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opgave10_hanne jacobs

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 18 Jul 2009 06:13:05 -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/Jul/18/t12479193031u9b7syadirw5e5.htm/, Retrieved Sat, 18 Jul 2009 14:15:07 +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/Jul/18/t12479193031u9b7syadirw5e5.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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.153600290204256
beta	0.00875809637850753
gamma	0.180419308731852

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	0.96	0.978002136752137	-0.0180021367521371
14	0.83	0.855399266204118	-0.0253992662041179
15	0.87	0.885792692827306	-0.0157926928273064
16	0.79	0.808473780183224	-0.0184737801832237
17	1.12	1.13655153329496	-0.0165515332949606
18	0.88	0.89156894486688	-0.0115689448668803
19	0.64	0.971086120388833	-0.331086120388833
20	0.64	0.538163306031463	0.101836693968537
21	0.58	0.48770789034878	0.0922921096512194
22	0.5	0.66424391268317	-0.164243912683169
23	0.99	0.758238312382045	0.231761687617955
24	1.07	1.15378773039326	-0.0837877303932648
25	0.89	0.854673568162874	0.0353264318371262
26	0.89	0.73885568916299	0.151144310837010
27	0.83	0.797794044863255	0.0322059551367447
28	0.86	0.727463682910733	0.132536317089267
29	0.9	1.07925868164790	-0.179258681647904
30	1.12	0.810054732829124	0.309945267170876
31	0.88	0.890606268236178	-0.0106062682361777
32	0.88	0.573892801155152	0.306107198844848
33	0.89	0.554503934468388	0.335496065531612
34	0.82	0.73069657974282	0.0893034202571799
35	0.88	0.925925007719033	-0.0459250077190331
36	0.81	1.23207787030021	-0.422077870300208
37	0.88	0.900179468848156	-0.0201794688481559
38	0.76	0.794435057706646	-0.0344350577066463
39	1.13	0.807369023675621	0.322630976324378
40	0.85	0.798023212830682	0.0519767871693178
41	1.45	1.09077668970331	0.359223310296690
42	1.55	0.98065859382777	0.569341406172231
43	0.71	1.05412205611671	-0.344122056116706
44	0.81	0.73611514255196	0.0738848574480397
45	0.83	0.686802701135157	0.143197298864843
46	0.73	0.796862170407452	-0.0668621704074522
47	0.9	0.948242403690176	-0.0482424036901755
48	0.94	1.19738426983259	-0.257384269832594
49	1.78	0.95316312099194	0.82683687900806
50	0.88	0.977490814745658	-0.0974908147456585
51	1.04	1.03732807625044	0.00267192374955916
52	0.83	0.939137538199761	-0.109137538199761
53	1.41	1.25547754334222	0.154522456657784
54	0.96	1.14714352308623	-0.187143523086233
55	1.3	0.965040607328539	0.334959392671461
56	0.83	0.81620890739413	0.0137910926058705
57	1.4	0.769205276730065	0.630794723269935
58	0.91	0.92369301630739	-0.0136930163073893
59	0.87	1.08776562301761	-0.217765623017610
60	0.97	1.28038543731481	-0.310385437314809
61	1.19	1.19497415063005	-0.00497415063004802
62	1.23	0.950648127184446	0.279351872815554
63	1.33	1.08443488671062	0.245565113289383
64	1.17	1.00757630890499	0.162423691095011
65	1.09	1.40735376844290	-0.317353768442903
66	0.63	1.17519278102677	-0.545192781026773
67	0.89	1.01816851655071	-0.128168516550711
68	0.63	0.748879044002418	-0.118879044002418
69	1.51	0.775262857326527	0.734737142673473
70	0.97	0.846983252152128	0.123016747847872
71	0.84	1.00075990393264	-0.160759903932638
72	0.92	1.18793749048538	-0.267937490485378
73	0.95	1.15568707680261	-0.205687076802607
74	0.73	0.923682473266993	-0.193682473266993
75	1.02	0.978747654737433	0.0412523452625672
76	0.79	0.856631565189815	-0.0666315651898147
77	1.27	1.14647388383010	0.123526116169896
78	0.95	0.946345806308966	0.00365419369103404
79	0.75	0.937151602454259	-0.187151602454259
80	0.52	0.659986074116214	-0.139986074116214
81	0.95	0.813217684012273	0.136782315987727
82	0.82	0.698610555666976	0.121389444333023
83	0.76	0.807732831927355	-0.0477328319273547
84	1.24	0.994986924607375	0.245013075392625
85	0.94	1.05080424285307	-0.110804242853069
86	1.04	0.83510680764229	0.204893192357709
87	1.81	0.987705617918293	0.822294382081707
88	0.95	0.970570028161343	-0.020570028161343
89	1.39	1.29807458545431	0.0919254145456918
90	0.86	1.0762936490887	-0.216293649088699
91	1.15	1.00538843841614	0.144611561583860
92	1.51	0.788041028617531	0.721958971382469
93	0.6	1.11874830605443	-0.518748306054429
94	0.72	0.903035266158807	-0.183035266158807
95	1.1	0.941096541392478	0.158903458607522
96	1.62	1.20659716347372	0.413402836526276
97	1.84	1.23597281122229	0.604027188777706
98	1.73	1.18127383201011	0.548726167989891
99	1.36	1.48442039791460	-0.124420397914597
100	1.07	1.19533792884992	-0.125337928849916
101	1	1.52596794750683	-0.525967947506834
102	1.49	1.16341904681991	0.326580953180089
103	0.9	1.23295032852915	-0.332950328529151
104	1.43	1.03170983801076	0.398290161989240
105	1.54	1.12409723694927	0.415902763050731
106	0.81	1.10533013461671	-0.29533013461671
107	1.61	1.18032578806579	0.429674211934212
108	1.3	1.52861144507659	-0.228611445076588
109	1.4	1.48995026025923	-0.0899502602592306
110	1.03	1.32074483120732	-0.290744831207323
111	0.79	1.39155855329633	-0.60155855329633
112	1.11	1.0278097808923	0.0821902191077004
113	1.15	1.32817878041062	-0.178178780410619
114	1.03	1.14874986181696	-0.118749861816962
115	1.59	1.04807358420476	0.541926415795239
116	1.11	1.09296710034830	0.0170328996516975
117	1.33	1.12905720566231	0.200942794337688
118	0.93	0.967947247546804	-0.0379472475468036
119	1.07	1.19282155448416	-0.122821554484157
120	1.14	1.35460716613285	-0.214607166132855
121	1.12	1.33817858879710	-0.218178588797097
122	0.86	1.11734907941166	-0.257349079411659
123	0.82	1.14460847424558	-0.324608474245583
124	1.02	0.926964462171016	0.0930355378289837
125	1.07	1.18840579173005	-0.118405791730054
126	1.31	1.02648024975253	0.283519750247474
127	0.98	1.08827067174577	-0.108270671745768
128	0.89	0.952052392565045	-0.0620523925650451
129	0.8	1.00288638739959	-0.202886387399587
130	0.8	0.741531866754733	0.0584681332452672
131	0.78	0.966648281378973	-0.186648281378973
132	0.97	1.10292150023691	-0.132921500236906

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
133	1.09691207417237	0.545154188001452	1.64866996034329
134	0.902324350982898	0.343982413542959	1.46066628842284
135	0.957898960496919	0.392936892990835	1.522861028003
136	0.85338597605766	0.28176798939863	1.42500396271669
137	1.06761729484722	0.489307883001851	1.64592670669259
138	0.984783799801966	0.399747733339552	1.56981986626438
139	0.942343119897104	0.35054543973826	1.53414080005595
140	0.829105441310241	0.230511452668283	1.4276994299522
141	0.867340207732156	0.26191547424075	1.47276494122356
142	0.676708474809603	0.0644188128304275	1.28899813678878
143	0.85498331148686	0.235794784591202	1.47417183838252
144	1.02795139593341	0.401830309551795	1.65407248231502

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jul/18/t12479193031u9b7syadirw5e5/1lly01247919182.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jul/18/t12479193031u9b7syadirw5e5/1lly01247919182.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jul/18/t12479193031u9b7syadirw5e5/21wgm1247919182.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jul/18/t12479193031u9b7syadirw5e5/21wgm1247919182.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jul/18/t12479193031u9b7syadirw5e5/38cxw1247919182.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jul/18/t12479193031u9b7syadirw5e5/38cxw1247919182.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=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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