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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: Wed, 29 Dec 2010 09:58:39 +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/Dec/29/t1293616610vstam1sk29xvqyx.htm/, Retrieved Wed, 29 Dec 2010 10:56:50 +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/29/t1293616610vstam1sk29xvqyx.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:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

7.24 7.52 7.57 7.59 7.58 7.55 7.52 7.55 7.62 7.64 7.68 7.69 7.7 7.6 7.51 7.66 7.69 7.66 7.7 7.72 7.74 7.76 7.72 7.73 7.75 8.1 8.22 8.32 8.07 8.18 8.33 8.34 8.25 8.36 8.36 8.34 8.41 8.39 8.43 8.44 8.49 8.47 8.53 8.52 8.51 8.53 8.54 8.53 8.47 8.63 8.67 8.73 8.57 8.55 8.63 8.65 8.44 8.62 8.37 8.59 8.84 8.72 8.8 8.69 8.68 8.57 8.85 8.85 8.85 8.93 8.75 8.78 8.77 9.03 9.01 9.07 8.99 9.02 8.99 8.98 8.94 8.94 8.75 8.86

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	3 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.508302927087735
beta	0.00202277055986297
gamma	0.695819962431208

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	7.7	7.65636752136752	0.0436324786324764
14	7.6	7.57312761330967	0.0268723866903322
15	7.51	7.49389613111518	0.016103868884815
16	7.66	7.65129087081217	0.0087091291878334
17	7.69	7.68826913056361	0.00173086943638712
18	7.66	7.66503543343643	-0.00503543343643376
19	7.7	7.6308572274205	0.0691427725795046
20	7.72	7.6827884452114	0.0372115547885983
21	7.74	7.78019385838409	-0.0401938583840913
22	7.76	7.78862921360613	-0.0286292136061261
23	7.72	7.81583014229573	-0.0958301422957293
24	7.73	7.7771074449082	-0.0471074449081987
25	7.75	7.77511363066171	-0.0251136306617079
26	8.1	7.65111124570213	0.448888754297865
27	8.22	7.78305711206157	0.436942887938426
28	8.32	8.15261772854859	0.167382271451412
29	8.07	8.26880781850052	-0.198807818500519
30	8.18	8.14206385429702	0.037936145702977
31	8.33	8.15589030368484	0.174109696315156
32	8.34	8.25114301974713	0.0888569802528707
33	8.25	8.34926135188351	-0.0992613518835128
34	8.36	8.33251275396747	0.0274872460325319
35	8.36	8.36618749438794	-0.00618749438794453
36	8.34	8.3907334932471	-0.0507334932471029
37	8.41	8.3954510723871	0.0145489276128981
38	8.39	8.45485147158106	-0.0648514715810631
39	8.43	8.32211689197928	0.107883108020722
40	8.44	8.43239392675858	0.00760607324141915
41	8.49	8.34212339962733	0.147876600372667
42	8.47	8.47299410548398	-0.00299410548397638
43	8.53	8.51295904889718	0.0170409511028193
44	8.52	8.49939807463362	0.0206019253663836
45	8.51	8.49858311203715	0.011416887962854
46	8.53	8.5816935876789	-0.0516935876789084
47	8.54	8.56375400659804	-0.0237540065980433
48	8.53	8.56426695004882	-0.0342669500488242
49	8.47	8.59984339308978	-0.129843393089779
50	8.63	8.5586884484769	0.0713115515231078
51	8.67	8.55440923328873	0.115590766711268
52	8.73	8.6344491355605	0.095550864439497
53	8.57	8.6371158404428	-0.0671158404428027
54	8.55	8.6071099272806	-0.0571099272806013
55	8.63	8.62638910669707	0.00361089330293574
56	8.65	8.60717293159056	0.0428270684094407
57	8.44	8.6144884359516	-0.174488435951602
58	8.62	8.58129525632481	0.0387047436751864
59	8.37	8.61874211865705	-0.248742118657054
60	8.59	8.50094246116244	0.0890575388375634
61	8.84	8.56627841807682	0.273721581923178
62	8.72	8.79926647691246	-0.0792664769124567
63	8.8	8.73363062587593	0.0663693741240738
64	8.69	8.78177748913779	-0.0917774891377867
65	8.68	8.6333610908434	0.0466389091565969
66	8.57	8.66450739598698	-0.0945073959869767
67	8.85	8.68542045247449	0.164579547525509
68	8.85	8.76147629903783	0.0885237009621651
69	8.85	8.71774984298288	0.132250157017118
70	8.93	8.91380955013868	0.0161904498613161
71	8.75	8.84184064575374	-0.0918406457537433
72	8.78	8.91990134564693	-0.139901345646926
73	8.77	8.93233560799874	-0.162335607998738
74	9.03	8.82275661966846	0.207243380331539
75	9.01	8.9527267643729	0.0572732356271057
76	9.07	8.94227889634129	0.127721103658713
77	8.99	8.95315279314077	0.0368472068592318
78	9.02	8.93138287215713	0.0886171278428716
79	8.99	9.13456072744822	-0.144560727448217
80	8.98	9.0276805956285	-0.0476805956284974
81	8.94	8.92976341791745	0.0102365820825447
82	8.94	9.02405207516776	-0.0840520751677634
83	8.75	8.86402219194334	-0.11402219194334
84	8.86	8.91419556014425	-0.054195560144251

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	8.96243769898914	8.72431508851662	9.20056030946165
86	9.06190518838717	8.7946749411417	9.32913543563264
87	9.0350959298499	8.7415297862222	9.32866207347758
88	9.0194522312357	8.70163196059635	9.33727250187503
89	8.93399667851783	8.59355864279955	9.2744347142361
90	8.91085399597433	8.54912730940816	9.27258068254051
91	8.98876323834113	8.60685452785276	9.3706719488295
92	8.98821172453844	8.58706040873814	9.38936304033874
93	8.9340972362033	8.51451332239731	9.35368115000928
94	8.99066400286305	8.55335492371816	9.42797308200795
95	8.86293132217521	8.40852158637713	9.3173410579733
96	8.99147542490022	8.52052137993652	9.46242946986393

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616610vstam1sk29xvqyx/1gcpf1293616714.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616610vstam1sk29xvqyx/1gcpf1293616714.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616610vstam1sk29xvqyx/2gcpf1293616714.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616610vstam1sk29xvqyx/2gcpf1293616714.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616610vstam1sk29xvqyx/3q4oi1293616714.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616610vstam1sk29xvqyx/3q4oi1293616714.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=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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