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*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: Tue, 07 Dec 2010 19:37:06 +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/07/t1291750494vkgxh2vd8vu0aa7.htm/, Retrieved Tue, 07 Dec 2010 20:34:57 +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/07/t1291750494vkgxh2vd8vu0aa7.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 «
103,48 103,93 103,89 104,4 104,79 104,77 105,13 105,26 104,96 104,75 105,01 105,15 105,2 105,77 105,78 106,26 106,13 106,12 106,57 106,44 106,54 107,1 108,1 108,4 108,84 109,62 110,42 110,67 111,66 112,28 112,87 112,18 112,36 112,16 111,49 111,25 111,36 111,74 111,1 111,33 111,25 111,04 110,97 111,31 111,02 111,07 111,36 111,54 112,05 112,52 112,94 113,33 113,78 113,77 113,82 113,89 114,25 114,41
 
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
alpha0.867063638016424
beta0.00881242346206717
gamma1


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13105.2104.3933146367520.806685363247837
14105.77105.7020480967550.0679519032454579
15105.78105.804938517938-0.0249385179378265
16106.26106.2483464790750.0116535209253641
17106.13106.0506544436440.0793455563557188
18106.12105.9947619847150.125238015284737
19106.57106.964201476668-0.394201476668044
20106.44106.751491806342-0.311491806342318
21106.54106.1710332626410.368966737359244
22107.1106.2725614957580.827438504242068
23108.1107.2708529949640.829147005035992
24108.4108.1782113289230.221788671076638
25108.84108.5737171591910.266282840808515
26109.62109.3314778924330.288522107567431
27110.42109.6307487536650.789251246334771
28110.67110.808677185860-0.138677185859734
29111.66110.5121906466121.14780935338825
30112.28111.4195421831070.86045781689252
31112.87112.993746511072-0.123746511071573
32112.18113.064935034215-0.88493503421465
33112.36112.1117421661640.248257833835794
34112.16112.202653102221-0.0426531022214078
35111.49112.473196054056-0.983196054055725
36111.25111.740998749006-0.49099874900557
37111.36111.531542193046-0.171542193046477
38111.74111.916446549854-0.176446549854404
39111.1111.879381694617-0.779381694617129
40111.33111.562120883960-0.232120883960093
41111.25111.343190326818-0.09319032681762
42111.04111.114391078504-0.0743910785039503
43110.97111.718116643191-0.748116643190926
44111.31111.1129073891390.197092610860565
45111.02111.222972078447-0.202972078447033
46111.07110.8549457003060.215054299693875
47111.36111.1968545126310.163145487368737
48111.54111.5057478130640.0342521869362287
49112.05111.7799066625660.270093337434261
50112.52112.536181694502-0.0161816945021940
51112.94112.5482457687340.39175423126629
52113.33113.3184548713180.0115451286823998
53113.78113.3303986873210.449601312679121
54113.77113.5800123812200.189987618780194
55113.82114.330707519984-0.510707519984095
56113.89114.066112835040-0.176112835040314
57114.25113.8056629424230.444337057576519
58114.41114.0656731637450.344326836254879


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
59114.524964165043113.613629459136115.436298870950
60114.686213997454113.475438672413115.896989322494
61114.972712825290113.519243485227116.426182165353
62115.465366558980113.800909701716117.129823416244
63115.554437528022113.699820481710117.409054574333
64115.940180617336113.910344816586117.970016418086
65116.006012902556113.812294466321118.199731338790
66115.833511408653113.484851585253118.182171232053
67116.327105508442113.830760675910118.823450340974
68116.554487004848113.916476158164119.192497851532
69116.535244626342113.760647167581119.309842085102
70116.399322324955113.492484869076119.306159780834
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750494vkgxh2vd8vu0aa7/12wof1291750623.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750494vkgxh2vd8vu0aa7/12wof1291750623.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750494vkgxh2vd8vu0aa7/22wof1291750623.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750494vkgxh2vd8vu0aa7/22wof1291750623.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750494vkgxh2vd8vu0aa7/3vn5i1291750623.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750494vkgxh2vd8vu0aa7/3vn5i1291750623.ps (open in new window)


 
Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
 
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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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Software written by Ed van Stee & Patrick Wessa


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