
+ ,262262
+ ,261631
+ ,258953
+ ,259966
+ ,262850
+ ,262204
+ ,263418
+ ,262752
+ ,266433
+ ,267722
+ ,266003
+ ,262971
+ ,265521
+ ,264676
+ ,270223
+ ,269508
+ ,268457
+ ,265814
+ ,266680
+ ,263018
+ ,269285
+ ,269829
+ ,270911
+ ,266844
+ ,271244
+ ,269907
+ ,271296
+ ,270157
+ ,271322
+ ,267179
+ ,264101
+ ,265518
+ ,269419
+ ,268714
+ ,272482
+ ,268351
+ ,268175
+ ,270674
+ ,272764
+ ,272599
+ ,270333
+ ,270846
+ ,270491
+ ,269160
+ ,274027
+ ,273784
+ ,276663
+ ,274525
+ ,271344
+ ,271115
+ ,270798
+ ,273911
+ ,273985
+ ,271917
+ ,273338
+ ,270601
+ ,273547
+ ,275363
+ ,281229
+ ,277793
+ ,279913
+ ,282500
+ ,280041
+ ,282166
+ ,290304
+ ,283519
+ ,287816
+ ,285226
+ ,287595
+ ,289741
+ ,289148
+ ,288301
+ ,290155
+ ,289648
+ ,288225
+ ,289351
+ ,294735
+ ,305333
+ ,309030
+ ,310215
+ ,321935
+ ,325734
+ ,320846
+ ,323023
+ ,319753
+ ,321753
+ ,320757
+ ,324479
+ ,324641
+ ,322767
+ ,324181
+ ,321389
+ ,327897
+ ,334287
+ ,332653
+ ,334819
+ ,335264
+ ,339622
+ ,342440
+ ,346585
+ ,335378
+ ,337010
+ ,339130
+ ,341193
+ ,343507
+ ,348915
+ ,346431
+ ,348322
+ ,348288
+ ,346597
+ ,351076
+ ,355215
+ ,350562
+ ,355266
+ ,361565
+ ,363462
+ ,366183
+ ,365423
+ ,369208
+ ,366713
+ ,369354
+ ,371970
+ ,371824
+ ,373187
+ ,367270
+ ,368140
+ ,373742
+ ,364815
+ ,368558
+ ,371503
+ ,372611
+ ,370197
+ ,375441
+ ,375888
+ ,375132
+ ,381142
+ ,372024
+ ,376070
+ ,376864
+ ,371401
+ ,375687
+ ,384304
+ ,380738
+ ,379908
+ ,384007
+ ,384499
+ ,385106
+ ,387935
+ ,380435
+ ,379281
+ ,384153
+ ,380599)
> par3 = 'multiplicative'
> par2 = 'Triple'
> par1 = '12'
> par3 <- 'multiplicative'
> par2 <- 'Triple'
> par1 <- '12'
> #'GNU S' R Code compiled by R2WASP v. 1.2.327 ()
> #Author: root
> #To cite this work: Wessa P., (2013), Exponential Smoothing (v1.0.5) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_exponentialsmoothing.wasp/
> #Source of accompanying publication: 
> #
> par1 <- as.numeric(par1)
> if (par2 == 'Single') K <- 1
> if (par2 == 'Double') K <- 2
> if (par2 == 'Triple') K <- par1
> nx <- length(x)
> nxmK <- nx - K
> x <- ts(x, frequency = par1)
> if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
> if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
> if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
> fit
Holt-Winters exponential smoothing with trend and multiplicative seasonal component.

Call:
HoltWinters(x = x, seasonal = par3)

Smoothing parameters:
 alpha: 0.7890513
 beta : 0.01234488
 gamma: 0.9374388

Coefficients:
            [,1]
a   3.821990e+05
b   7.887929e+02
s1  1.006378e+00
s2  1.013495e+00
s3  1.005270e+00
s4  9.992780e-01
s5  1.001961e+00
s6  1.000068e+00
s7  9.995997e-01
s8  1.005989e+00
s9  9.905870e-01
s10 9.982519e-01
s11 1.007814e+00
s12 9.958029e-01
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/wessaorg/rcomp/tmp/185mj1461604180.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/2mgzi1461604180.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/3ffu11461604180.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$alpha)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'beta',header=TRUE)
> a<-table.element(a,fit$beta)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'gamma',header=TRUE)
> a<-table.element(a,fit$gamma)
> a<-table.row.end(a)
> a<-table.end(a)
> table.save(a,file="/var/wessaorg/rcomp/tmp/43wg71461604180.tab") 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'t',header=TRUE)
> a<-table.element(a,'Observed',header=TRUE)
> a<-table.element(a,'Fitted',header=TRUE)
> a<-table.element(a,'Residuals',header=TRUE)
> a<-table.row.end(a)
> for (i in 1:nxmK) {
+ a<-table.row.start(a)
+ a<-table.element(a,i+K,header=TRUE)
+ a<-table.element(a,x[i+K])
+ a<-table.element(a,fit$fitted[i,'xhat'])
+ a<-table.element(a,myresid[i])
+ a<-table.row.end(a)
+ }
> a<-table.end(a)
> table.save(a,file="/var/wessaorg/rcomp/tmp/54m8s1461604180.tab") 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'t',header=TRUE)
> a<-table.element(a,'Forecast',header=TRUE)
> a<-table.element(a,'95% Lower Bound',header=TRUE)
> a<-table.element(a,'95% Upper Bound',header=TRUE)
> a<-table.row.end(a)
> for (i in 1:np) {
+ a<-table.row.start(a)
+ a<-table.element(a,nx+i,header=TRUE)
+ a<-table.element(a,p[i,'fit'])
+ a<-table.element(a,p[i,'lwr'])
+ a<-table.element(a,p[i,'upr'])
+ a<-table.row.end(a)
+ }
> a<-table.end(a)
> table.save(a,file="/var/wessaorg/rcomp/tmp/655zc1461604180.tab") 
> 
> try(system("convert tmp/185mj1461604180.ps tmp/185mj1461604180.png",intern=TRUE))
character(0)
> try(system("convert tmp/2mgzi1461604180.ps tmp/2mgzi1461604180.png",intern=TRUE))
character(0)
> try(system("convert tmp/3ffu11461604180.ps tmp/3ffu11461604180.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.719   0.255   1.978