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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 15 Dec 2016 12:40:03 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/15/t1481802078e9rikg3hpnbal7o.htm/, Retrieved Fri, 03 May 2024 10:19:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299892, Retrieved Fri, 03 May 2024 10:19:03 +0000
QR Codes:

Original text written by user:sezonaliteit = 6 forecasts = 18 exponential smoothing = double additive sesonality
IsPrivate?No (this computation is public)
User-defined keywordsf1competitie forecasts
Estimated Impact61
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2016-12-15 11:40:03] [d92250bd36540c2281a4ec15b45df1dd] [Current]
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Dataseries X:
649
655
618
640
707
730
768
753
773
797
810
794
809
828
828
849
865
879
908
961




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299892&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299892&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299892&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0845509488027033
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0845509488027033 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299892&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0845509488027033[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299892&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299892&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
alpha1
beta0.0845509488027033
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3618661-43
4640620.36430920148419.6356907985163
5707644.02452548889562.9754745111052
6730716.34916161010913.6508383898907
7768740.50335294792727.4966470520732
8753780.828220545073-27.8282205450727
9773763.4753180944969.52468190550405
10797784.2806389866512.7193610133497
11810809.3560730284930.643926971506971
12794822.410517664894-28.4105176648936
13809804.0083814403514.99161855964905
14828819.430427525638.56957247436958
15828839.154993009172-11.1549930091719
16849838.21182776635910.7881722336411
17865860.123977964564.87602203543975
18879876.5362502540392.46374974596051
19908890.74456263267317.2554373673271
20961921.20352623408639.796473765914

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 618 & 661 & -43 \tabularnewline
4 & 640 & 620.364309201484 & 19.6356907985163 \tabularnewline
5 & 707 & 644.024525488895 & 62.9754745111052 \tabularnewline
6 & 730 & 716.349161610109 & 13.6508383898907 \tabularnewline
7 & 768 & 740.503352947927 & 27.4966470520732 \tabularnewline
8 & 753 & 780.828220545073 & -27.8282205450727 \tabularnewline
9 & 773 & 763.475318094496 & 9.52468190550405 \tabularnewline
10 & 797 & 784.28063898665 & 12.7193610133497 \tabularnewline
11 & 810 & 809.356073028493 & 0.643926971506971 \tabularnewline
12 & 794 & 822.410517664894 & -28.4105176648936 \tabularnewline
13 & 809 & 804.008381440351 & 4.99161855964905 \tabularnewline
14 & 828 & 819.43042752563 & 8.56957247436958 \tabularnewline
15 & 828 & 839.154993009172 & -11.1549930091719 \tabularnewline
16 & 849 & 838.211827766359 & 10.7881722336411 \tabularnewline
17 & 865 & 860.12397796456 & 4.87602203543975 \tabularnewline
18 & 879 & 876.536250254039 & 2.46374974596051 \tabularnewline
19 & 908 & 890.744562632673 & 17.2554373673271 \tabularnewline
20 & 961 & 921.203526234086 & 39.796473765914 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299892&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]3[/C][C]618[/C][C]661[/C][C]-43[/C][/ROW]
[ROW][C]4[/C][C]640[/C][C]620.364309201484[/C][C]19.6356907985163[/C][/ROW]
[ROW][C]5[/C][C]707[/C][C]644.024525488895[/C][C]62.9754745111052[/C][/ROW]
[ROW][C]6[/C][C]730[/C][C]716.349161610109[/C][C]13.6508383898907[/C][/ROW]
[ROW][C]7[/C][C]768[/C][C]740.503352947927[/C][C]27.4966470520732[/C][/ROW]
[ROW][C]8[/C][C]753[/C][C]780.828220545073[/C][C]-27.8282205450727[/C][/ROW]
[ROW][C]9[/C][C]773[/C][C]763.475318094496[/C][C]9.52468190550405[/C][/ROW]
[ROW][C]10[/C][C]797[/C][C]784.28063898665[/C][C]12.7193610133497[/C][/ROW]
[ROW][C]11[/C][C]810[/C][C]809.356073028493[/C][C]0.643926971506971[/C][/ROW]
[ROW][C]12[/C][C]794[/C][C]822.410517664894[/C][C]-28.4105176648936[/C][/ROW]
[ROW][C]13[/C][C]809[/C][C]804.008381440351[/C][C]4.99161855964905[/C][/ROW]
[ROW][C]14[/C][C]828[/C][C]819.43042752563[/C][C]8.56957247436958[/C][/ROW]
[ROW][C]15[/C][C]828[/C][C]839.154993009172[/C][C]-11.1549930091719[/C][/ROW]
[ROW][C]16[/C][C]849[/C][C]838.211827766359[/C][C]10.7881722336411[/C][/ROW]
[ROW][C]17[/C][C]865[/C][C]860.12397796456[/C][C]4.87602203543975[/C][/ROW]
[ROW][C]18[/C][C]879[/C][C]876.536250254039[/C][C]2.46374974596051[/C][/ROW]
[ROW][C]19[/C][C]908[/C][C]890.744562632673[/C][C]17.2554373673271[/C][/ROW]
[ROW][C]20[/C][C]961[/C][C]921.203526234086[/C][C]39.796473765914[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299892&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299892&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
3618661-43
4640620.36430920148419.6356907985163
5707644.02452548889562.9754745111052
6730716.34916161010913.6508383898907
7768740.50335294792727.4966470520732
8753780.828220545073-27.8282205450727
9773763.4753180944969.52468190550405
10797784.2806389866512.7193610133497
11810809.3560730284930.643926971506971
12794822.410517664894-28.4105176648936
13809804.0083814403514.99161855964905
14828819.430427525638.56957247436958
15828839.154993009172-11.1549930091719
16849838.21182776635910.7881722336411
17865860.123977964564.87602203543975
18879876.5362502540392.46374974596051
19908890.74456263267317.2554373673271
20961921.20352623408639.796473765914







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
21977.568355849996929.1843452838231025.95236641617
22994.136711699992922.7600335290421065.51338987094
231010.70506754999919.6318866487471101.77824845123
241027.27342339998917.8496329728781136.69721382709
251043.84177924998916.6968767279791170.98668177198
261060.41013509998915.8259851669131204.99428503304
271076.97849094997915.042430760271238.91455113967
281093.54684679997914.2274922234681272.86620137647
291110.11520264996913.3044367490851306.92596855084
301126.68355849996912.2216768268941341.14544017303
311143.25191434996910.9435730678751375.56025563204
321159.82027019995909.4450538852281410.19548651467
331176.38862604995907.7082948165191445.06895728338
341192.95698189994905.7205793930041480.19338440688
351209.52533774994903.4728721502821515.5778033496
361226.09369359994900.9588387013511551.22854849852
371242.66204944993898.1741562073321587.14994269253
381259.23040529993895.1160180302831623.34479256957

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
21 & 977.568355849996 & 929.184345283823 & 1025.95236641617 \tabularnewline
22 & 994.136711699992 & 922.760033529042 & 1065.51338987094 \tabularnewline
23 & 1010.70506754999 & 919.631886648747 & 1101.77824845123 \tabularnewline
24 & 1027.27342339998 & 917.849632972878 & 1136.69721382709 \tabularnewline
25 & 1043.84177924998 & 916.696876727979 & 1170.98668177198 \tabularnewline
26 & 1060.41013509998 & 915.825985166913 & 1204.99428503304 \tabularnewline
27 & 1076.97849094997 & 915.04243076027 & 1238.91455113967 \tabularnewline
28 & 1093.54684679997 & 914.227492223468 & 1272.86620137647 \tabularnewline
29 & 1110.11520264996 & 913.304436749085 & 1306.92596855084 \tabularnewline
30 & 1126.68355849996 & 912.221676826894 & 1341.14544017303 \tabularnewline
31 & 1143.25191434996 & 910.943573067875 & 1375.56025563204 \tabularnewline
32 & 1159.82027019995 & 909.445053885228 & 1410.19548651467 \tabularnewline
33 & 1176.38862604995 & 907.708294816519 & 1445.06895728338 \tabularnewline
34 & 1192.95698189994 & 905.720579393004 & 1480.19338440688 \tabularnewline
35 & 1209.52533774994 & 903.472872150282 & 1515.5778033496 \tabularnewline
36 & 1226.09369359994 & 900.958838701351 & 1551.22854849852 \tabularnewline
37 & 1242.66204944993 & 898.174156207332 & 1587.14994269253 \tabularnewline
38 & 1259.23040529993 & 895.116018030283 & 1623.34479256957 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299892&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]21[/C][C]977.568355849996[/C][C]929.184345283823[/C][C]1025.95236641617[/C][/ROW]
[ROW][C]22[/C][C]994.136711699992[/C][C]922.760033529042[/C][C]1065.51338987094[/C][/ROW]
[ROW][C]23[/C][C]1010.70506754999[/C][C]919.631886648747[/C][C]1101.77824845123[/C][/ROW]
[ROW][C]24[/C][C]1027.27342339998[/C][C]917.849632972878[/C][C]1136.69721382709[/C][/ROW]
[ROW][C]25[/C][C]1043.84177924998[/C][C]916.696876727979[/C][C]1170.98668177198[/C][/ROW]
[ROW][C]26[/C][C]1060.41013509998[/C][C]915.825985166913[/C][C]1204.99428503304[/C][/ROW]
[ROW][C]27[/C][C]1076.97849094997[/C][C]915.04243076027[/C][C]1238.91455113967[/C][/ROW]
[ROW][C]28[/C][C]1093.54684679997[/C][C]914.227492223468[/C][C]1272.86620137647[/C][/ROW]
[ROW][C]29[/C][C]1110.11520264996[/C][C]913.304436749085[/C][C]1306.92596855084[/C][/ROW]
[ROW][C]30[/C][C]1126.68355849996[/C][C]912.221676826894[/C][C]1341.14544017303[/C][/ROW]
[ROW][C]31[/C][C]1143.25191434996[/C][C]910.943573067875[/C][C]1375.56025563204[/C][/ROW]
[ROW][C]32[/C][C]1159.82027019995[/C][C]909.445053885228[/C][C]1410.19548651467[/C][/ROW]
[ROW][C]33[/C][C]1176.38862604995[/C][C]907.708294816519[/C][C]1445.06895728338[/C][/ROW]
[ROW][C]34[/C][C]1192.95698189994[/C][C]905.720579393004[/C][C]1480.19338440688[/C][/ROW]
[ROW][C]35[/C][C]1209.52533774994[/C][C]903.472872150282[/C][C]1515.5778033496[/C][/ROW]
[ROW][C]36[/C][C]1226.09369359994[/C][C]900.958838701351[/C][C]1551.22854849852[/C][/ROW]
[ROW][C]37[/C][C]1242.66204944993[/C][C]898.174156207332[/C][C]1587.14994269253[/C][/ROW]
[ROW][C]38[/C][C]1259.23040529993[/C][C]895.116018030283[/C][C]1623.34479256957[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299892&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299892&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
21977.568355849996929.1843452838231025.95236641617
22994.136711699992922.7600335290421065.51338987094
231010.70506754999919.6318866487471101.77824845123
241027.27342339998917.8496329728781136.69721382709
251043.84177924998916.6968767279791170.98668177198
261060.41013509998915.8259851669131204.99428503304
271076.97849094997915.042430760271238.91455113967
281093.54684679997914.2274922234681272.86620137647
291110.11520264996913.3044367490851306.92596855084
301126.68355849996912.2216768268941341.14544017303
311143.25191434996910.9435730678751375.56025563204
321159.82027019995909.4450538852281410.19548651467
331176.38862604995907.7082948165191445.06895728338
341192.95698189994905.7205793930041480.19338440688
351209.52533774994903.4728721502821515.5778033496
361226.09369359994900.9588387013511551.22854849852
371242.66204944993898.1741562073321587.14994269253
381259.23040529993895.1160180302831623.34479256957



Parameters (Session):
par4 = 12 ;
Parameters (R input):
par1 = 6 ; par2 = Double ; par3 = additive ; par4 = 18 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')