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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 20 Dec 2011 08:28:32 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/20/t13243877554bshg3qjgb1jn0k.htm/, Retrieved Mon, 06 May 2024 08:40:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157954, Retrieved Mon, 06 May 2024 08:40:43 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact105
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opdracht10] [2011-12-20 13:28:32] [d8250b9ce3002d69b5d9e1c2e7e991dc] [Current]
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Dataseries X:
217,5
218,6
220,4
221,8
222,5
223,4
225,5
226,5
227,8
228,5
229,1
229,9
230,8
231,9
236
237,5
239,1
240,5
241,4
243,2
243,6
244,3
244,5
245,1
245,8
246,7
247,7
248,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157954&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157954&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157954&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999951622803792
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999951622803792 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157954&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.999951622803792[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157954&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157954&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999951622803792
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2218.6217.51.09999999999999
3220.4218.5999467850841.80005321491583
4221.8220.3999129184721.40008708152757
5222.5221.7999322677130.700067732287437
6223.4222.4999661326860.90003386731405
7225.5223.3999564588852.10004354111499
8226.5225.4998984057821.00010159421842
9227.8226.4999516178891.30004838211107
10228.5227.7999371073040.700062892695655
11229.1228.499966132920.600033867079901
12229.9229.0999709720440.800029027956128
13230.8229.8999612968390.900038703161272
14231.9230.7999564586511.10004354134892
15236231.8999467829784.10005321702224
16237.5235.9998016509211.50019834907894
17239.1237.499927424611.60007257538987
18240.5239.0999225929751.40007740702492
19241.4240.4999322681810.900067731819433
20243.2241.3999564572471.80004354275326
21243.6243.199912918940.400087081059667
22244.3243.5999806449090.700019355091229
23244.5244.2999661350260.200033864973676
24245.1244.4999903229220.600009677077537
25245.8245.0999709732140.700029026785899
26246.7245.7999661345580.900033865441543
27247.7246.6999564588851.00004354111491
28248.5247.6999516206970.800048379302609

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 218.6 & 217.5 & 1.09999999999999 \tabularnewline
3 & 220.4 & 218.599946785084 & 1.80005321491583 \tabularnewline
4 & 221.8 & 220.399912918472 & 1.40008708152757 \tabularnewline
5 & 222.5 & 221.799932267713 & 0.700067732287437 \tabularnewline
6 & 223.4 & 222.499966132686 & 0.90003386731405 \tabularnewline
7 & 225.5 & 223.399956458885 & 2.10004354111499 \tabularnewline
8 & 226.5 & 225.499898405782 & 1.00010159421842 \tabularnewline
9 & 227.8 & 226.499951617889 & 1.30004838211107 \tabularnewline
10 & 228.5 & 227.799937107304 & 0.700062892695655 \tabularnewline
11 & 229.1 & 228.49996613292 & 0.600033867079901 \tabularnewline
12 & 229.9 & 229.099970972044 & 0.800029027956128 \tabularnewline
13 & 230.8 & 229.899961296839 & 0.900038703161272 \tabularnewline
14 & 231.9 & 230.799956458651 & 1.10004354134892 \tabularnewline
15 & 236 & 231.899946782978 & 4.10005321702224 \tabularnewline
16 & 237.5 & 235.999801650921 & 1.50019834907894 \tabularnewline
17 & 239.1 & 237.49992742461 & 1.60007257538987 \tabularnewline
18 & 240.5 & 239.099922592975 & 1.40007740702492 \tabularnewline
19 & 241.4 & 240.499932268181 & 0.900067731819433 \tabularnewline
20 & 243.2 & 241.399956457247 & 1.80004354275326 \tabularnewline
21 & 243.6 & 243.19991291894 & 0.400087081059667 \tabularnewline
22 & 244.3 & 243.599980644909 & 0.700019355091229 \tabularnewline
23 & 244.5 & 244.299966135026 & 0.200033864973676 \tabularnewline
24 & 245.1 & 244.499990322922 & 0.600009677077537 \tabularnewline
25 & 245.8 & 245.099970973214 & 0.700029026785899 \tabularnewline
26 & 246.7 & 245.799966134558 & 0.900033865441543 \tabularnewline
27 & 247.7 & 246.699956458885 & 1.00004354111491 \tabularnewline
28 & 248.5 & 247.699951620697 & 0.800048379302609 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157954&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]218.6[/C][C]217.5[/C][C]1.09999999999999[/C][/ROW]
[ROW][C]3[/C][C]220.4[/C][C]218.599946785084[/C][C]1.80005321491583[/C][/ROW]
[ROW][C]4[/C][C]221.8[/C][C]220.399912918472[/C][C]1.40008708152757[/C][/ROW]
[ROW][C]5[/C][C]222.5[/C][C]221.799932267713[/C][C]0.700067732287437[/C][/ROW]
[ROW][C]6[/C][C]223.4[/C][C]222.499966132686[/C][C]0.90003386731405[/C][/ROW]
[ROW][C]7[/C][C]225.5[/C][C]223.399956458885[/C][C]2.10004354111499[/C][/ROW]
[ROW][C]8[/C][C]226.5[/C][C]225.499898405782[/C][C]1.00010159421842[/C][/ROW]
[ROW][C]9[/C][C]227.8[/C][C]226.499951617889[/C][C]1.30004838211107[/C][/ROW]
[ROW][C]10[/C][C]228.5[/C][C]227.799937107304[/C][C]0.700062892695655[/C][/ROW]
[ROW][C]11[/C][C]229.1[/C][C]228.49996613292[/C][C]0.600033867079901[/C][/ROW]
[ROW][C]12[/C][C]229.9[/C][C]229.099970972044[/C][C]0.800029027956128[/C][/ROW]
[ROW][C]13[/C][C]230.8[/C][C]229.899961296839[/C][C]0.900038703161272[/C][/ROW]
[ROW][C]14[/C][C]231.9[/C][C]230.799956458651[/C][C]1.10004354134892[/C][/ROW]
[ROW][C]15[/C][C]236[/C][C]231.899946782978[/C][C]4.10005321702224[/C][/ROW]
[ROW][C]16[/C][C]237.5[/C][C]235.999801650921[/C][C]1.50019834907894[/C][/ROW]
[ROW][C]17[/C][C]239.1[/C][C]237.49992742461[/C][C]1.60007257538987[/C][/ROW]
[ROW][C]18[/C][C]240.5[/C][C]239.099922592975[/C][C]1.40007740702492[/C][/ROW]
[ROW][C]19[/C][C]241.4[/C][C]240.499932268181[/C][C]0.900067731819433[/C][/ROW]
[ROW][C]20[/C][C]243.2[/C][C]241.399956457247[/C][C]1.80004354275326[/C][/ROW]
[ROW][C]21[/C][C]243.6[/C][C]243.19991291894[/C][C]0.400087081059667[/C][/ROW]
[ROW][C]22[/C][C]244.3[/C][C]243.599980644909[/C][C]0.700019355091229[/C][/ROW]
[ROW][C]23[/C][C]244.5[/C][C]244.299966135026[/C][C]0.200033864973676[/C][/ROW]
[ROW][C]24[/C][C]245.1[/C][C]244.499990322922[/C][C]0.600009677077537[/C][/ROW]
[ROW][C]25[/C][C]245.8[/C][C]245.099970973214[/C][C]0.700029026785899[/C][/ROW]
[ROW][C]26[/C][C]246.7[/C][C]245.799966134558[/C][C]0.900033865441543[/C][/ROW]
[ROW][C]27[/C][C]247.7[/C][C]246.699956458885[/C][C]1.00004354111491[/C][/ROW]
[ROW][C]28[/C][C]248.5[/C][C]247.699951620697[/C][C]0.800048379302609[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157954&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157954&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2218.6217.51.09999999999999
3220.4218.5999467850841.80005321491583
4221.8220.3999129184721.40008708152757
5222.5221.7999322677130.700067732287437
6223.4222.4999661326860.90003386731405
7225.5223.3999564588852.10004354111499
8226.5225.4998984057821.00010159421842
9227.8226.4999516178891.30004838211107
10228.5227.7999371073040.700062892695655
11229.1228.499966132920.600033867079901
12229.9229.0999709720440.800029027956128
13230.8229.8999612968390.900038703161272
14231.9230.7999564586511.10004354134892
15236231.8999467829784.10005321702224
16237.5235.9998016509211.50019834907894
17239.1237.499927424611.60007257538987
18240.5239.0999225929751.40007740702492
19241.4240.4999322681810.900067731819433
20243.2241.3999564572471.80004354275326
21243.6243.199912918940.400087081059667
22244.3243.5999806449090.700019355091229
23244.5244.2999661350260.200033864973676
24245.1244.4999903229220.600009677077537
25245.8245.0999709732140.700029026785899
26246.7245.7999661345580.900033865441543
27247.7246.6999564588851.00004354111491
28248.5247.6999516206970.800048379302609







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
29248.499961295903247.043993731257249.955928860549
30248.499961295903246.440962024513250.558960567292
31248.499961295903245.978232831166251.021689760639
32248.499961295903245.588131819414251.411790772391
33248.499961295903245.244444846792251.755477745013
34248.499961295903244.933727456022252.066195135783
35248.499961295903244.647992935312252.351929656493
36248.499961295903244.382037462067252.617885129738
37248.499961295903244.132246429802252.867676162003
38248.499961295903243.895988055121253.103934536684
39248.499961295903243.671275547988253.328647043817
40248.499961295903243.456565366333253.543357225472

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
29 & 248.499961295903 & 247.043993731257 & 249.955928860549 \tabularnewline
30 & 248.499961295903 & 246.440962024513 & 250.558960567292 \tabularnewline
31 & 248.499961295903 & 245.978232831166 & 251.021689760639 \tabularnewline
32 & 248.499961295903 & 245.588131819414 & 251.411790772391 \tabularnewline
33 & 248.499961295903 & 245.244444846792 & 251.755477745013 \tabularnewline
34 & 248.499961295903 & 244.933727456022 & 252.066195135783 \tabularnewline
35 & 248.499961295903 & 244.647992935312 & 252.351929656493 \tabularnewline
36 & 248.499961295903 & 244.382037462067 & 252.617885129738 \tabularnewline
37 & 248.499961295903 & 244.132246429802 & 252.867676162003 \tabularnewline
38 & 248.499961295903 & 243.895988055121 & 253.103934536684 \tabularnewline
39 & 248.499961295903 & 243.671275547988 & 253.328647043817 \tabularnewline
40 & 248.499961295903 & 243.456565366333 & 253.543357225472 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157954&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]29[/C][C]248.499961295903[/C][C]247.043993731257[/C][C]249.955928860549[/C][/ROW]
[ROW][C]30[/C][C]248.499961295903[/C][C]246.440962024513[/C][C]250.558960567292[/C][/ROW]
[ROW][C]31[/C][C]248.499961295903[/C][C]245.978232831166[/C][C]251.021689760639[/C][/ROW]
[ROW][C]32[/C][C]248.499961295903[/C][C]245.588131819414[/C][C]251.411790772391[/C][/ROW]
[ROW][C]33[/C][C]248.499961295903[/C][C]245.244444846792[/C][C]251.755477745013[/C][/ROW]
[ROW][C]34[/C][C]248.499961295903[/C][C]244.933727456022[/C][C]252.066195135783[/C][/ROW]
[ROW][C]35[/C][C]248.499961295903[/C][C]244.647992935312[/C][C]252.351929656493[/C][/ROW]
[ROW][C]36[/C][C]248.499961295903[/C][C]244.382037462067[/C][C]252.617885129738[/C][/ROW]
[ROW][C]37[/C][C]248.499961295903[/C][C]244.132246429802[/C][C]252.867676162003[/C][/ROW]
[ROW][C]38[/C][C]248.499961295903[/C][C]243.895988055121[/C][C]253.103934536684[/C][/ROW]
[ROW][C]39[/C][C]248.499961295903[/C][C]243.671275547988[/C][C]253.328647043817[/C][/ROW]
[ROW][C]40[/C][C]248.499961295903[/C][C]243.456565366333[/C][C]253.543357225472[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157954&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157954&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
29248.499961295903247.043993731257249.955928860549
30248.499961295903246.440962024513250.558960567292
31248.499961295903245.978232831166251.021689760639
32248.499961295903245.588131819414251.411790772391
33248.499961295903245.244444846792251.755477745013
34248.499961295903244.933727456022252.066195135783
35248.499961295903244.647992935312252.351929656493
36248.499961295903244.382037462067252.617885129738
37248.499961295903244.132246429802252.867676162003
38248.499961295903243.895988055121253.103934536684
39248.499961295903243.671275547988253.328647043817
40248.499961295903243.456565366333253.543357225472



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')