Home » date » 2009 » Jun » 07 »

opdracht 10 oefening 2

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 07 Jun 2009 14:07:23 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/07/t12444052782fr3u51ebywvawp.htm/, Retrieved Sun, 07 Jun 2009 22:07:58 +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/2009/Jun/07/t12444052782fr3u51ebywvawp.htm/},
    year = {2009},
}
@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 = {2009},
    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:

thomas cammaert

Dataseries X:

» Textbox « » Textfile « » CSV «

8.9722 8.8284 8.7446 8.7519 8.6337 8.7272 8.6330 8.5865 8.5968 8.5114 8.3884 8.2671 8.2410 8.3177 8.4070 8.3917 8.4145 8.5245 8.6289 8.6622 8.9055 8.9770 9.1264 9.1120 9.0576 9.2106 9.2637 9.3107 9.6744 9.5780 9.4166 9.4359 9.2275 9.1828 9.0594 9.1358 9.2208 9.1137 9.2689 9.2489 9.1679 9.1051 9.0818 9.0961 9.1733 9.1455 9.2265 9.1541 9.1559 9.1182 9.1856 9.2378 9.0682 9.0105 8.9939 9.0228 9.1368 9.1763 9.2346 9.1653 9.1277 9.1430 9.1962 9.1861 9.0920 9.0620 8.9981 8.9819 9.0476 9.0852 9.0884 9.1670 9.1931 9.2628 9.4276 9.3398 9.3342 9.4223 9.5614 9.4316 9.3111 9.3414 9.4017 9.3346 9.3310 9.2349 9.2170 9.2098 9.2665 9.2533 9.1008 9.0377 9.0795 9.1896 9.2992 9.2372 9.2061 9.3290 9.1842 9.3231 9.2835 9.1735 9.2889 9.4319 9.4314 9.3642 9.4020 9.3699 9.3106 9.3739 9.4566 9.3984 9.5637 9.8506

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.992290585513234
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	8.241	8.3819770181997	-0.140977018199701
14	8.3177	8.31585744262818	0.00184255737182326
15	8.407	8.3910670779966	0.0159329220033975
16	8.3917	8.35969287637122	0.0320071236287838
17	8.4145	8.36484799852158	0.0496520014784192
18	8.5245	8.45879443148934	0.0657055685106567
19	8.6289	8.6333521255316	-0.00445212553160879
20	8.6622	8.63437083296879	0.0278291670312107
21	8.9055	8.7083573220379	0.197142677962091
22	8.977	8.84571797651906	0.131282023480942
23	9.1264	8.8715001187277	0.254899881272301
24	9.112	9.01120274663895	0.100797253361051
25	9.0576	9.09053184558146	-0.0329318455814551
26	9.2106	9.14014686139465	0.0704531386053482
27	9.2637	9.29143080129675	-0.0277308012967481
28	9.3107	9.2120555940278	0.098644405972209
29	9.6744	9.2805714855982	0.393828514401807
30	9.578	9.72285221171003	-0.144852211710033
31	9.4166	9.7013970074293	-0.284797007429304
32	9.4359	9.42500069480678	0.0108993051932167
33	9.2275	9.48771479612216	-0.260214796122158
34	9.1828	9.16858275646035	0.0142172435396475
35	9.0594	9.07672762191811	-0.0173276219181133
36	9.1358	8.94594327460625	0.189856725393746
37	9.2208	9.11256011055628	0.108239889443716
38	9.1137	9.30454081328385	-0.190840813283854
39	9.2689	9.19495240277794	0.0739475972220642
40	9.2489	9.217412560946	0.0314874390540094
41	9.1679	9.2216235892913	-0.0537235892913053
42	9.1051	9.21315757624781	-0.108057576247809
43	9.0818	9.2210982165426	-0.139298216542608
44	9.0961	9.09105783669703	0.00504216330296714
45	9.1733	9.14402183186521	0.0292781681347876
46	9.1455	9.11461333784643	0.0308866621535682
47	9.2265	9.03948982199062	0.187010178009382
48	9.1541	9.1109865988198	0.0431134011802037
49	9.1559	9.1313083923065	0.0245916076934929
50	9.1182	9.23736886492803	-0.119168864928033
51	9.1856	9.20098535062063	-0.0153853506206261
52	9.2378	9.13493299243316	0.102867007566836
53	9.0682	9.20934956930592	-0.141149569305922
54	9.0105	9.1132251529313	-0.102725152931301
55	8.9939	9.12501604266818	-0.131116042668175
56	9.0228	9.0041185702758	0.0186814297242055
57	9.1368	9.07041406291554	0.0663859370844566
58	9.1763	9.07807468858107	0.0982253114189255
59	9.2346	9.07060169975421	0.163998300245789
60	9.1653	9.11806775790668	0.0472322420933189
61	9.1277	9.14230658597763	-0.0146065859776243
62	9.143	9.20810377195893	-0.0651037719589294
63	9.1962	9.22639784314708	-0.0301978431470857
64	9.1861	9.1464912530014	0.0396087469986046
65	9.092	9.1564056091722	-0.0644056091722032
66	9.062	9.13683926387122	-0.074839263871219
67	8.9981	9.17672348946052	-0.178623489460515
68	8.9819	9.00984580539766	-0.0279458053976569
69	9.0476	9.03002062842226	0.0175793715777353
70	9.0852	8.99005524172292	0.095144758277078
71	9.0884	8.98105560207107	0.107344397928927
72	9.167	8.97325205235057	0.193747947649433
73	9.1931	9.14239959557267	0.0507004044273334
74	9.2628	9.27317649362574	-0.0103764936257349
75	9.4276	9.34713469611821	0.0804653038817857
76	9.3398	9.37633515005932	-0.0365351500593238
77	9.3342	9.30938112156126	0.0248188784387384
78	9.4223	9.3794442673417	0.0428557326583068
79	9.5614	9.53979027166188	0.0216097283381256
80	9.4316	9.57348466577655	-0.141884665776550
81	9.3111	9.48337166335031	-0.17227166335031
82	9.3414	9.25394612379134	0.0874538762086576
83	9.4017	9.23449313600997	0.167206863990032
84	9.3346	9.28282243372659	0.0517775662734099
85	9.331	9.30954754510425	0.021452454895746
86	9.2349	9.4120295595693	-0.177129559569302
87	9.217	9.32097199836443	-0.103971998364429
88	9.2098	9.1674010774133	0.0423989225866954
89	9.2665	9.17966688474067	0.0868331152593314
90	9.2533	9.31106993029959	-0.0577699302995889
91	9.1008	9.36929712285692	-0.268497122856916
92	9.0377	9.11331815031477	-0.0756181503147708
93	9.0795	9.0865995592292	-0.00709955922919292
94	9.1896	9.02447348430168	0.165126515698322
95	9.2992	9.08441750303624	0.214782496963759
96	9.2372	9.18037614000364	0.0568238599963564
97	9.2061	9.21213532599548	-0.0060353259954784
98	9.329	9.2847189402321	0.0442810597678989
99	9.1842	9.41478571155857	-0.230585711558568
100	9.3231	9.13686997935832	0.186230020641679
101	9.2835	9.29183641964926	-0.00833641964926457
102	9.1735	9.32776731824655	-0.154267318246552
103	9.2889	9.28758854880838	0.00131145119162390
104	9.4319	9.3010667974472	0.130833202552795
105	9.4314	9.48186116181237	-0.0504611618123718
106	9.3642	9.37592629508195	-0.0117262950819512
107	9.402	9.2587570770869	0.143242922913091
108	9.3699	9.2812125339421	0.0886874660579018
109	9.3106	9.34374615358706	-0.0331461535870563
110	9.3739	9.39071271615963	-0.0168127161596257
111	9.4566	9.45839864756825	-0.00179864756824522
112	9.3984	9.409328986761	-0.0109289867609910
113	9.5637	9.36690303993556	0.196796960064443
114	9.8506	9.60653354441693	0.244066455583072

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
115	9.97121531651625	9.73676056930803	10.2056700637245
116	9.9853436576308	9.65418784176747	10.3164994734941
117	10.0378223935374	9.63469650208294	10.4409482849918
118	9.97868549201678	9.5171098638781	10.4402611201554
119	9.86748232183899	9.3558285919222	10.3791360517558
120	9.74142564470864	9.18067139061393	10.3021798988033
121	9.71396816463448	9.1024281380515	10.3255081912175
122	9.797416175066	9.13797531812443	10.4568570320076
123	9.88571800618774	9.1895491740406	10.5818868383349
124	9.83621376578563	9.10430465103645	10.5681228805348
125	9.80480499402076	9.03355695235378	10.5760530356877
126	9.8506	NA	NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t12444052782fr3u51ebywvawp/1rp6p1244405238.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t12444052782fr3u51ebywvawp/1rp6p1244405238.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t12444052782fr3u51ebywvawp/25fvl1244405238.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t12444052782fr3u51ebywvawp/25fvl1244405238.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t12444052782fr3u51ebywvawp/33kha1244405238.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t12444052782fr3u51ebywvawp/33kha1244405238.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=0, beta=0)

if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)

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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