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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: Mon, 31 May 2010 18:05:52 +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/May/31/t1275329183gjbby2pilkdp70l.htm/, Retrieved Mon, 31 May 2010 20:06:23 +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/2010/May/31/t1275329183gjbby2pilkdp70l.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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

132.8 132.5 131.4 131.4 130.7 131.5 131.2 130.1 130.5 129 128.2 128.4 127.3 127.7 127 123.9 125.4 124.6 124.5 124.8 124.1 124.2 122.8 122.3 121.1 121.7 122.2 122.2 122.7 121.7 121 119.8 120.2 116.6 116 118 117.1 116.2 113.3 114.3 113.6 113 112.9 112.7 112.5 113 111.9 110.9 109.8 108.3 109.2 109.2 108.7 109.8 110.8 110 109.6 109.5 110.8 111.6 113.1 114.3 114.1 113.8 112.6 112.7 111.5 110.7 110.4 109.7 110 111.3 109 108.2 107.2 108.7 110.3 110.3 109.5 109.5 109.4 109.6 111.3 110 109.5 110.693 109.195 108.095 108.199 106.87 105.278 108.711 111.192 109.641 109.42 109.935 111.126 110.733 110.34 111.766 111.294 111.54 112.008 111.007 114.963 112.045 110.703 108.894 107.51 111.35 112.964 115.203 115.182 115.191 112.346 110.774 113.07 111.138 109.092 107.971 107.051

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	0.815582747009687
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	127.3	130.810637626263	-3.51063762626266
14	127.7	128.847422147280	-1.14742214727978
15	127	127.699104440422	-0.699104440421593
16	123.9	124.495593587123	-0.595593587122551
17	125.4	125.934837733236	-0.534837733235804
18	124.6	125.177799972226	-0.577799972225591
19	124.5	126.031556283656	-1.53155628365568
20	124.8	124.111612069299	0.688387930701452
21	124.1	125.456382722162	-1.35638272216170
22	124.2	123.345973708958	0.85402629104209
23	122.8	123.775836150758	-0.975836150757843
24	122.3	123.688294355625	-1.38829435562475
25	121.1	121.375269950793	-0.275269950793131
26	121.7	122.486582235014	-0.786582235014251
27	122.2	121.715236854998	0.484763145001978
28	122.2	119.496357166335	2.70364283366544
29	122.7	123.637606043225	-0.937606043225358
30	121.7	122.544154419449	-0.8441544194486
31	121	123.004787520158	-2.00478752015819
32	119.8	121.108280087767	-1.30828008776702
33	120.2	120.447511766465	-0.247511766465024
34	116.6	119.649116331588	-3.04911633158767
35	116	116.558184786386	-0.558184786385723
36	118	116.735207829185	1.26479217081528
37	117.1	116.791255924892	0.308744075108322
38	116.2	118.284585165773	-2.08458516577342
39	113.3	116.689069012447	-3.38906901244653
40	114.3	111.719958348256	2.58004165174394
41	113.6	115.088891118331	-1.48889111833141
42	113	113.563054990359	-0.563054990358609
43	112.9	114.038907167466	-1.13890716746577
44	112.7	112.977044799074	-0.277044799074119
45	112.5	113.352958167211	-0.85295816721127
46	113	111.544106875781	1.45589312421889
47	111.9	112.586754070804	-0.686754070803559
48	110.9	112.995106626148	-2.09510662614763
49	109.8	110.134567467816	-0.334567467816143
50	108.3	110.661851709232	-2.36185170923171
51	109.2	108.599632419164	0.600367580836476
52	109.2	107.985044402229	1.21495559777104
53	108.7	109.490255134441	-0.790255134440912
54	109.8	108.704954616809	1.09504538319072
55	110.8	110.426927774763	0.373072225236996
56	110	110.757152003328	-0.757152003328429
57	109.6	110.635289857648	-1.03528985764846
58	109.5	109.103523997993	0.396476002006708
59	110.8	108.886987756419	1.91301224358060
60	111.6	111.155940354534	0.444059645466282
61	113.1	110.690975194481	2.40902480551919
62	114.3	113.082019768025	1.21798023197465
63	114.1	114.485733990629	-0.385733990628566
64	113.8	113.180239179012	0.619760820988191
65	112.6	113.830223865268	-1.23022386526817
66	112.7	113.033774384073	-0.333774384072896
67	111.5	113.457282484737	-1.95728248473745
68	110.7	111.678476769940	-0.978476769939817
69	110.4	111.324812544079	-0.92481254407933
70	109.7	110.14719240207	-0.447192402070058
71	110	109.522250213665	0.477749786334726
72	111.3	110.349727311302	0.950272688698092
73	109	110.659994252659	-1.65999425265876
74	108.2	109.512767916658	-1.31276791665766
75	107.2	108.556695040696	-1.35669504069567
76	108.7	106.644731739680	2.05526826031985
77	110.3	108.124322432746	2.17567756725407
78	110.3	110.270988148698	0.0290118513019877
79	109.5	110.690975539655	-1.19097553965483
80	109.5	109.717665209314	-0.217665209314490
81	109.4	109.994402375143	-0.594402375142565
82	109.6	109.174340460917	0.425659539083128
83	111.3	109.431856553971	1.86814344602901
84	110	111.480456107635	-1.48045610763479
85	109.5	109.326884321146	0.173115678853534
86	110.693	109.738745345710	0.95425465428987
87	109.195	110.623516046148	-1.42851604614764
88	108.095	109.282201671490	-1.18720167148965
89	108.199	108.139495384093	0.0595046159068033
90	106.87	108.164364756814	-1.29436475681351
91	105.278	107.280042295072	-2.00204229507204
92	108.711	105.824735129769	2.88626487023123
93	111.192	108.563507283177	2.62849271682262
94	109.641	110.560100017482	-0.919100017482208
95	109.42	109.986872336927	-0.566872336926934
96	109.935	109.431975498264	0.50302450173568
97	111.126	109.201043442293	1.92495655770674
98	110.733	111.185731167210	-0.452731167209521
99	110.34	110.483564479264	-0.14356447926437
100	111.766	110.234736967381	1.53126303261907
101	111.294	111.539077739818	-0.245077739817759
102	111.54	111.065858127541	0.474141872459242
103	112.008	111.493391212998	0.514608787002174
104	111.007	112.992109429676	-1.98510942967562
105	114.963	111.710335117425	3.25266488257519
106	112.045	113.561754594492	-1.51675459449223
107	110.703	112.566047013531	-1.86304701353136
108	108.894	111.151319907488	-2.25731990748849
109	107.51	108.931327379251	-1.42132737925061
110	111.35	107.748357019891	3.60164298010902
111	112.964	110.409883607728	2.55411639227209
112	115.203	112.670105160582	2.53289483941819
113	115.182	114.463771667873	0.718228332127353
114	115.191	114.908844373157	0.282155626843348
115	112.346	115.187259586243	-2.84125958624323
116	110.774	113.487998289697	-2.71399828969705
117	113.07	112.577690749174	0.492309250826281
118	111.138	111.298248559056	-0.160248559056427
119	109.092	111.345021600161	-2.25302160016095
120	107.971	109.539527225459	-1.56852722545864
121	107.051	108.035473570529	-0.984473570528891

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
122	108.135116036053	105.193744413258	111.076487658848
123	107.666022772661	103.870427758045	111.461617787277
124	107.839237441642	103.349090895417	112.329383987867
125	107.232462805545	102.141658301524	112.323267309567
126	107.011341544320	101.383627533306	112.639055555334
127	106.483623842636	100.365941317255	112.601306368017
128	107.125114023127	100.553895416738	113.696332629516
129	109.019595091960	102.024183133787	116.015007050132
130	107.218291051959	99.8229774713097	114.613604632609
131	107.009816597691	99.235143778354	114.784489417027
132	107.168080340990	99.0317167835196	115.304443898460
133	107.051	98.5683538072768	115.533646192723

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/31/t1275329183gjbby2pilkdp70l/192771275329148.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/31/t1275329183gjbby2pilkdp70l/192771275329148.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/31/t1275329183gjbby2pilkdp70l/2kboa1275329148.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/31/t1275329183gjbby2pilkdp70l/2kboa1275329148.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/31/t1275329183gjbby2pilkdp70l/3kboa1275329148.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/31/t1275329183gjbby2pilkdp70l/3kboa1275329148.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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