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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: Wed, 22 Dec 2010 12:32:43 +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/Dec/22/t1293021211ynd2qrgc1y8unmq.htm/, Retrieved Wed, 22 Dec 2010 13:33:34 +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/2010/Dec/22/t1293021211ynd2qrgc1y8unmq.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:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

105,23 105,22 105,13 105 105,01 105,01 105,01 105,01 105,57 106,05 106,09 106,2 106,19 106,2 106,09 106,23 106,23 106,22 106,22 106,61 106,95 107,74 107,8 107,8 107,2 107,56 107,72 108,14 108,16 108,16 108,16 108,1 108,95 110,49 110,72 110,82 110,82 110,75 110,71 110,86 110,84 110,84 110,84 110,92 111,46 112,46 113,04 113,15 113,15 113,21 113,37 113,47 113,71 113,71 113,71 113,8 115,46 117 117,94 118,08 118,08 118,47 118,49 118,45 118,54 118,55 118,55 118,55 119,04 121,37 122 122,14

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	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.938027433409238
beta	0.0620541839691078
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	106.19	105.613982371795	0.576017628205136
14	106.2	106.190138082228	0.00986191777190015
15	106.09	106.108714919066	-0.0187149190664542
16	106.23	106.24564653112	-0.0156465311200549
17	106.23	106.230795613716	-0.00079561371580894
18	106.22	106.223578952746	-0.00357895274564157
19	106.22	106.357293117842	-0.137293117841750
20	106.61	106.280921431030	0.329078568970289
21	106.95	107.221174359354	-0.271174359353694
22	107.74	107.492172247262	0.247827752737777
23	107.8	107.813600709393	-0.0136007093935007
24	107.8	107.959843758246	-0.159843758246112
25	107.2	107.875716503113	-0.675716503112625
26	107.56	107.201320585597	0.358679414403014
27	107.72	107.424326425275	0.295673574724916
28	108.14	107.853652917905	0.286347082095475
29	108.16	108.137878940018	0.0221210599816288
30	108.16	108.168198498953	-0.00819849895314917
31	108.16	108.305236137954	-0.145236137954029
32	108.1	108.265796924267	-0.165796924267383
33	108.95	108.691318869248	0.258681130752166
34	110.49	109.509016763138	0.980983236862315
35	110.72	110.562156817856	0.157843182143907
36	110.82	110.930328407856	-0.110328407855775
37	110.82	110.933732692014	-0.113732692013883
38	110.75	110.956364166402	-0.206364166401798
39	110.71	110.718315628215	-0.00831562821501564
40	110.86	110.917095794235	-0.0570957942349679
41	110.84	110.897978779773	-0.0579787797726681
42	110.84	110.881811585024	-0.0418115850237086
43	110.84	111.007398159038	-0.167398159037560
44	110.92	110.973177644372	-0.0531776443720844
45	111.46	111.564482447818	-0.104482447818015
46	112.46	112.098983530486	0.361016469514482
47	113.04	112.496175968430	0.543824031570168
48	113.15	113.208866599562	-0.0588665995624922
49	113.15	113.262405712819	-0.112405712818855
50	113.21	113.282691774758	-0.0726917747575726
51	113.37	113.192236511128	0.177763488871747
52	113.47	113.583303680854	-0.113303680854344
53	113.71	113.528898346789	0.181101653211215
54	113.71	113.769404540243	-0.059404540242511
55	113.71	113.901088918017	-0.191088918017215
56	113.8	113.880728756492	-0.0807287564916521
57	115.46	114.470411057479	0.989588942521038
58	117	116.151114251901	0.848885748098681
59	117.94	117.136753633781	0.803246366219327
60	118.08	118.190022961225	-0.110022961224772
61	118.08	118.323864025975	-0.243864025974972
62	118.47	118.347253742122	0.122746257877736
63	118.49	118.590976213751	-0.100976213751323
64	118.45	118.821644832206	-0.371644832205973
65	118.54	118.647220923428	-0.107220923428486
66	118.55	118.689652470034	-0.139652470033809
67	118.55	118.820514781338	-0.270514781337923
68	118.55	118.810480533070	-0.260480533069696
69	119.04	119.365408234687	-0.325408234687316
70	121.37	119.794871378746	1.57512862125446
71	122	121.492174751962	0.507825248037676
72	122.14	122.227793936455	-0.0877939364546307

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	122.391546495267	121.649783695245	123.13330929529
74	122.697956637059	121.650918023435	123.744995250682
75	122.837079715853	121.530157807041	124.144001624664
76	123.175975060776	121.630269527286	124.721680594266
77	123.418466423437	121.645474457061	125.191458389814
78	123.617620638530	121.623966175420	125.611275101641
79	123.937656256187	121.727134393499	126.148178118876
80	124.264025740627	121.838644251646	126.689407229608
81	125.156461378494	122.517031137683	127.795891619305
82	126.125082841271	123.27157880495	128.978586877592
83	126.303178231142	123.234972936919	129.371383525365
84	126.520420996310	123.236442339935	129.804399652685

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293021211ynd2qrgc1y8unmq/15lc71293021160.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293021211ynd2qrgc1y8unmq/15lc71293021160.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293021211ynd2qrgc1y8unmq/25lc71293021160.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293021211ynd2qrgc1y8unmq/25lc71293021160.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293021211ynd2qrgc1y8unmq/3gvbb1293021160.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293021211ynd2qrgc1y8unmq/3gvbb1293021160.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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