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taak 10

*Unverified author*
R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)
Title produced by software: Exponential Smoothing
Date of computation: Sun, 06 Jun 2010 19:17:39 +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/Jun/06/t1275852129h1codrpwmzrf8ts.htm/, Retrieved Sun, 06 Jun 2010 21:22:13 +0200
 
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/Jun/06/t1275852129h1codrpwmzrf8ts.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:
KDGP2W62
 
Dataseries X:
» Textbox « » Textfile « » CSV «
41086 39690 43129 93.2 96 95.2 77.1 70.9 64.8 70.1 77.3 79.5 100.6 100.7 107.1 95.9 82.8 83.3 80 80.4 67.5 75.7 71.1 89.3 101.1 105.2 114.1 96.3 84.4 91.2 81.9 80.5 70.4 74.8 75.9 86.3 98.7 100.9 113.8 89.8 84.4 87.2 85.6 72 69.2 77.5 78.1 94.3 97.7 100.2 116.4 97.1 93 96 80.5 76.1 69.9 73.6 92.6 94.2 93.5 108.5 109.4 105.1 92.5 97.1
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.891950774998702
beta0.0308709918356764
gammaFALSE


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
343129382944835
493.241343.7156807425-41250.5156807425
5962151.5702742753-2055.5702742753
695.2-2137.214161060582232.41416106058
777.1-2539.857127856522616.95712785652
870.9-2527.447722772482598.34772277248
964.8-2460.090433856892524.89043385689
1070.1-2388.729549807652458.82954980765
1177.3-2308.586854775112385.88685477511
1279.5-2227.809092055492307.30909205549
13100.6-2153.586135167232254.18613516723
14100.7-2064.676312459252165.37631245925
15107.1-1995.355966001212102.45596600121
1695.9-1924.265494615972020.16549461597
1782.8-1870.947997709031953.74799770903
1883.3-1823.074396075531906.37439607553
1980-1764.962923879011844.96292387901
2080.4-1710.825660411761791.22566041176
2167.5-1655.297266568361722.79726656836
2275.7-1613.365711017751689.06571101775
2371.1-1555.011934001171626.11193400117
2489.3-1508.034176354651597.33417635465
25101.1-1442.741518329151543.84151832915
26105.2-1382.651376479941487.85137647994
27114.1-1331.533094676151445.63309467615
2896.3-1278.265349168891374.56534916889
2984.4-1250.537320628331334.93732062833
3091.2-1221.397502959181312.59750295919
3181.9-1176.040799005571257.94079900557
3280.5-1144.797275018871225.29727501887
3370.4-1108.931110724031179.33111072403
3474.8-1081.591142423351156.39114242335
3575.9-1042.870798074541118.77079807454
3686.3-1006.900141892381093.20014189238
3798.7-963.6355435546031062.33554355460
38100.9-918.6488080879631019.54880808796
39113.8-883.752045037863997.552045037863
4089.8-841.007312176484930.807312176484
4184.4-832.165439113764916.565439113764
4287.2-810.788615106704897.988615106704
4385.6-781.25492338406866.85492338406
4472-755.621750649923827.621750649923
4569.2-742.19373657389811.39373657389
4677.5-720.898257003334798.398257003334
4778.1-689.209886075235767.309886075235
4894.3-664.122623145102758.422623145102
4997.7-626.078887113266723.778887113266
50100.2-599.00611342959699.20611342959
51116.4-574.598120700283690.998120700283
5297.1-538.484340275212635.584340275212
5393-534.295851965767627.295851965767
5496-520.227441830582616.227441830582
5580.5-499.063436453368579.563436453368
5676.1-494.643405087192570.743405087192
5769.9-482.374756670464552.274756670464
5873.6-471.37212437476544.97212437476
5992.6-451.877052405792544.477052405792
6094.2-417.831164061492512.031164061492
6193.5-398.626425448836492.126425448836
62108.5-383.624833386274492.124833386274
63109.4-355.073804721626464.473804721626
64105.1-338.396658135913443.496658135913
6592.5-328.218233565508420.718233565508
6697.1-326.772395452768423.872395452768


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
67-310.841702083763-10869.060922989410247.3775188219
68-672.984320339411-15016.063157392713670.0945167139
69-1035.12693859506-18519.438245827416449.1843686373
70-1397.26955685071-21684.623476783118890.0843630817
71-1759.41217510635-24639.965357844521121.1410076318
72-2121.55479336200-27453.335985843923210.2263991199
73-2483.69741161765-30165.533410131825198.1385868965
74-2845.84002987330-32803.200951885727111.5208921391
75-3207.98264812895-35384.782795782628968.8174995247
76-3570.12526638459-37923.612267104830783.3617343356
77-3932.26788464024-40429.655727889832565.1199586093
78-4294.41050289589-42910.56334632234321.7423405302
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Jun/06/t1275852129h1codrpwmzrf8ts/1rodu1275851857.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jun/06/t1275852129h1codrpwmzrf8ts/1rodu1275851857.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Jun/06/t1275852129h1codrpwmzrf8ts/2rodu1275851857.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jun/06/t1275852129h1codrpwmzrf8ts/2rodu1275851857.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Jun/06/t1275852129h1codrpwmzrf8ts/3rodu1275851857.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jun/06/t1275852129h1codrpwmzrf8ts/3rodu1275851857.ps (open in new window)


 
Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
 
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
 
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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Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa


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