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Opgave 10 oefening 2

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R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Tue, 19 Jan 2010 10:48:25 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/19/t1263923353sboft419iinsbb9.htm/, Retrieved Tue, 19 Jan 2010 18:49:17 +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/Jan/19/t1263923353sboft419iinsbb9.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 «

100,09 100,09 100,06 100,11 100,08 100,08 100,08 100,08 99,94 99,79 99,98 99,98 99,98 99,98 99,93 99,93 99,93 99,93 99,93 99,93 99,76 99,48 99,55 99,56 99,57 99,56 99,65 99,5 99,5 99,49 99,49 99,46 99,52 99,49 99,55 99,57 99,57 99,57 99,57 99,57 99,57 99,57 99,57 99,53 100,38 100,32 100,46 100,47 100,47 100,47 100,51 100,5 100,51 100,51 100,51 100,51 101,65 102,13 102,2 102,13 102,13 102,12 102,13 102,05 102 102,01 102,01 102,02 102,78 103,39 103,41 103,5 103,5 103,49 103,38 103,24 103,25 103,25 103,25 103,25 103,83 104,33 104,36 104,48 104,5 104,48 104,35 104,48 104,48 104,47 104,47 104,86 105,22 105,96 106,03 106,03

Output produced by software:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.805432048964002
beta	0.0400555709654088
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	99.98	100.056026080726	-0.0760260807263364
14	99.98	99.9894142160589	-0.00941421605888593
15	99.93	99.9273995275427	0.00260047245728856
16	99.93	99.9318135632775	-0.00181356327745164
17	99.93	99.9430369798857	-0.0130369798857259
18	99.93	99.9493926268917	-0.0193926268916869
19	99.93	99.8807096461471	0.049290353852868
20	99.93	99.9119441638902	0.0180558361097809
21	99.76	99.7796609650187	-0.0196609650187014
22	99.48	99.6093286667098	-0.129328666709796
23	99.55	99.6864859490623	-0.136485949062291
24	99.56	99.5627546164881	-0.00275461648813291
25	99.57	99.5319162312653	0.0380837687347082
26	99.56	99.5628321115556	-0.00283211155557694
27	99.65	99.5015794684123	0.148420531587661
28	99.5	99.6202070215222	-0.120207021522205
29	99.5	99.527635224943	-0.0276352249430403
30	99.49	99.514240465384	-0.0242404653841106
31	99.49	99.4483368437222	0.0416631562778349
32	99.46	99.4603251872479	-0.00032518724786712
33	99.52	99.2989491745507	0.221050825449339
34	99.49	99.3017501474772	0.188249852522759
35	99.55	99.6436567937717	-0.0936567937717427
36	99.57	99.5922707859568	-0.0222707859568203
37	99.57	99.5648513202444	0.00514867975563504
38	99.57	99.571411737407	-0.00141173740699685
39	99.57	99.550874919209	0.0191250807909569
40	99.57	99.519105554924	0.0508944450759401
41	99.57	99.5939106459389	-0.0239106459389262
42	99.57	99.5958534595258	-0.0258534595258340
43	99.57	99.5530632819972	0.0169367180028104
44	99.53	99.5477633308832	-0.0177633308831702
45	100.38	99.4254972043923	0.954502795607695
46	100.32	100.045325529682	0.274674470317706
47	100.46	100.439795689661	0.0202043103392526
48	100.47	100.534848558395	-0.0648485583945302
49	100.47	100.517568201039	-0.0475682010389562
50	100.47	100.517841675767	-0.0478416757673159
51	100.51	100.499704602518	0.0102953974815705
52	100.5	100.502260013732	-0.00226001373219731
53	100.51	100.553802081625	-0.0438020816253584
54	100.51	100.572847276984	-0.062847276983831
55	100.51	100.540575244873	-0.0305752448729635
56	100.51	100.520588403206	-0.0105884032060573
57	101.65	100.623483529554	1.02651647044583
58	102.13	101.198623155551	0.931376844448621
59	102.2	102.128217819249	0.0717821807507306
60	102.13	102.304674947031	-0.174674947031377
61	102.13	102.254796868257	-0.124796868256709
62	102.12	102.242856712216	-0.122856712216446
63	102.13	102.223152374765	-0.0931523747653245
64	102.05	102.183475917548	-0.133475917548068
65	102	102.16141160718	-0.161411607179957
66	102.01	102.118488968804	-0.108488968803996
67	102.01	102.090370631631	-0.0803706316307569
68	102.02	102.066965518238	-0.0469655182383093
69	102.78	102.377025189081	0.402974810919275
70	103.39	102.438403407218	0.951596592782167
71	103.41	103.228532419715	0.181467580284917
72	103.5	103.460957371917	0.0390426280828251
73	103.5	103.615869397064	-0.115869397063804
74	103.49	103.634643508598	-0.144643508598023
75	103.38	103.625628357974	-0.24562835797407
76	103.24	103.472105246967	-0.232105246966967
77	103.25	103.379491254403	-0.129491254403462
78	103.25	103.388246551634	-0.138246551633856
79	103.25	103.355986363042	-0.105986363042319
80	103.25	103.331805950095	-0.0818059500950596
81	103.83	103.718129933297	0.111870066703219
82	104.33	103.651118282643	0.678881717356617
83	104.36	104.064054390805	0.295945609194931
84	104.48	104.358381412519	0.121618587480512
85	104.5	104.550002703813	-0.0500027038132913
86	104.48	104.618845407868	-0.138845407867848
87	104.35	104.597456454143	-0.247456454143233
88	104.48	104.447318458697	0.0326815413028640
89	104.48	104.599583821849	-0.119583821848664
90	104.47	104.626603128107	-0.156603128107491
91	104.47	104.596981309612	-0.126981309611551
92	104.86	104.570876764188	0.289123235811758
93	105.22	105.322398830352	-0.102398830351973
94	105.96	105.206306941881	0.753693058118785
95	106.03	105.618396343367	0.411603656632536
96	106.03	105.992253162990	0.0377468370102605

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	106.101069445953	105.578672561934	106.623466329971
98	106.213113045307	105.531659391492	106.894566699122
99	106.306737881186	105.487755376750	107.125720385622
100	106.443550588108	105.498523081704	107.388578094511
101	106.571773618395	105.508028046882	107.635519189908
102	106.724152181374	105.546299324511	107.902005038237
103	106.867608062265	105.579034116346	108.156182008185
104	107.071334462219	105.673671470408	108.468997454029
105	107.556964544593	106.048285030223	109.065644058963
106	107.729150492297	106.114410522878	109.343890461715
107	107.475790585857	105.761837740730	109.189743430984
108	107.444598443947	102.684829795156	112.204367092738

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/19/t1263923353sboft419iinsbb9/1mzkq1263923303.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/19/t1263923353sboft419iinsbb9/1mzkq1263923303.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/19/t1263923353sboft419iinsbb9/230591263923303.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/19/t1263923353sboft419iinsbb9/230591263923303.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/19/t1263923353sboft419iinsbb9/3p33a1263923303.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/19/t1263923353sboft419iinsbb9/3p33a1263923303.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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')

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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