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opgave10_hanne jacobs_verbetering

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 18 Aug 2009 12:12:37 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Aug/18/t1250619226un6r2cpxqykitx5.htm/, Retrieved Tue, 18 Aug 2009 20:13:46 +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/2009/Aug/18/t1250619226un6r2cpxqykitx5.htm/},
    year = {2009},
}
@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 = {2009},
    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:

Dataseries X:

» Textbox « » Textfile « » CSV «

0.88 1.03 0.69 0.71 1.11 1.05 1.03 0.65 0.59 0.77 0.9 1.26 0.96 0.83 0.87 0.79 1.12 0.88 0.64 0.64 0.58 0.5 0.99 1.07 0.89 0.89 0.83 0.86 0.9 1.12 0.88 0.88 0.89 0.82 0.88 0.81 0.88 0.76 1.13 0.85 1.45 1.55 0.71 0.81 0.83 0.73 0.9 0.94 1.78 0.88 1.04 0.83 1.41 0.96 1.3 0.83 1.4 0.91 0.87 0.97 1.19 1.23 1.33 1.17 1.09 0.63 0.89 0.63 1.51 0.97 0.84 0.92 0.95 0.73 1.02 0.79 1.27 0.95 0.75 0.52 0.95 0.82 0.76 1.24 0.94 1.04 1.81 0.95 1.39 0.86 1.15 1.51 0.6 0.72 1.1 1.62 1.84 1.73 1.36 1.07 1 1.49 0.9 1.43 1.54 0.81 1.61 1.3 1.4 1.03 0.79 1.11 1.15 1.03 1.59 1.11 1.33 0.93 1.07 1.14 1.12 0.86 0.82 1.02 1.07 1.31 0.98 0.89 0.8 0.8 0.78 0.97

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.125224748724491
beta	0.00097099762190841
gamma	0.212367616296001

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	0.96	0.978218492913525	-0.0182184929135246
14	0.83	0.85406704310582	-0.0240670431058204
15	0.87	0.886464128110635	-0.0164641281106354
16	0.79	0.80824190251969	-0.0182419025196893
17	1.12	1.14435940868487	-0.0243594086848700
18	0.88	0.894502420320822	-0.0145024203208223
19	0.64	0.964826068801091	-0.324826068801091
20	0.64	0.581802604429366	0.0581973955706335
21	0.58	0.530965802431698	0.049034197568302
22	0.5	0.68703651045602	-0.187036510456020
23	0.99	0.766031411352103	0.223968588647897
24	1.07	1.11101242327162	-0.0410124232716242
25	0.89	0.85513207262983	0.0348679273701705
26	0.89	0.750082840267355	0.139917159732645
27	0.83	0.80037838292472	0.0296216170752797
28	0.86	0.733773092107518	0.126226907892482
29	0.9	1.06403082131679	-0.164030821316790
30	1.12	0.818069690540778	0.301930309459222
31	0.88	0.867042115588673	0.0129578844113271
32	0.88	0.595898739413786	0.284101260586214
33	0.89	0.568695481461476	0.321304518538524
34	0.82	0.726546182004914	0.0934538179950863
35	0.88	0.947773736420089	-0.0677737364200888
36	0.81	1.24148598574152	-0.431485985741516
37	0.88	0.932273251398703	-0.0522732513987033
38	0.76	0.829555047432056	-0.0695550474320562
39	1.13	0.833850173341046	0.296149826658954
40	0.85	0.814658068862088	0.0353419311379124
41	1.45	1.09514320238410	0.354856797615897
42	1.55	0.981669671423456	0.568330328576544
43	0.71	1.00501116557717	-0.295011165577174
44	0.81	0.718302438518354	0.0916975614816462
45	0.83	0.666397316628654	0.163602683371346
46	0.73	0.764166112476198	-0.0341661124761977
47	0.9	0.940479163017474	-0.0404791630174745
48	0.94	1.16874646554381	-0.228746465543811
49	1.78	0.950133689266295	0.829866310733705
50	0.88	0.94065371922092	-0.0606537192209202
51	1.04	1.02509946637753	0.0149005336224732
52	0.83	0.91158886297128	-0.0815888629712807
53	1.41	1.26572943546606	0.144270564533945
54	0.96	1.15091707776968	-0.190917077769678
55	1.3	0.922284563118872	0.377715436881128
56	0.83	0.780818220571969	0.0491817794280308
57	1.4	0.733649772186006	0.666350227813994
58	0.91	0.864099707032759	0.0459002929672413
59	0.87	1.07809735673952	-0.208097356739520
60	0.97	1.27699405605982	-0.306994056059820
61	1.19	1.23016944679741	-0.0401694467974052
62	1.23	0.94246979950866	0.28753020049134
63	1.33	1.09161515851543	0.238384841484567
64	1.17	0.976763268873482	0.193236731126518
65	1.09	1.46082417848526	-0.370824178485256
66	0.63	1.20371914882395	-0.57371914882395
67	0.89	1.02593397149463	-0.135933971494629
68	0.63	0.766338727156386	-0.136338727156386
69	1.51	0.794782162618796	0.715217837381204
70	0.97	0.819846806403314	0.150153193596686
71	0.84	0.991272649343572	-0.151272649343572
72	0.92	1.16859261206379	-0.248592612063794
73	0.95	1.17684925767621	-0.226849257676213
74	0.73	0.937075327576103	-0.207075327576103
75	1.02	1.00110389908400	0.0188961009159958
76	0.79	0.870060874544225	-0.0800608745442245
77	1.27	1.1512032501674	0.118796749832599
78	0.95	0.94404946228566	0.00595053771433929
79	0.75	0.92121887173072	-0.171218871730719
80	0.52	0.676875031376488	-0.156875031376488
81	0.95	0.829375991296465	0.120624008703535
82	0.82	0.70232208069962	0.117677919300379
83	0.76	0.795489236574378	-0.0354892365743783
84	1.24	0.93806348248323	0.301936517516771
85	0.94	1.01298720963013	-0.0729872096301276
86	1.04	0.813840647487391	0.226159352512609
87	1.81	0.969286346275972	0.840713653724028
88	0.95	0.912912913593765	0.0370870864062351
89	1.39	1.27435712276166	0.115642877238337
90	0.86	1.02595622787438	-0.165956227874384
91	1.15	0.944851266760192	0.205148733239808
92	1.51	0.723978133039435	0.786021866960565
93	0.6	1.11708490493514	-0.517084904935141
94	0.72	0.879906555323419	-0.159906555323419
95	1.1	0.91912426367198	0.18087573632802
96	1.62	1.19266352255836	0.427336477441636
97	1.84	1.20848696054761	0.631513039452389
98	1.73	1.1131085263519	0.6168914736481
99	1.36	1.4977527443149	-0.137752744314901
100	1.07	1.10782758001556	-0.0378275800155559
101	1	1.54786348788537	-0.547863487885366
102	1.49	1.12369400025756	0.366305999742438
103	0.9	1.18021747698010	-0.280217476980098
104	1.43	0.968764969057727	0.461235030942273
105	1.54	1.07645783541013	0.463542164589874
106	0.81	1.00897401639684	-0.198974016396842
107	1.61	1.12966382504202	0.480336174957979
108	1.3	1.54955081263107	-0.249550812631069
109	1.4	1.51167154942183	-0.111671549421827
110	1.03	1.30145390491299	-0.271453904912995
111	0.79	1.42940411534341	-0.639404115343414
112	1.11	1.02048155399035	0.0895184460096494
113	1.15	1.35629070103301	-0.206290701033012
114	1.03	1.14830322506779	-0.118303225067790
115	1.59	1.0312741668333	0.558725833166699
116	1.11	1.05758801914697	0.0524119808530332
117	1.33	1.10789229366873	0.222107706331272
118	0.93	0.90319137517595	0.0268086248240504
119	1.07	1.16216476116275	-0.0921647611627545
120	1.14	1.35064595779376	-0.210645957793758
121	1.12	1.34040532417100	-0.220405324171002
122	0.86	1.11006198056912	-0.250061980569117
123	0.82	1.15464873677918	-0.334648736779178
124	1.02	0.93709547826295	0.0829045217370505
125	1.07	1.18979577460339	-0.119795774603390
126	1.31	1.02319416151525	0.286805838484753
127	0.98	1.07499867226716	-0.0949986722671556
128	0.89	0.940847153475755	-0.0508471534757552
129	0.8	0.998248083419452	-0.198248083419452
130	0.8	0.750204184740329	0.0497958152596712
131	0.78	0.948974283473725	-0.168974283473725
132	0.97	1.07151006727841	-0.101510067278412

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
133	1.06853807737389	0.89306839686948	1.24400775787830
134	0.89142029320319	0.706172607849642	1.07666797855674
135	0.940455027279966	0.73941555002005	1.14149450453988
136	0.85188152218926	0.644590498702069	1.05917254567645
137	1.03185263074211	0.794420690414361	1.26928457106986
138	0.961421734437685	0.721113513890497	1.20172995498487
139	0.91277562332929	0.667744761515157	1.15780648514342
140	0.81238716840466	0.570846119549726	1.05392821725959
141	0.842764593419352	0.585142340323869	1.10038684651483
142	0.682809257391078	0.442294991279238	0.923323523502918
143	0.816973742782035	0.538750336441543	1.09519714912253
144	0.958537267942376	-34.4703634071978	36.3874379430825

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250619226un6r2cpxqykitx5/1532j1250619151.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250619226un6r2cpxqykitx5/1532j1250619151.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250619226un6r2cpxqykitx5/2ffxo1250619151.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250619226un6r2cpxqykitx5/2ffxo1250619151.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250619226un6r2cpxqykitx5/3q09r1250619151.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250619226un6r2cpxqykitx5/3q09r1250619151.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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=0, beta=0)

if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)

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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