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Oefening 10 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, 15 Jan 2011 09:22:02 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/15/t1295083378hwj8dbnl2n3p2z7.htm/, Retrieved Sat, 15 Jan 2011 10:23:02 +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/2011/Jan/15/t1295083378hwj8dbnl2n3p2z7.htm/},
    year = {2011},
}
@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 = {2011},
    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 «

78.1 66.7 79 65.2 66.5 77.2 80.2 77.9 78 86.8 92.9 185.8 91 79.1 84.2 70.1 71.3 79.6 92.3 78.7 82.5 98.2 115.4 205.6 94 83.2 80.3 70.4 71.1 78.8 86.3 77.5 80.1 89.8 99.9 218 85.4 77.5 78.6 68.8 64.8 79.8 94.3 79.9 87.5 99.1 109.9 273.6 91.3 80.6 80.4 71.8 75.5 86.6 91.5 86.8 84.6 88.6 102.1 260.3 79 70.6 79.3 66.8 61.2 72.5 83.5 75.8 83.4 89.4 104.9 251.6 80 76.3 81.1 63.1 63.5 78.8 91.7 83.8 83.8 95.8 108.9 258.2 88.7 79.5 74.3 70.5 59.1 73.2 81.2 75 74.6 89.5 107 246.4 83.6 72.1 68.7 60.1 61.1 72.7 85.3 71.4 75.2 89.8 100.9 222.7

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' @ www.wessa.org

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.202668867194516
beta	0.0361437398259691
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	91	88.0907318376069	2.90926816239312
14	79.1	76.8732955384115	2.22670446158848
15	84.2	82.850502573438	1.34949742656197
16	70.1	69.0181457388467	1.08185426115332
17	71.3	69.6894707776347	1.61052922236534
18	79.6	77.2297392379897	2.37026076201026
19	92.3	87.1163442886052	5.18365571139479
20	78.7	85.5444416107519	-6.84444161075187
21	82.5	84.205514429794	-1.70551442979406
22	98.2	92.908094546464	5.29190545353599
23	115.4	100.384264813856	15.0157351861442
24	205.6	196.84531273027	8.75468726972954
25	94	106.417054500701	-12.4170545007014
26	83.2	91.7097731065047	-8.50977310650472
27	80.3	94.8935116008563	-14.5935116008563
28	70.4	77.5817227413766	-7.18172274137662
29	71.1	76.9043943348688	-5.80439433486879
30	78.8	83.3979177075786	-4.59791770757859
31	86.3	93.914725388047	-7.61472538804696
32	77.5	79.864090092618	-2.36409009261804
33	80.1	83.2689140735638	-3.16891407356385
34	89.8	96.9817464180764	-7.18174641807644
35	99.9	109.319212890896	-9.4192128908961
36	218	195.293142911239	22.7068570887611
37	85.4	90.371082648054	-4.97108264805395
38	77.5	79.90222471164	-2.40222471163999
39	78.6	79.131717771645	-0.531717771645091
40	68.8	70.3411711063421	-1.54117110634215
41	64.8	71.7082163191013	-6.90821631910134
42	79.8	78.7349275783317	1.06507242166825
43	94.3	87.830471826106	6.46952817389402
44	79.9	80.7603608180068	-0.860360818006839
45	87.5	83.7788374096996	3.72116259030041
46	99.1	95.6895936101202	3.41040638987981
47	109.9	108.468423751075	1.431576248925
48	273.6	222.414736736672	51.1852632633285
49	91.3	101.562640129634	-10.2626401296337
50	80.6	92.3975772484612	-11.7975772484612
51	80.4	91.4735139396573	-11.0735139396573
52	71.8	79.9235596060426	-8.12355960604263
53	75.5	75.8109847655769	-0.310984765576919
54	86.6	90.7141643328644	-4.11416433286442
55	91.5	103.213303879361	-11.7133038793611
56	86.8	86.6246816431135	0.175318356886478
57	84.6	93.5245674170871	-8.92456741708712
58	88.6	102.550537618654	-13.9505376186541
59	102.1	110.031774821288	-7.93177482128804
60	260.3	261.48071595557	-1.18071595557046
61	79	80.3678716777832	-1.3678716777832
62	70.6	71.1933367828603	-0.59333678286032
63	79.3	72.6111043304612	6.68889566953878
64	66.8	66.6370031715901	0.162996828409902
65	61.2	70.1176405671158	-8.91764056711581
66	72.5	79.8656559948387	-7.36565599483866
67	83.5	85.2445015194096	-1.74450151940964
68	75.8	79.8261500314943	-4.02615003149432
69	83.4	78.2588663240669	5.1411336759331
70	89.4	85.87114753383	3.52885246617002
71	104.9	101.564893916301	3.33510608369942
72	251.6	260.633676763997	-9.03367676399748
73	80	77.676098448208	2.32390155179208
74	76.3	69.790416571153	6.50958342884701
75	81.1	78.4291906846765	2.67080931532351
76	63.1	66.38312799317	-3.28312799316996
77	63.5	61.845506475575	1.65449352442499
78	78.8	74.9714912733168	3.82850872668324
79	91.7	87.1808478758934	4.51915212410664
80	83.8	81.3384780961003	2.46152190389965
81	83.8	88.5686912908092	-4.76869129080919
82	95.8	92.9877330172143	2.81226698278569
83	108.9	108.477216189309	0.42278381069066
84	258.2	257.167859347466	1.03214065253366
85	88.7	85.4539068696607	3.24609313033926
86	79.5	81.2471014758121	-1.74710147581214
87	74.3	85.2458490309654	-10.9458490309654
88	70.5	65.6872296762975	4.81277032370252
89	59.1	66.7809938570242	-7.6809938570242
90	73.2	79.7336713928898	-6.53367139288984
91	81.2	90.3029984040844	-9.10299840408436
92	75	79.8688352820427	-4.86883528204272
93	74.6	79.6044479095331	-5.00444790953311
94	89.5	89.7744248869431	-0.274424886943137
95	107	102.464693451173	4.53530654882677
96	246.4	252.236372272151	-5.83637227215129
97	83.6	80.6070221497752	2.9929778502248
98	72.1	72.07721738649	0.0227826135099605
99	68.7	68.8227110399023	-0.122711039902256
100	60.1	63.8242178936079	-3.72421789360791
101	61.1	52.9653732282369	8.13462677176308
102	72.7	69.8932733884642	2.80672661153582
103	85.3	80.2305170379047	5.06948296209534
104	71.4	76.0720343238506	-4.67203432385058
105	75.2	75.7681754027945	-0.568175402794523
106	89.8	90.6699091439106	-0.869909143910562
107	100.9	107.131345980209	-6.23134598020853
108	222.7	246.429334884454	-23.7293348844543

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	78.0605220888371	61.321890915703	94.7991532619712
110	66.3809486238104	49.2772328610168	83.4846643866041
111	62.8306953052581	45.3444313773371	80.3169592331792
112	54.8112541851752	36.9252584979176	72.6972498724329
113	54.0156751316866	35.7130685417922	72.3182817215811
114	64.8403077122598	46.1045346211004	83.5760808034192
115	76.1857901624215	57.0006327190111	95.370947605832
116	62.9684398543034	43.3180277775428	82.618851931064
117	66.6535887438471	46.5224052792684	86.7847722084257
118	81.2040516734978	60.5769361890322	101.831167157963
119	93.3474832011578	72.2096309037197	114.485335498596
120	219.782858241138	198.119817464553	241.445899017723

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/15/t1295083378hwj8dbnl2n3p2z7/106mm1295083321.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/15/t1295083378hwj8dbnl2n3p2z7/106mm1295083321.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/15/t1295083378hwj8dbnl2n3p2z7/27r2d1295083321.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/15/t1295083378hwj8dbnl2n3p2z7/27r2d1295083321.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/15/t1295083378hwj8dbnl2n3p2z7/3be2h1295083321.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/15/t1295083378hwj8dbnl2n3p2z7/3be2h1295083321.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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