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Paper ES

*The author of this computation has been verified*
R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)
Title produced by software: Exponential Smoothing
Date of computation: Mon, 13 Dec 2010 14:25:18 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/13/t1292250232rjek651fq4mkmev.htm/, Retrieved Mon, 13 Dec 2010 15:23:56 +0100
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/13/t1292250232rjek651fq4mkmev.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
2 1 -8 -1 1 -1 2 2 1 -1 -2 -2 -1 -8 -4 -6 -3 -3 -7 -9 -11 -13 -11 -9 -17 -22 -25 -20 -24 -24 -22 -19 -18 -17 -11 -11 -12 -10 -15 -15 -15 -13 -8 -13 -9 -7 -4 -4 -2 0
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.842236341974113
betaFALSE
gammaFALSE


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
212-1
3-81.15776365802589-9.15776365802589
4-1-6.55523770597335.5552377059733
51-1.876414621697692.87641462169769
6-10.546206307281824-1.54620630728182
72-0.756064836900522.75606483690052
821.565193129574050.434806870425947
911.93140327758681-0.931403277586815
10-11.14694158816940-2.14694158816940
11-2-0.661290641482488-1.33870935851751
12-2-1.78880031456679-0.211199685433212
13-1-1.966680365052140.96668036505214
14-8-1.15250703053243-6.84749296946757
15-4-6.919714460830252.91971446083025
16-6-4.46062483373166-1.53937516626834
17-3-5.75714254269532.7571425426953
18-3-3.434976893234410.434976893234406
19-7-3.06862354583340-3.9313764541666
20-9-6.37977166951383-2.62022833048617
21-11-8.58662319371944-2.41337680628056
22-13-10.6192568468463-2.38074315315366
23-11-12.62440525133841.62440525133839
24-9-11.25627211456762.25627211456760
25-17-9.35595774229599-7.64404225770401
26-22-15.7940479313202-6.20595206867985
27-25-21.0209263001117-3.97907369988826
28-20-24.3722467775514.37224677755103
29-24-20.6897816454183-3.31021835458165
30-24-23.4777678435168-0.522232156483238
31-22-23.91761074465451.91761074465446
32-19-22.30252928574643.30252928574643
33-18-19.52101910085701.52101910085698
34-17-18.23996153727841.23996153727844
35-11-17.19562086793256.19562086793245
36-11-11.97744381186650.977443811866546
37-12-11.1542051112748-0.845794888725166
38-10-11.86656430441511.86656430441512
39-15-10.2944760126051-4.70552398739493
40-15-14.2576393228200-0.742360677179983
41-15-14.8828824639935-0.117117536006489
42-13-14.98152310910061.98152310910064
43-8-13.31261233415455.31261233415455
44-13-8.83813715550967-4.16186284449033
45-9-12.34340929345123.34340929345118
46-7-9.52746848041262.52746848041261
47-4-7.398742673015023.39874267301502
48-4-4.536198076783530.536198076783532
49-2-4.084592570019822.08459257001982
500-2.328872949339912.32887294933991


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
51-0.367411515565401-7.096730054617846.36190702348704
52-0.367411515565401-9.16549576077468.43067272964379
53-0.367411515565401-10.833014449537310.0981914184065
54-0.367411515565401-12.269151016887311.5343279857565
55-0.367411515565401-13.549746723831412.8149236927006
56-0.367411515565401-14.716506258051813.9816832269210
57-0.367411515565401-15.795278455444515.0604554243137
58-0.367411515565401-16.803397543193316.0685745120625
59-0.367411515565401-17.753158410253117.0183353791223
60-0.367411515565401-18.653656440970517.9188334098397
61-0.367411515565401-19.511844436330318.7770214051995
62-0.367411515565401-20.333178974980319.5983559438495
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/13/t1292250232rjek651fq4mkmev/194wg1292250315.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/13/t1292250232rjek651fq4mkmev/194wg1292250315.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/13/t1292250232rjek651fq4mkmev/294wg1292250315.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/13/t1292250232rjek651fq4mkmev/294wg1292250315.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/13/t1292250232rjek651fq4mkmev/32vv11292250315.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/13/t1292250232rjek651fq4mkmev/32vv11292250315.ps (open in new window)


 
Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
 
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
 
R code (references can be found in the software module):
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
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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='mytable.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='mytable1.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='mytable2.tab')
 




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