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GuyVanHasseltOpgave 10

*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 11:57:23 -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/t12506182876a6s2sc989p87fe.htm/, Retrieved Tue, 18 Aug 2009 19:58:07 +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/Aug/18/t12506182876a6s2sc989p87fe.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 «

0.8800 1.0300 0.6900 0.7100 1.1100 1.0500 1.0300 0.6500 0.5900 0.7700 0.9000 1.2600 0.9600 0.8300 0.8700 0.7900 1.1200 0.8800 0.6400 0.6400 0.5800 0.5000 0.9900 1.0700 0.8900 0.8900 0.8300 0.8600 0.9000 1.1200 0.8800 0.8800 0.8900 0.8200 0.8800 0.8100 0.8800 0.7600 1.1300 0.8500 1.4500 1.5500 0.7100 0.8100 0.8300 0.7300 0.9000 0.9400 1.7800 0.8800 1.0400 0.8300 1.4100 0.9600 1.3000 0.8300 1.4000 0.9100 0.8700 0.9700 1.1900 1.2300 1.3300 1.1700 1.0900 0.6300 0.8900 0.6300 1.5100 0.9700 0.8400 0.9200 0.9500 0.7300 1.0200 0.7900 1.2700 0.9500 0.7500 0.5200 0.9500 0.8200 0.7600 1.2400 0.9400 1.0400 1.8100 0.9500 1.3900 0.8600 1.1500 1.5100 0.6000 0.7200 1.1000 1.6200 1.8400 1.7300 1.3600 1.0700 1.0000 1.4900 0.9000 1.4300 1.5400 0.8100 1.6100 1.3000 1.4000 1.0300 0.7900 1.1100 1.1500 1.0300 1.5900 1.1100 1.3300 0.9300 1.0700 1.1400 1.1200 0.8600 0.8200 1.0200 1.0700 1.3100 0.9800 0.8900 etc...

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	0.123215267387331
beta	0
gamma	0.172216746810459

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	0.96	0.984482323232324	-0.0244823232323237
14	0.83	0.868132393895657	-0.0381323938956566
15	0.87	0.904267234119018	-0.0342672341190178
16	0.79	0.831711654371085	-0.0417116543710853
17	1.12	1.16407214172458	-0.0440721417245842
18	0.88	0.922808447664324	-0.0428084476643238
19	0.64	1.00545046000559	-0.365450460005594
20	0.64	0.585421383859182	0.0545786161408183
21	0.58	0.532979635973936	0.0470203640260635
22	0.5	0.707939929366724	-0.207939929366724
23	0.99	0.8085685553693	0.181431444630699
24	1.07	1.19759034599861	-0.127590345998609
25	0.89	0.901505843022384	-0.0115058430223839
26	0.89	0.784693694249334	0.105306305750666
27	0.83	0.839085999789387	-0.00908599978938707
28	0.86	0.76850904733124	0.0914909526687607
29	0.9	1.11692570298516	-0.216925702985162
30	1.12	0.85455462518542	0.26544537481458
31	0.88	0.926460234134148	-0.046460234134148
32	0.88	0.609158760381252	0.270841239618748
33	0.89	0.582222595971043	0.307777404028957
34	0.82	0.750813894702628	0.0691861052973722
35	0.88	0.944382594095245	-0.0643825940952453
36	0.81	1.25645497447559	-0.446454974475589
37	0.88	0.938609894397542	-0.0586098943975419
38	0.76	0.833632093038398	-0.0736320930383976
39	1.13	0.848703559329938	0.281296440670062
40	0.85	0.829092976446526	0.0209070235534741
41	1.45	1.12224262023601	0.327757379763993
42	1.55	0.999821406652744	0.550178593347256
43	0.71	1.05971367956122	-0.349713679561217
44	0.81	0.752958326614725	0.0570416733852755
45	0.83	0.705256042029533	0.124743957970467
46	0.73	0.8152682520169	-0.0852682520169006
47	0.9	0.969637341661197	-0.069637341661197
48	0.94	1.22337046822984	-0.283370468229835
49	1.78	0.984183338299728	0.795816661700272
50	0.88	0.982215626369967	-0.102215626369967
51	1.04	1.04735831384033	-0.00735831384032704
52	0.83	0.952863033656425	-0.122863033656425
53	1.41	1.27463149903029	0.135368500969709
54	0.96	1.16208997747290	-0.202089977472904
55	1.3	0.993410230876597	0.306589769123403
56	0.83	0.828940326693948	0.00105967330605183
57	1.4	0.784563047834016	0.615436952165984
58	0.91	0.923324909630874	-0.0133249096308743
59	0.87	1.08891873823856	-0.218918738238562
60	0.97	1.29198505364232	-0.321985053642322
61	1.19	1.21099405173992	-0.0209940517399161
62	1.23	0.97278259510192	0.257217404898080
63	1.33	1.09653609060465	0.233463909395346
64	1.17	1.01427291721934	0.155727082780661
65	1.09	1.40936012900906	-0.319360129009059
66	0.63	1.18983387502388	-0.559833875023882
67	0.89	1.05388374140742	-0.163883741407416
68	0.63	0.785310185577734	-0.155310185577734
69	1.51	0.814434887507956	0.695565112492044
70	0.97	0.868128598165327	0.101871401834673
71	0.84	1.01687231681326	-0.176872316813263
72	0.92	1.20955668737438	-0.289556687374377
73	0.95	1.17801009791213	-0.228010097912132
74	0.73	0.95630020308896	-0.226300203088961
75	1.02	1.0168902403369	0.00310975966309934
76	0.79	0.894505890078289	-0.104505890078289
77	1.27	1.18579167602011	0.0842083239798916
78	0.95	0.979680399212409	-0.0296803992124086
79	0.75	0.968840555863587	-0.218840555863587
80	0.52	0.694790062778179	-0.174790062778179
81	0.95	0.849994175983726	0.100005824016274
82	0.82	0.740659911946438	0.079340088053562
83	0.76	0.844537959470516	-0.0845379594705165
84	1.24	1.03158432904724	0.208415670952758
85	0.94	1.07068888811715	-0.130688888117146
86	1.04	0.861228641194394	0.178771358805606
87	1.81	1.00636989867925	0.803630101320755
88	0.95	0.966372234563684	-0.0163722345636839
89	1.39	1.297012715315	0.0929872846849997
90	0.86	1.07478628333307	-0.214786283333073
91	1.15	1.01257595009782	0.137424049902180
92	1.51	0.789074188606982	0.720925811393018
93	0.6	1.09613753120049	-0.496137531200491
94	0.72	0.910228839820232	-0.190228839820232
95	1.1	0.95614678393098	0.143853216069019
96	1.62	1.21556955679404	0.404430443205959
97	1.84	1.22762235248268	0.612377647517316
98	1.73	1.15644682076571	0.573553179234289
99	1.36	1.44458303029565	-0.084583030295649
100	1.07	1.17132604323048	-0.101326043230479
101	1	1.50801187862358	-0.508011878623576
102	1.49	1.16526028418272	0.324739715817284
103	0.9	1.22271049992060	-0.322710499920601
104	1.43	1.03062016066523	0.399379839334773
105	1.54	1.11429119938424	0.425708800615758
106	0.81	1.08815934931670	-0.278159349316703
107	1.61	1.17368830516004	0.436311694839965
108	1.3	1.50849281097775	-0.208492810977747
109	1.4	1.47642351099803	-0.0764235109980345
110	1.03	1.31451478156523	-0.284514781565226
111	0.79	1.39754731522462	-0.60754731522462
112	1.11	1.05732499899430	0.052675001005704
113	1.15	1.35157776732695	-0.201577767326946
114	1.03	1.17232653826326	-0.142326538263258
115	1.59	1.07446401113035	0.515535988869652
116	1.11	1.09469192241281	0.0153080775871859
117	1.33	1.13501505085532	0.194984949144678
118	0.93	0.974172510632916	-0.0441725106329157
119	1.07	1.19641521184384	-0.126415211843843
120	1.14	1.36451961620046	-0.22451961620046
121	1.12	1.35041763910797	-0.230417639107973
122	0.86	1.13811332144572	-0.278113321445724
123	0.82	1.17315766461991	-0.353157664619906
124	1.02	0.96397163573682	0.0560283642631807
125	1.07	1.22024618072322	-0.150246180723223
126	1.31	1.05626654551077	0.253733454489234
127	0.98	1.10653993370559	-0.126539933705590
128	0.89	0.972121367429986	-0.0821213674299863
129	0.8	1.02757037189790	-0.227570371897902
130	0.8	0.778550502432437	0.0214494975675626
131	0.78	0.996460434599164	-0.216460434599164
132	0.97	1.13865642060915	-0.168656420609148

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
133	1.13054705824923	0.582599700663313	1.67849441583514
134	0.939431805972249	0.387340647965527	1.49152296397897
135	0.997412484652666	0.441208397277338	1.55361657202799
136	0.893526740501712	0.333239914958901	1.45381356604452
137	1.11175089518437	0.547410867416834	1.67609092295190
138	1.02728360206020	0.458919276117342	1.59564792800305
139	0.988873008578475	0.416512678831299	1.56123333832565
140	0.876753164956845	0.300424537234680	1.45308179267901
141	0.920358410262768	0.340088621978102	1.50062819854744
142	0.736979941811703	0.152795581134570	1.32116430248884
143	0.916323278969964	0.328250403108843	1.50439615483108
144	1.09240875869208	0.500472911334121	1.68434460605004

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t12506182876a6s2sc989p87fe/180441250618238.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t12506182876a6s2sc989p87fe/180441250618238.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t12506182876a6s2sc989p87fe/218ss1250618238.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t12506182876a6s2sc989p87fe/218ss1250618238.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t12506182876a6s2sc989p87fe/3twon1250618238.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t12506182876a6s2sc989p87fe/3twon1250618238.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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