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Oef 10 eigen reeks

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 16 Jan 2011 10:37:02 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/16/t1295174234z3h1pfdfozbw94o.htm/, Retrieved Sun, 16 Jan 2011 11:37:18 +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/2011/Jan/16/t1295174234z3h1pfdfozbw94o.htm/},
    year = {2011},
}
@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 = {2011},
    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 «

95.05 96.84 96.92 97.44 97.78 97.69 96.67 98.29 98.2 98.71 98.54 98.2 96.92 99.06 99.65 99.82 99.99 100.33 99.31 101.1 101.1 100.93 100.85 100.93 99.6 101.88 101.81 102.38 102.74 102.82 101.72 103.47 102.98 102.68 102.9 103.03 101.29 103.69 103.68 104.2 104.08 104.16 103.05 104.66 104.46 104.95 105.85 106.23 104.86 107.44 108.23 108.45 109.39 110.15 109.13 110.28 110.17 109.99 109.26 109.11 107.06 109.53 108.92 109.24 109.12 109 107.23 109.49 109.04 109.02 109.23 109.46

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	1 seconds
R Server	'Gwilym Jenkins' @ www.wessa.org

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.839609756658078
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	96.92	95.727887047296	1.19211295270411
14	99.06	98.8487199090604	0.211280090939638
15	99.65	99.5887572425202	0.0612427574798033
16	99.82	99.8076239830416	0.0123760169583988
17	99.99	100.010119190138	-0.0201191901382174
18	100.33	100.334018833715	-0.00401883371455369
19	99.31	99.1375490136702	0.172450986329821
20	101.1	100.982068691946	0.117931308054267
21	101.1	100.987203841497	0.112796158503414
22	100.93	101.598450835749	-0.668450835748814
23	100.85	100.878253803231	-0.0282538032312516
24	100.93	100.510484395141	0.419515604859185
25	99.6	99.7298619234008	-0.12986192340081
26	101.88	101.632187201947	0.247812798052678
27	101.81	102.388005016662	-0.578005016662289
28	102.38	102.061142191047	0.318857808952927
29	102.74	102.515132982109	0.224867017891199
30	102.82	103.05088109085	-0.230881090849579
31	101.72	101.657600712141	0.062399287859165
32	103.47	103.436700252881	0.0332997471185479
33	102.98	103.362779918081	-0.382779918080601
34	102.68	103.435473316207	-0.755473316207357
35	102.9	102.739934559805	0.160065440195226
36	103.03	102.592176467746	0.437823532253759
37	101.29	101.710067548379	-0.420067548379052
38	103.69	103.462061136265	0.227938863735389
39	103.68	104.071839373849	-0.391839373848569
40	104.2	104.046716358212	0.153283641787837
41	104.08	104.345839755097	-0.265839755096749
42	104.16	104.397254524234	-0.237254524233691
43	103.05	103.027412988485	0.0225870115147302
44	104.66	104.788107920917	-0.128107920917117
45	104.46	104.50729605908	-0.0472960590800113
46	104.95	104.802905303382	0.147094696618282
47	105.85	105.009233930805	0.84076606919524
48	106.23	105.465038831361	0.764961168639005
49	104.86	104.672140661174	0.187859338825831
50	107.44	107.108229917362	0.331770082637519
51	108.23	107.709413102009	0.52058689799091
52	108.45	108.545512138583	-0.095512138582734
53	109.39	108.563995496448	0.826004503551815
54	110.15	109.540006255599	0.609993744400697
55	109.13	108.847519969975	0.28248003002453
56	110.28	110.890403901729	-0.610403901729413
57	110.17	110.197317126773	-0.0273171267728145
58	109.99	110.549331001305	-0.559331001305367
59	109.26	110.272003742513	-1.01200374251302
60	109.11	109.143324199726	-0.0333241997262803
61	107.06	107.540451122751	-0.480451122750992
62	109.53	109.483752007306	0.0462479926938073
63	108.92	109.877890495608	-0.957890495608495
64	109.24	109.374508207608	-0.134508207607581
65	109.12	109.507465484342	-0.387465484342073
66	109	109.429465967802	-0.429465967801519
67	107.23	107.826001432288	-0.596001432287935
68	109.49	108.963658818814	0.526341181185899
69	109.04	109.320879329347	-0.280879329347314
70	109.02	109.3735197325	-0.353519732499947
71	109.23	109.195898521769	0.0341014782313351
72	109.46	109.102616346668	0.357383653332107

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	107.750807798455	106.892810333566	108.608805263344
74	110.19629940668	109.066318720502	111.326280092858
75	110.389311105429	109.049363613969	111.72925859689
76	110.825208958003	109.301781319208	112.348636596798
77	111.03025025919	109.345158035655	112.715342482725
78	111.271109369494	109.43811488829	113.104103850698
79	109.970260455435	108.022408602312	111.918112308558
80	111.829036005119	109.726414876233	113.931657134006
81	111.605681470026	109.390422853021	113.820940087032
82	111.883886601712	109.55323058314	114.214542620284
83	112.064471549247	109.625606462945	114.503336635549
84	111.986964880676	107.269251912329	116.704677849023

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295174234z3h1pfdfozbw94o/16dzz1295174221.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295174234z3h1pfdfozbw94o/16dzz1295174221.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295174234z3h1pfdfozbw94o/2o5bx1295174221.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295174234z3h1pfdfozbw94o/2o5bx1295174221.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295174234z3h1pfdfozbw94o/3jm4t1295174221.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295174234z3h1pfdfozbw94o/3jm4t1295174221.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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