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Prijsevolutie korte sigaretten (Opgave 10, deel 2)

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 20 Dec 2010 10:32:02 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/20/t12928412109tgpd7ryayfafzl.htm/, Retrieved Mon, 20 Dec 2010 11:33:34 +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/20/t12928412109tgpd7ryayfafzl.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 «

4.23 4.38 4.43 4.44 4.44 4.44 4.44 4.44 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.46 4.46 4.46 4.48 4.58 4.67 4.68 4.68 4.69 4.69 4.69 4.69 4.69 4.69 4.69 4.73 4.78 4.79 4.79 4.8 4.8 4.81 5.16 5.26 5.29 5.29 5.29 5.3 5.3 5.3 5.3 5.3 5.3 5.3 5.3 5.35 5.44 5.47 5.47 5.48 5.48 5.48 5.48 5.48 5.48 5.48 5.5 5.55 5.57 5.58 5.58 5.58 5.59 5.59 5.59 5.55

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	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.500243980146683
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	4.43	4.53	-0.0999999999999996
4	4.44	4.52997560198533	-0.0899756019853308
5	4.44	4.49496584873210	-0.0549658487320954
6	4.44	4.46746951379021	-0.0274695137902112
7	4.44	4.4537280548791	-0.0137280548791017
8	4.44	4.44686067806671	-0.0068606780667082
9	4.45	4.44342866516411	0.00657133483588712
10	4.45	4.45671593585729	-0.00671593585729369
11	4.45	4.45335632937363	-0.00335632937363162
12	4.45	4.45167734580908	-0.00167734580908263
13	4.45	4.45083826366546	-0.000838263665464467
14	4.45	4.45041892731304	-0.000418927313040385
15	4.45	4.45020936144657	-0.000209361446573020
16	4.45	4.45010462964325	-0.000104629643249865
17	4.46	4.45005228929407	0.00994771070593092
18	4.46	4.46502857169095	-0.00502857169095172
19	4.46	4.46251305897382	-0.00251305897381737
20	4.48	4.46125591635041	0.0187440836495893
21	4.58	4.49063253135949	0.089367468640515
22	4.67	4.63533806956785	0.0346619304321507
23	4.68	4.7426774916068	-0.062677491606796
24	4.68	4.7213234537398	-0.0413234537398015
25	4.69	4.7006516447676	-0.0106516447675951
26	4.69	4.70532322359395	-0.0153232235939456
27	4.69	4.69765787323463	-0.00765787323463307
28	4.69	4.69382706824828	-0.00382706824828105
29	4.69	4.69191260039547	-0.00191260039546837
30	4.69	4.69095583356121	-0.000955833561208763
31	4.69	4.69047768357619	-0.000477683576192156
32	4.73	4.69023872524279	0.0397612747572129
33	4.78	4.75012906358304	0.0298709364169589
34	4.79	4.81507181970697	-0.0250718197069695
35	4.79	4.81252979282723	-0.0225297928272346
36	4.8	4.80125939959146	-0.00125939959145871
37	4.8	4.81062939252723	-0.0106293925272318
38	4.81	4.80531210290287	0.00468789709713135
39	5.16	4.81765719520526	0.342342804794745
40	5.26	5.33891212245036	-0.0789121224503582
41	5.29	5.39943680823397	-0.109436808233968
42	5.29	5.37469170370846	-0.0846917037084589
43	5.29	5.33232518875994	-0.0423251887599356
44	5.3	5.3111522678742	-0.0111522678742064
45	5.3	5.31557341300515	-0.0155734130051508
46	5.3	5.30778290689899	-0.00778290689898586
47	5.3	5.30388955457473	-0.00388955457472662
48	5.3	5.30194382831327	-0.00194382831326756
49	5.3	5.30097143990112	-0.000971439901117144
50	5.3	5.30048548293851	-0.00048548293850903
51	5.3	5.30024262302106	-0.000242623021056154
52	5.35	5.30012125231533	0.049878747684672
53	5.44	5.37507279558184	0.0649272044181606
54	5.47	5.49755223873978	-0.0275522387397791
55	5.47	5.51376939717064	-0.0437693971706397
56	5.48	5.49187401972138	-0.0118740197213771
57	5.48	5.49593411283562	-0.0159341128356161
58	5.48	5.48796316881062	-0.00796316881062076
59	5.48	5.48397964155022	-0.0039796415502158
60	5.48	5.48198884982158	-0.00198884982157921
61	5.48	5.48099393967092	-0.00099393967091821
62	5.48	5.48049672733391	-0.000496727333912261
63	5.5	5.48024824247535	0.0197517575246513
64	5.55	5.51012894027437	0.0398710597256278
65	5.57	5.58007419788419	-0.0100741978841858
66	5.58	5.59503464103782	-0.0150346410378157
67	5.58	5.59751365236498	-0.0175136523649817
68	5.58	5.58875255319902	-0.00875255319901846
69	5.59	5.5843741411503	0.00562585884970446
70	5.59	5.59718844317301	-0.00718844317301492
71	5.59	5.59359246774909	-0.00359246774908772
72	5.55	5.59179535738374	-0.0417953573837355

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	5.53088748145444	5.4255616427844	5.63621332012448
74	5.51177496290889	5.32187472485534	5.70167520096243
75	5.49266244436333	5.20901145276714	5.77631343595951
76	5.47354992581777	5.08646716099425	5.86063269064129
77	5.45443740727221	4.95469764854542	5.95417716599901
78	5.43532488872666	4.81425295682991	6.0563968206234
79	5.4162123701811	4.66564138625880	6.16678335410339
80	5.39709985163554	4.5093096855093	6.28489001776179
81	5.37798733308998	4.34564714848373	6.41032751769623
82	5.35887481454443	4.17499407070954	6.54275555837931
83	5.33976229599887	3.99764991756302	6.68187467443472
84	5.32064977745331	3.81388021988794	6.82741933501868

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t12928412109tgpd7ryayfafzl/1lp9w1292841119.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t12928412109tgpd7ryayfafzl/1lp9w1292841119.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t12928412109tgpd7ryayfafzl/2wh9z1292841119.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t12928412109tgpd7ryayfafzl/2wh9z1292841119.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t12928412109tgpd7ryayfafzl/3wh9z1292841119.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t12928412109tgpd7ryayfafzl/3wh9z1292841119.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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