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opgave 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: Sat, 18 Dec 2010 11:21:12 +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/18/t1292671163puau5zq94y9pjvb.htm/, Retrieved Sat, 18 Dec 2010 12:19:23 +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/18/t1292671163puau5zq94y9pjvb.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 «

68897 38683 44720 39525 45315 50380 40600 36279 42438 38064 31879 11379 70249 39253 47060 41697 38708 49267 39018 32228 40870 39383 34571 12066 70938 34077 45409 40809 37013 44953 37848 32745 43412 34931 33008 8620 68906 39556 50669 36432 40891 48428 36222 33425 39401 37967 34801 12657 69116 41519 51321 38529 41547 52073 38401 40898 40439 41888 37898 8771 68184 50530 47221 41756 45633 48138 39486 39341 41117 41629 29722 7054 56676 34870 35117 30169 30936 35699 33228 27733 33666 35429 27438 8170

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.422758923913050
beta	0.477844184477007
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	44720	8469	36251
4	39525	903.603143165987	38621.396856834
5	45315	2142.33283031470	43172.6671696853
6	50380	14026.5880606625	36353.4119393375
7	40600	30371.8002125007	10228.1997874993
8	36279	37738.5740196104	-1459.57401961042
9	42438	39869.3843785059	2568.61562149406
10	38064	44222.0413286801	-6158.04132868013
11	31879	43641.4224318185	-11762.4224318185
12	11379	38315.3404237785	-26936.3404237785
13	70249	21132.8611119413	49116.1388880587
14	39253	46024.3394358417	-6771.33943584168
15	47060	45920.9896928555	1139.01030714453
16	41697	49391.9056625523	-7694.9056625523
17	38708	47573.7346669561	-8865.7346669561
18	49267	43469.5925507119	5797.40744928814
19	39018	46735.5756687651	-7717.57566876514
20	32228	42728.9292775769	-10500.9292775769
21	40870	35424.2722049161	5445.72779508385
22	39383	35961.3139439187	3421.68605608126
23	34571	36333.8986752910	-1762.89867529104
24	12066	34158.5256828297	-22092.5256828297
25	70938	18925.6464212140	52012.353578786
26	34077	45528.4322029733	-11451.4322029733
27	45409	42987.9992492653	2421.00075073470
28	40809	46801.334489285	-5992.33448928497
29	37013	45847.3283493461	-8834.32834934613
30	44953	41907.1957137863	3045.80428621374
31	37848	43604.7869032431	-5756.78690324306
32	32745	40418.0589357797	-7673.05893577969
33	43412	34871.1530303936	8540.84696960635
34	34931	37904.1817449405	-2973.18174494048
35	33008	35468.9310238346	-2460.93102383461
36	8620	32753.0990701987	-24133.0990701987
37	68906	15999.9675086998	52906.0324913002
38	39556	42503.5169980974	-2947.51699809745
39	50669	44799.0435720099	5869.95642799015
40	36432	52008.0426043053	-15576.0426043053
41	40891	47003.9927319350	-6112.99273193495
42	48428	44765.6282924859	3662.37170751409
43	36222	47399.7327090261	-11177.7327090261
44	33425	41502.0044273972	-8077.00442739722
45	39401	35283.4776644658	4117.52233553418
46	37967	35052.0885133907	2914.91148660926
47	34801	34901.1345968503	-100.134596850323
48	12657	33455.3145628964	-20798.3145628964
49	69116	19057.6265404295	50058.3734595705
50	41519	44727.6725512194	-3208.67255121942
51	51321	47230.406284969	4090.59371503098
52	38529	53645.3226421855	-15116.3226421855
53	41547	48886.6516366273	-7339.65163662735
54	52073	45932.9334346069	6140.0665653931
55	38401	49918.2590058089	-11517.2590058089
56	40898	44112.157805532	-3214.15780553204
57	40439	41166.9654162397	-727.96541623972
58	41888	39125.7746461812	2762.22535381879
59	37898	39118.0983057955	-1220.09830579548
60	8771	37180.3835116219	-28409.3835116219
61	68184	18009.0940038727	50174.9059961273
62	50530	42195.992092592	8334.00790740797
63	47221	50377.8541793261	-3156.85417932607
64	41756	53064.1265291758	-11308.1265291758
65	45633	50019.9883947382	-4386.98839473825
66	48138	49015.594952092	-877.594952092048
67	39486	49317.5434094924	-9831.5434094924
68	39341	43848.0317232249	-4507.03172322489
69	41117	39719.026349529	1397.97365047099
70	41629	38368.8233951052	3260.17660489482
71	29722	38464.481066189	-8742.48106618904
72	7054	31719.8142019803	-24665.8142019803
73	56676	13260.6036654188	43415.3963345812
74	34870	32353.8022581639	2516.19774183613
75	35117	34664.804050695	452.195949305002
76	30169	36194.580078486	-6025.58007848597
77	30936	33768.5736183887	-2832.5736183887
78	35699	32120.2227414787	3578.77725852134
79	33228	33905.2868103312	-677.286810331163
80	27733	33754.2411452307	-6021.24114523068
81	33666	30127.6227514984	3538.37724850156
82	35429	31257.2161682204	4171.78383177962
83	27438	33497.3419922664	-6059.34199226636
84	8170	30188.1028656064	-22018.1028656064

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	15684.2145018833	-20477.2935874267	51845.7225911932
86	10488.6756122307	-32150.3248370596	53127.676061521
87	5293.13672257817	-46783.3620783369	57369.6355234932
88	97.597832925625	-63902.5230790567	64097.718744908
89	-5097.94105672692	-83052.8915909186	72857.0094774648
90	-10293.4799463795	-103896.722095331	83309.7622025718
91	-15489.018836032	-126198.196712498	95220.1590404335
92	-20684.5577256845	-149791.367747329	108422.252295960
93	-25880.0966153371	-174555.698614305	122795.505383631
94	-31075.6355049896	-200400.322065361	138249.051055381
95	-36271.1743946422	-227254.266961278	154711.918171993
96	-41466.7132842947	-255060.345768303	172126.919199714

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292671163puau5zq94y9pjvb/1piev1292671268.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292671163puau5zq94y9pjvb/1piev1292671268.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292671163puau5zq94y9pjvb/2hseg1292671268.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292671163puau5zq94y9pjvb/2hseg1292671268.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292671163puau5zq94y9pjvb/3hseg1292671268.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292671163puau5zq94y9pjvb/3hseg1292671268.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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