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opgave10; oefening 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: Sun, 16 Jan 2011 18:13:18 +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/16/t12952020631tpd0qi7rqgq4rf.htm/, Retrieved Sun, 16 Jan 2011 19:21:03 +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/16/t12952020631tpd0qi7rqgq4rf.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 «

17.88 18.11 18.16 18.27 18.29 18.35 18.35 18.38 18.41 18.41 18.42 18.43 18.48 18.54 18.65 18.66 18.69 18.72 18.72 18.73 18.84 18.83 18.91 18.91 18.94 18.97 19 19.08 19.18 19.24 19.23 19.25 19.3 19.33 19.35 19.35 19.31 19.47 19.7 19.76 19.9 19.97 20.1 20.26 20.44 20.43 20.57 20.6 20.69 20.93 20.98 21.11 21.14 21.16 21.32 21.32 21.48 21.58 21.74 21.75 21.81 21.89 22.21 22.37 22.47 22.51 22.55 22.61 22.58 22.85 22.93 22.98 23.01 23.11 23.18 23.18 23.21 23.22 23.12 23.15 23.16 23.21 23.21 23.22

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	0.967403347699123
beta	0.315348716873752
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	18.16	18.34	-0.180000000000000
4	18.27	18.3409549046228	-0.0709549046228268
5	18.29	18.4257542290714	-0.13575422907142
6	18.35	18.4064520083127	-0.0564520083127036
7	18.35	18.4466452408430	-0.0966452408430172
8	18.38	18.4184718996069	-0.0384718996069395
9	18.41	18.4348390439304	-0.0248390439303989
10	18.41	18.4568170261364	-0.0468170261364271
11	18.42	18.4432509925016	-0.0232509925016231
12	18.43	18.4453896522630	-0.0153896522630284
13	18.48	18.4504384868389	0.0295615131610951
14	18.54	18.5079915425422	0.0320084574578345
15	18.65	18.5776765814020	0.0723234185979713
16	18.66	18.7084261108668	-0.0484261108668029
17	18.69	18.7075888164949	-0.0175888164948965
18	18.72	18.7312178141602	-0.0112178141602293
19	18.72	18.7575879289278	-0.0375879289278238
20	18.73	18.7469805792995	-0.0169805792995348
21	18.84	18.7511285934756	0.0888714065243548
22	18.83	18.8847901201546	-0.0547901201546352
23	18.91	18.8627582156664	0.0472417843335755
24	18.91	18.9538443401615	-0.0438443401614919
25	18.94	18.9434378761519	-0.00343787615187807
26	18.97	18.9710719698638	-0.00107196986380487
27	19	19.0006678240313	-0.000667824031275188
28	19.08	19.0304509175506	0.0495490824493672
29	19.18	19.1239299235817	0.0560700764183331
30	19.24	19.240822625826	-0.000822625826000234
31	19.23	19.3024261794887	-0.0724261794887333
32	19.25	19.2726652041917	-0.0226652041916608
33	19.3	19.2841287026385	0.0158712973615209
34	19.33	19.3377143889295	-0.00771438892953569
35	19.35	19.3661297793088	-0.0161297793088231
36	19.35	19.3814833906962	-0.0314833906962093
37	19.31	19.3723792477801	-0.0623792477801004
38	19.47	19.3143563493240	0.155643650675966
39	19.7	19.5147316485192	0.185268351480786
40	19.76	19.8002856880873	-0.0402856880872875
41	19.9	19.8553480638197	0.0446519361803333
42	19.97	20.0062013211898	-0.0362013211898251
43	20.1	20.0677929512140	0.0322070487860273
44	20.26	20.2053884525539	0.0546115474460791
45	20.44	20.3813184531537	0.0586815468463442
46	20.43	20.5790877293438	-0.149087729343808
47	20.57	20.5303782074049	0.0396217925951312
48	20.6	20.6763143054005	-0.0763143054004729
49	20.69	20.6868122743805	0.00318772561948322
50	20.93	20.7751932518743	0.154806748125740
51	20.98	21.0574777817627	-0.0774777817626742
52	21.11	21.0914133790820	0.0185866209179686
53	21.14	21.2239522105225	-0.0839522105225434
54	21.16	21.2316833822965	-0.0716833822964844
55	21.32	21.2294150528264	0.0905849471736389
56	21.32	21.4117603443927	-0.0917603443927106
57	21.48	21.3897109168495	0.0902890831504841
58	21.58	21.5713211517785	0.00867884822147147
59	21.74	21.6766290232885	0.0633709767115356
60	21.75	21.8541787891139	-0.104178789113881
61	21.81	21.8378585894279	-0.0278585894278898
62	21.89	21.8868720031311	0.00312799686889775
63	22.21	21.9668162002933	0.243183799706657
64	22.37	22.3531791216908	0.0168208783092325
65	22.47	22.5256893304606	-0.055689330460595
66	22.51	22.6110638096493	-0.101063809649279
67	22.55	22.621711389555	-0.0717113895550021
68	22.61	22.6388776480230	-0.0288776480230304
69	22.58	22.6886717245608	-0.108671724560814
70	22.85	22.6281203260429	0.221879673957105
71	22.93	22.9550341570196	-0.0250341570195793
72	22.98	23.0354455659447	-0.0554455659446766
73	23.01	23.0695221302882	-0.0595221302882294
74	23.11	23.0814966318033	0.0285033681967093
75	23.18	23.1873228007946	-0.00732280079462555
76	23.18	23.2562566514916	-0.0762566514915797
77	23.21	23.2352400930027	-0.025240093002715
78	23.22	23.2558771438448	-0.0358771438448215
79	23.12	23.2552788571885	-0.135278857188450
80	23.15	23.1172495798865	0.0327504201134659
81	23.16	23.1517635391157	0.00823646088430507
82	23.21	23.1650753043375	0.044924695662484
83	23.21	23.2275845408534	-0.0175845408533561
84	23.22	23.2242576272969	-0.00425762729694057

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	23.2325243427059	23.0829547458548	23.382093939557
86	23.2449099010151	23.0028479282327	23.4869718737976
87	23.2572954593244	22.9192606867383	23.5953302319104
88	23.2696810176336	22.8297314504168	23.7096305848505
89	23.2820665759429	22.7337761672355	23.8303569846503
90	23.2944521342522	22.6314047828523	23.9574994856520
91	23.3068376925614	22.5227790809706	24.0908963041522
92	23.3192232508707	22.4081059412574	24.2303405604839
93	23.3316088091799	22.2875990594351	24.3756185589247
94	23.3439943674892	22.1614645562676	24.5265241787108
95	23.3563799257984	22.0298958612745	24.6828639903223
96	23.3687654841077	21.8930724111590	24.8444585570563

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/16/t12952020631tpd0qi7rqgq4rf/13mj11295201594.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t12952020631tpd0qi7rqgq4rf/13mj11295201594.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t12952020631tpd0qi7rqgq4rf/23v0i1295201594.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t12952020631tpd0qi7rqgq4rf/23v0i1295201594.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t12952020631tpd0qi7rqgq4rf/3n4md1295201594.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t12952020631tpd0qi7rqgq4rf/3n4md1295201594.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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