Home » date » 2010 » Aug » 15 »

tijdreeks B - stap 27

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 15 Aug 2010 13:53:17 +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/Aug/15/t12818803802ilui3t81ghh44g.htm/, Retrieved Sun, 15 Aug 2010 15:53:04 +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/Aug/15/t12818803802ilui3t81ghh44g.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:

Vanhille Olivier

Dataseries X:

» Textbox « » Textfile « » CSV «

31 30 29 27 25 24 25 27 28 28 29 31 31 27 25 16 20 21 25 24 28 27 23 36 37 30 27 22 22 25 33 35 35 29 25 34 31 29 21 19 18 25 23 22 20 15 17 25 26 26 23 24 24 42 40 45 47 40 39 49 55 54 48 44 48 62 57 60 56 57 54 62 65 68 69 67 72 82 72 77 79 78 76 79

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.520658832476764
beta	0.0678765650221037
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	31	33.4532585470086	-2.45325854700856
14	27	27.9437063932416	-0.94370639324157
15	25	25.1867648143935	-0.186764814393538
16	16	15.7339978528039	0.266002147196119
17	20	19.7763686665064	0.223631333493604
18	21	20.5545819923583	0.445418007641692
19	25	21.6306784855388	3.36932151446123
20	24	25.2648714500173	-1.26487145001733
21	28	25.6081963514624	2.39180364853759
22	27	27.2732623898038	-0.273262389803808
23	23	28.5827476842846	-5.58274768428455
24	36	27.5971719516467	8.40282804835326
25	37	30.8059890247375	6.19401097526254
26	30	30.9832039372554	-0.983203937255428
27	27	29.0280343300294	-2.02803433002937
28	22	19.2280559865024	2.77194401349764
29	22	25.0378508230883	-3.03785082308835
30	25	24.5919869542073	0.408013045792671
31	33	27.4165644467442	5.58343555325582
32	35	30.4268528484166	4.57314715158338
33	35	36.2135641724594	-1.21356417245944
34	29	35.2475476858378	-6.24754768583777
35	25	31.2138392076751	-6.21383920767509
36	34	36.893664703057	-2.89366470305702
37	31	33.0529844221021	-2.05298442210209
38	29	25.0954388777109	3.90456112228908
39	21	24.9564784361844	-3.95647843618443
40	19	16.1572949530758	2.84270504692423
41	18	18.9255881332679	-0.92558813326794
42	25	21.0124152164847	3.98758478351532
43	23	28.0892037074704	-5.08920370747038
44	22	24.5889209187551	-2.58892091875512
45	20	23.1502235058480	-3.15022350584795
46	15	17.9718243487926	-2.97182434879256
47	17	14.984525480689	2.01547451931101
48	25	26.156057971405	-1.15605797140502
49	26	23.3000043929839	2.69999560701610
50	26	20.5177633091297	5.48223669087033
51	23	17.3327961938800	5.66720380611997
52	24	17.0441849675908	6.95581503240918
53	24	20.5338551851002	3.46614481489981
54	42	27.803717090431	14.1962829095690
55	40	36.7470111008024	3.25298889919762
56	45	39.9856056445666	5.0143943554334
57	47	43.7022438614486	3.29775613855138
58	40	43.6600891697479	-3.66008916974786
59	39	44.3742660117102	-5.37426601171016
60	49	51.5860705744416	-2.58607057444163
61	55	51.1913479564231	3.80865204357686
62	54	51.7166762658159	2.28332373418412
63	48	48.238472867004	-0.238472867003964
64	44	46.567637215551	-2.56763721555102
65	48	44.1644653155483	3.83553468445174
66	62	57.5214746833746	4.47852531662537
67	57	56.5675547520905	0.432445247909548
68	60	59.4902366714996	0.509763328500441
69	56	60.1877617203684	-4.18776172036841
70	57	52.797600284895	4.20239971510503
71	54	56.946216368561	-2.94621636856097
72	62	67.0069523359703	-5.00695233597027
73	65	68.579723856218	-3.57972385621802
74	68	64.428661004104	3.57133899589599
75	69	60.359377007644	8.64062299235602
76	67	62.4559524697236	4.54404753027639
77	72	67.3370724590954	4.66292754090462
78	82	81.9745501287923	0.0254498712076980
79	72	77.1467373538709	-5.14673735387086
80	77	77.3885519880269	-0.388551988026904
81	79	75.5218188247705	3.47818117522954
82	78	76.5708412871303	1.42915871286971
83	76	76.17700439504	-0.177004395040044
84	79	87.1177103046551	-8.11771030465512

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	88.0709825874344	79.9318722909175	96.2100928839512
86	89.654057753689	80.3414952710306	98.9666202363473
87	86.4715524088686	75.9887759251402	96.954328892597
88	82.116601038448	70.4587736691284	93.7744284077678
89	84.5391646783512	71.6963338922907	97.3819954644116
90	94.2114816823078	80.1703219083364	108.252641456279
91	86.5758442362093	71.3207464430091	101.830942029410
92	91.6447039946182	75.1584885600217	108.130919429215
93	91.7140466131396	73.9784464277361	109.449646798543
94	89.7273100976916	70.7233071895518	108.731313005831
95	87.5263293599821	67.2343947243924	107.818263995572
96	94.4660027198954	72.8662702628792	116.065735176912

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/15/t12818803802ilui3t81ghh44g/1k5w81281880395.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/15/t12818803802ilui3t81ghh44g/1k5w81281880395.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/15/t12818803802ilui3t81ghh44g/2k5w81281880395.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/15/t12818803802ilui3t81ghh44g/2k5w81281880395.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/15/t12818803802ilui3t81ghh44g/3k5w81281880395.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/15/t12818803802ilui3t81ghh44g/3k5w81281880395.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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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