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Opgave 10 oefening 2 Exponential Smoothing

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 31 May 2010 15:05:24 +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/May/31/t127531836597j092n6j3org1k.htm/, Retrieved Mon, 31 May 2010 17:06:06 +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/2010/May/31/t127531836597j092n6j3org1k.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 «

41086 39690 43129 37863 35953 29133 24693 22205 21725 27192 21790 13253 37702 30364 32609 30212 29965 28352 25814 22414 20506 28806 22228 13971 36845 35338 35022 34777 26887 23970 22780 17351 21382 24561 17409 11514 31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698 31956 29506 34506 27165 26736 23691 18157 17328 18205 20995 17382 9367 31124 26551 30651 25859 25100 25778 20418 18688 20424 24776 19814 12738 31566 30111 30019 31934 25826 26835 20205 17789 20520 22518 15572 11509 25447 24090 27786 26195 20516 22759 19028 16971 20036 22485 18730 14538

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	1
beta	1
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	37702	41487.9961256583	-3785.99612565827
14	30364	26985.9661303211	3378.03386967886
15	32609	32727.9358210002	-118.935821000206
16	30212	30145.8777182379	66.1222817621128
17	29965	29887.9020499618	77.0979500382091
18	28352	28391.3748481016	-39.3748481016046
19	25814	22414.0196224931	3399.9803775069
20	22414	26784.6171673481	-4370.61716734807
21	20506	21340.5520439118	-834.552043911786
22	28806	23717.1159273104	5088.88407268965
23	22228	25561.4177256393	-3333.41772563932
24	13971	12837.671960038	1133.32803996199
25	36845	40601.5340145322	-3756.53401453224
26	35338	27298.9372480281	8039.06275197186
27	35022	44169.1342060279	-9147.13420602795
28	34777	29660.5384748421	5116.4615251579
29	26887	36705.4820559147	-9818.4820559147
30	23970	18314.5307848454	5655.46921515461
31	22780	17792.0531868026	4987.94681319737
32	17351	24394.9811555839	-7043.98115558389
33	21382	13941.302066818	7440.69793318201
34	24561	32526.7733061008	-7965.77330610083
35	17409	17693.0108338551	-284.01083385514
36	11514	9048.62009766836	2465.37990233164
37	31514	35051.2864794491	-3537.28647944907
38	27071	24344.484559837	2726.51544016304
39	29462	30993.2773260638	-1531.27732606379
40	26105	27597.7751894846	-1492.7751894846
41	22397	24647.8615532109	-2250.86155321087
42	23843	17930.7867942609	5912.21320573911
43	21705	20938.1454020331	766.854597966936
44	18089	22518.2329109566	-4429.23291095655
45	20764	16418.6787760518	4345.3212239482
46	25316	29981.5307429842	-4665.5307429842
47	17704	19578.8057375386	-1874.80573753865
48	15548	9031.5631155527	6516.4368844473
49	28029	57475.3424653159	-29446.3424653159
50	29383	9524.39222229387	19858.6077777061
51	36438	38979.699162503	-2541.69916250305
52	32034	38213.6173641055	-6179.61736410549
53	22679	29985.4261796034	-7306.42617960342
54	24319	12927.1553973278	11391.8446026722
55	18004	21479.2311892206	-3475.23118922059
56	17537	15397.1394332197	2139.8605667803
57	20366	18719.161823632	1646.83817636797
58	22782	29672.6780384295	-6890.67803842952
59	19169	15850.8961244703	3318.10387552967
60	13807	12106.8166832106	1700.18331678943
61	29743	45014.8164697156	-15271.8164697156
62	25591	16257.9261430452	9333.07385695475
63	29096	29340.4209292218	-244.420929221818
64	26482	28394.0018115126	-1912.00181151256
65	22405	25728.3604886563	-3323.36048865629
66	27044	17593.8675474604	9450.13245253962
67	17970	25984.3096810551	-8014.30968105509
68	18730	13365.9769347333	5364.02306526672
69	19684	21153.1133629432	-1469.11336294321
70	19785	26373.6035376064	-6588.60353760635
71	18479	11664.1606321177	6814.83936788228
72	10698	12765.8235286875	-2067.82352868753
73	31956	28541.1294322283	3414.87056777168
74	29506	26919.6386551179	2586.36134488209
75	34506	35849.4789327642	-1343.47893276417
76	27165	34513.3508750869	-7348.35087508686
77	26736	22126.4181600186	4609.58183998139
78	23691	25137.1476304567	-1446.14763045668
79	18157	17464.253448161	692.746551839035
80	17328	16131.0595314059	1196.94046859407
81	18205	18157.193264769	47.8067352310027
82	20995	24385.0774564696	-3390.07745646963
83	17382	15200.5198051526	2181.48019484744
84	9367	10808.7908846448	-1441.79088464483
85	31124	22889.4206634265	8234.5793365735
86	26551	28623.8134118605	-2072.81341186048
87	30651	30211.7736790038	439.22632099616
88	25859	30317.5117468502	-4458.51174685019
89	25100	23072.9965897536	2027.00341024635
90	25778	23266.3268667986	2511.67313320136
91	20418	21977.5195299962	-1559.51952999621
92	18688	18763.4129777217	-75.4129777216986
93	20424	18811.5758631851	1612.42413681493
94	24776	28331.3280990513	-3555.32809905126
95	19814	19052.9011431531	761.098856846937
96	12738	11896.906659231	841.093340768961
97	31566	37808.6848699408	-6242.68486994076
98	30111	21631.0465134341	8479.95348656592
99	30019	37488.1358370153	-7469.1358370153
100	31934	25601.573248766	6332.426751234
101	25826	35663.8163727304	-9837.81637273038
102	26835	18965.0591992382	7869.94080076176
103	20205	23104.6686210557	-2899.6686210557
104	17789	17609.655864695	179.344135304989
105	20520	17197.4400112226	3322.55998877743
106	22518	29742.4407326765	-7224.44073267652
107	15572	15256.8323835081	315.167616491928
108	11509	7817.87427377746	3691.12572622254
109	25447	38233.1770809934	-12786.1770809934
110	24090	14603.7967177617	9486.2032822383
111	27786	29825.2075899902	-2039.20758999023
112	26195	27463.0014345558	-1268.00143455579
113	20516	26360.0760125685	-5844.07601256846
114	22759	14293.6318910283	8465.3681089717
115	19028	20629.239528044	-1601.23952804403
116	16971	18399.4112133541	-1428.41121335415
117	20036	16635.198977721	3400.80102227902
118	22485	29556.8562177491	-7071.85621774909
119	18730	15712.1207918091	3017.87920819086
120	14538	11716.5270212753	2821.47297872474

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	49938.8861707181	37811.3720798114	62066.4002616249
122	47050.4085011136	24092.0787898346	70008.7382123925
123	58046.0567468415	15420.1830365067	100671.930457176
124	60632.5866213685	1707.4597081531	119557.713534584
125	66753.6356380269	-13344.3217216522	146851.592997706
126	69477.4872993832	-29128.3404435172	168083.315042284
127	59902.5221855174	-38063.2768795174	157868.321250552
128	59492.040879766	-50808.9184176144	169793.000177146
129	64584.5287470717	-69499.3606420824	198668.418136226
130	89074.7858480441	-115565.007657598	293714.579353686
131	77805.1252187176	-117880.470648379	273490.721085814
132	50847.8472650804	-87718.127610297	189413.822140458

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/31/t127531836597j092n6j3org1k/1ypmw1275318319.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/31/t127531836597j092n6j3org1k/1ypmw1275318319.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/31/t127531836597j092n6j3org1k/29g3z1275318319.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/31/t127531836597j092n6j3org1k/29g3z1275318319.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/31/t127531836597j092n6j3org1k/39g3z1275318319.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/31/t127531836597j092n6j3org1k/39g3z1275318319.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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