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opdracht 10 deel 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: Sun, 16 Jan 2011 18:29:05 +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/t1295202407lzf39qcs74ys4y0.htm/, Retrieved Sun, 16 Jan 2011 19:26:51 +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/t1295202407lzf39qcs74ys4y0.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 «

110.04 111.73 110.99 115.83 125.33 123.03 123.46 130.34 131.21 132.97 133.91 133.14 135.31 133.09 135.39 131.85 130.25 127.65 118.3 119.73 122.51 123.28 133.52 153.2 163.63 168.45 166.26 162.31 161.56 156.59 157.97 158.68 163.55 162.89 164.95 159.82 159.05 166.76 164.55 163.22 160.68 155.24 157.6 156.56 154.82 151.11 149.65 148.99 148.53 146.7 145.11 142.7 143.59 140.96 140.77 139.81 140.58 139.59 138.05 136.06 135.98 134.75 132.22 135.37 138.84 138.83 136.55 135.63 139.14 136.09 135.97 134.51 134.54 134.08 132.86 134.48 129.08 133.13 134.78 134.13 132.43 127.84 128.12

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	'Herman Ole Andreas Wold' @ www.yougetit.org

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0586130494653002
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	110.99	113.42	-2.43000000000001
4	115.83	112.537570289799	3.29242971020068
5	125.33	117.570549635264	7.75945036473567
6	123.03	127.525354683316	-4.49535468331612
7	123.46	124.961868236899	-1.50186823689886
8	130.34	125.303839159639	5.03616084036088
9	131.21	132.47902390409	-1.2690239040904
10	132.97	133.274642543227	-0.304642543227317
11	133.91	135.016786514772	-1.1067865147719
12	133.14	135.891914382034	-2.75191438203404
13	135.31	134.960616288236	0.349383711764403
14	133.09	137.151094733016	-4.06109473301564
15	135.39	134.693061586546	0.696938413453864
16	131.85	137.033911272248	-5.18391127224814
17	130.25	133.190066424424	-2.94006642442415
18	127.65	131.417740165658	-3.7677401656581
19	118.3	128.596901424956	-10.296901424956
20	119.73	118.643368632396	1.08663136760428
21	122.51	120.137059410496	2.37294058950434
22	123.28	123.056144694647	0.223855305353496
23	133.52	123.839265536732	9.68073446326775
24	153.2	134.646682904688	18.5533170953118
25	163.63	155.414149397341	8.21585060265889
26	168.45	166.325705455114	2.12429454488571
27	166.26	171.270216836353	-5.01021683635253
28	162.31	168.786552749091	-6.4765527490915
29	161.56	164.456942242444	-2.8969422424444
30	156.59	163.53714362349	-6.94714362348986
31	157.97	158.159950350644	-0.189950350643727
32	158.68	159.528816781345	-0.848816781345477
33	163.55	160.189065041354	3.36093495864651
34	162.89	165.256059688334	-2.36605968833433
35	164.95	164.457377714784	0.492622285215873
36	159.82	166.546251809155	-6.72625180915517
37	159.05	161.022005679149	-1.97200567914908
38	166.76	160.136420412731	6.6235795872687
39	164.55	168.234648610717	-3.6846486107172
40	163.22	165.808680119435	-2.58868011943503
41	160.68	164.326949683545	-3.6469496835447
42	155.24	161.573190841346	-6.33319084134564
43	157.6	155.761983213289	1.83801678671131
44	156.56	158.229714982126	-1.66971498212624
45	154.82	157.091847895286	-2.27184789528593
46	151.11	155.218687962222	-4.10868796222186
47	149.65	151.267865231455	-1.61786523145472
48	148.99	149.713037216615	-0.723037216615239
49	148.53	149.010657800473	-0.480657800472528
50	146.7	148.522484981038	-1.82248498103755
51	145.11	146.585663578694	-1.4756635786942
52	142.7	144.909170436362	-2.20917043636211
53	143.59	142.369684220298	1.22031577970171
54	140.96	143.331210649457	-2.37121064945725
55	140.77	140.562226762368	0.20777323763204
56	139.81	140.384404985423	-0.574404985422859
57	140.58	139.390737357599	1.18926264240085
58	139.59	140.230443667685	-0.640443667685446
59	138.05	139.202905311312	-1.15290531131163
60	136.06	137.595330015271	-1.53533001527094
61	135.98	135.51533964114	0.464660358859703
62	134.75	135.462574801739	-0.712574801738697
63	132.22	134.190808619637	-1.97080861963667
64	135.37	131.545293516527	3.82470648347274
65	138.84	134.919471226833	3.92052877316669
66	138.83	138.619265373745	0.210734626254947
67	136.55	138.621617172818	-2.07161717281778
68	135.63	136.220193372994	-0.590193372994264
69	139.14	135.265600339629	3.87439966037115
70	136.09	139.002690718571	-2.9126907185705
71	135.97	135.781969033406	0.18803096659417
72	134.51	135.672990101752	-1.16299010175183
73	134.54	134.14482370539	0.395176294609826
74	134.08	134.197986193094	-0.117986193093657
75	132.86	133.731070662522	-0.871070662521646
76	134.48	132.460014554691	2.01998544530849
77	129.08	134.198412061517	-5.11841206151652
78	133.13	128.498406322171	4.6315936778289
79	134.78	132.819878151513	1.96012184848715
80	134.13	134.584766870376	-0.454766870376233
81	132.43	133.908111597308	-1.47811159730767
82	127.84	132.121474969139	-4.28147496913948
83	128.12	127.280524664989	0.839475335011144

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
84	127.609728874325	119.669801764698	135.549655983952
85	127.09945774865	115.53694563977	138.661969857529
86	126.589186622974	112.015892740242	141.162480505706
87	126.078915497299	108.771598235899	143.386232758699
88	125.568644371624	105.678650451113	145.458638292134
89	125.058373245949	102.674898537738	147.441847954159
90	124.548102120273	99.7247131562471	149.3714910843
91	124.037830994598	96.8057337488157	151.26992824038
92	123.527559868923	93.9030337874236	153.152085950422
93	123.017288743248	91.006195690753	155.028381795742
94	122.507017617572	88.1077024747243	156.90633276042
95	121.996746491897	85.2019897933534	158.791503190441

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295202407lzf39qcs74ys4y0/1qimv1295202543.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295202407lzf39qcs74ys4y0/1qimv1295202543.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295202407lzf39qcs74ys4y0/2ok7z1295202543.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295202407lzf39qcs74ys4y0/2ok7z1295202543.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295202407lzf39qcs74ys4y0/3sfn81295202543.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295202407lzf39qcs74ys4y0/3sfn81295202543.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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