Free Statistics

of Irreproducible Research!

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 12:30:56 +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/t1481801933keck0hqspqjesxz.htm/, Retrieved Fri, 03 May 2024 13:10:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299889, Retrieved Fri, 03 May 2024 13:10:50 +0000
QR Codes:

Original text written by user:sezonaliteit = 6 exponential smoothing = triple additive sesonality forecast = 18
IsPrivate?No (this computation is public)
User-defined keywordsf1competitie forecasts
Estimated Impact47
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 11:30:56] [d92250bd36540c2281a4ec15b45df1dd] [Current]
Feedback Forum

Post a new message
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=299889&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=299889&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299889&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
alpha0.656476200735818
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.656476200735818 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299889&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]0.656476200735818[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299889&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299889&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
alpha0.656476200735818
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
7768701.51190476190566.4880952380953
8753729.52166167987623.4783383201244
9773772.0465367817660.953463218234447
10797761.45103412138535.5489658786153
11810854.733322276703-44.7333222767032
12794848.31219891744-54.3121989174402
13809868.526347429112-59.5263474291115
14828799.03574668518328.9642533148173
15828837.424163747396-9.42416374739594
16849831.90037447531317.0996255246873
17865885.492233128266-20.4922331282658
18879891.694235778558-12.6942357785584
19908937.438402507349-29.4384025073491
20961918.09844890033242.9015510996683

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
7 & 768 & 701.511904761905 & 66.4880952380953 \tabularnewline
8 & 753 & 729.521661679876 & 23.4783383201244 \tabularnewline
9 & 773 & 772.046536781766 & 0.953463218234447 \tabularnewline
10 & 797 & 761.451034121385 & 35.5489658786153 \tabularnewline
11 & 810 & 854.733322276703 & -44.7333222767032 \tabularnewline
12 & 794 & 848.31219891744 & -54.3121989174402 \tabularnewline
13 & 809 & 868.526347429112 & -59.5263474291115 \tabularnewline
14 & 828 & 799.035746685183 & 28.9642533148173 \tabularnewline
15 & 828 & 837.424163747396 & -9.42416374739594 \tabularnewline
16 & 849 & 831.900374475313 & 17.0996255246873 \tabularnewline
17 & 865 & 885.492233128266 & -20.4922331282658 \tabularnewline
18 & 879 & 891.694235778558 & -12.6942357785584 \tabularnewline
19 & 908 & 937.438402507349 & -29.4384025073491 \tabularnewline
20 & 961 & 918.098448900332 & 42.9015510996683 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299889&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]7[/C][C]768[/C][C]701.511904761905[/C][C]66.4880952380953[/C][/ROW]
[ROW][C]8[/C][C]753[/C][C]729.521661679876[/C][C]23.4783383201244[/C][/ROW]
[ROW][C]9[/C][C]773[/C][C]772.046536781766[/C][C]0.953463218234447[/C][/ROW]
[ROW][C]10[/C][C]797[/C][C]761.451034121385[/C][C]35.5489658786153[/C][/ROW]
[ROW][C]11[/C][C]810[/C][C]854.733322276703[/C][C]-44.7333222767032[/C][/ROW]
[ROW][C]12[/C][C]794[/C][C]848.31219891744[/C][C]-54.3121989174402[/C][/ROW]
[ROW][C]13[/C][C]809[/C][C]868.526347429112[/C][C]-59.5263474291115[/C][/ROW]
[ROW][C]14[/C][C]828[/C][C]799.035746685183[/C][C]28.9642533148173[/C][/ROW]
[ROW][C]15[/C][C]828[/C][C]837.424163747396[/C][C]-9.42416374739594[/C][/ROW]
[ROW][C]16[/C][C]849[/C][C]831.900374475313[/C][C]17.0996255246873[/C][/ROW]
[ROW][C]17[/C][C]865[/C][C]885.492233128266[/C][C]-20.4922331282658[/C][/ROW]
[ROW][C]18[/C][C]879[/C][C]891.694235778558[/C][C]-12.6942357785584[/C][/ROW]
[ROW][C]19[/C][C]908[/C][C]937.438402507349[/C][C]-29.4384025073491[/C][/ROW]
[ROW][C]20[/C][C]961[/C][C]918.098448900332[/C][C]42.9015510996683[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299889&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299889&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
7768701.51190476190566.4880952380953
8753729.52166167987623.4783383201244
9773772.0465367817660.953463218234447
10797761.45103412138535.5489658786153
11810854.733322276703-44.7333222767032
12794848.31219891744-54.3121989174402
13809868.526347429112-59.5263474291115
14828799.03574668518328.9642533148173
15828837.424163747396-9.42416374739594
16849831.90037447531317.0996255246873
17865885.492233128266-20.4922331282658
18879891.694235778558-12.6942357785584
19908937.438402507349-29.4384025073491
20961918.09844890033242.9015510996683







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
21952.449035383918877.0815978536061027.81647291423
22962.223538185466872.0669125386811052.38016383225
23991.676201534103888.835627556011094.5167755122
241014.00966520926899.8862663627761128.13306405573
251062.33527584301937.9483124087291186.72223927729
261087.17142857143953.3055136396181221.03734350324
271078.62046395535924.9964625089061232.24446540179
281088.39496675689927.000108324091249.7898251897
291117.84763010553949.039256981821286.65600322924
301140.18109378068964.2713631095151316.09082445185
311188.506704414441005.771377088461371.24203174042
321213.342857142861024.027864706811402.65784957891
331204.791892526771001.026299256111408.55748579744
341214.566395328321004.880002090531424.25278856612
351244.019058676961028.574518209571459.46359914435
361266.352522352111045.299776326791487.40526837743
371314.678132985871088.155986091881541.20027987986
381339.514285714291107.65171965071571.37685177787

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
21 & 952.449035383918 & 877.081597853606 & 1027.81647291423 \tabularnewline
22 & 962.223538185466 & 872.066912538681 & 1052.38016383225 \tabularnewline
23 & 991.676201534103 & 888.83562755601 & 1094.5167755122 \tabularnewline
24 & 1014.00966520926 & 899.886266362776 & 1128.13306405573 \tabularnewline
25 & 1062.33527584301 & 937.948312408729 & 1186.72223927729 \tabularnewline
26 & 1087.17142857143 & 953.305513639618 & 1221.03734350324 \tabularnewline
27 & 1078.62046395535 & 924.996462508906 & 1232.24446540179 \tabularnewline
28 & 1088.39496675689 & 927.00010832409 & 1249.7898251897 \tabularnewline
29 & 1117.84763010553 & 949.03925698182 & 1286.65600322924 \tabularnewline
30 & 1140.18109378068 & 964.271363109515 & 1316.09082445185 \tabularnewline
31 & 1188.50670441444 & 1005.77137708846 & 1371.24203174042 \tabularnewline
32 & 1213.34285714286 & 1024.02786470681 & 1402.65784957891 \tabularnewline
33 & 1204.79189252677 & 1001.02629925611 & 1408.55748579744 \tabularnewline
34 & 1214.56639532832 & 1004.88000209053 & 1424.25278856612 \tabularnewline
35 & 1244.01905867696 & 1028.57451820957 & 1459.46359914435 \tabularnewline
36 & 1266.35252235211 & 1045.29977632679 & 1487.40526837743 \tabularnewline
37 & 1314.67813298587 & 1088.15598609188 & 1541.20027987986 \tabularnewline
38 & 1339.51428571429 & 1107.6517196507 & 1571.37685177787 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299889&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]952.449035383918[/C][C]877.081597853606[/C][C]1027.81647291423[/C][/ROW]
[ROW][C]22[/C][C]962.223538185466[/C][C]872.066912538681[/C][C]1052.38016383225[/C][/ROW]
[ROW][C]23[/C][C]991.676201534103[/C][C]888.83562755601[/C][C]1094.5167755122[/C][/ROW]
[ROW][C]24[/C][C]1014.00966520926[/C][C]899.886266362776[/C][C]1128.13306405573[/C][/ROW]
[ROW][C]25[/C][C]1062.33527584301[/C][C]937.948312408729[/C][C]1186.72223927729[/C][/ROW]
[ROW][C]26[/C][C]1087.17142857143[/C][C]953.305513639618[/C][C]1221.03734350324[/C][/ROW]
[ROW][C]27[/C][C]1078.62046395535[/C][C]924.996462508906[/C][C]1232.24446540179[/C][/ROW]
[ROW][C]28[/C][C]1088.39496675689[/C][C]927.00010832409[/C][C]1249.7898251897[/C][/ROW]
[ROW][C]29[/C][C]1117.84763010553[/C][C]949.03925698182[/C][C]1286.65600322924[/C][/ROW]
[ROW][C]30[/C][C]1140.18109378068[/C][C]964.271363109515[/C][C]1316.09082445185[/C][/ROW]
[ROW][C]31[/C][C]1188.50670441444[/C][C]1005.77137708846[/C][C]1371.24203174042[/C][/ROW]
[ROW][C]32[/C][C]1213.34285714286[/C][C]1024.02786470681[/C][C]1402.65784957891[/C][/ROW]
[ROW][C]33[/C][C]1204.79189252677[/C][C]1001.02629925611[/C][C]1408.55748579744[/C][/ROW]
[ROW][C]34[/C][C]1214.56639532832[/C][C]1004.88000209053[/C][C]1424.25278856612[/C][/ROW]
[ROW][C]35[/C][C]1244.01905867696[/C][C]1028.57451820957[/C][C]1459.46359914435[/C][/ROW]
[ROW][C]36[/C][C]1266.35252235211[/C][C]1045.29977632679[/C][C]1487.40526837743[/C][/ROW]
[ROW][C]37[/C][C]1314.67813298587[/C][C]1088.15598609188[/C][C]1541.20027987986[/C][/ROW]
[ROW][C]38[/C][C]1339.51428571429[/C][C]1107.6517196507[/C][C]1571.37685177787[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299889&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299889&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
21952.449035383918877.0815978536061027.81647291423
22962.223538185466872.0669125386811052.38016383225
23991.676201534103888.835627556011094.5167755122
241014.00966520926899.8862663627761128.13306405573
251062.33527584301937.9483124087291186.72223927729
261087.17142857143953.3055136396181221.03734350324
271078.62046395535924.9964625089061232.24446540179
281088.39496675689927.000108324091249.7898251897
291117.84763010553949.039256981821286.65600322924
301140.18109378068964.2713631095151316.09082445185
311188.506704414441005.771377088461371.24203174042
321213.342857142861024.027864706811402.65784957891
331204.791892526771001.026299256111408.55748579744
341214.566395328321004.880002090531424.25278856612
351244.019058676961028.574518209571459.46359914435
361266.352522352111045.299776326791487.40526837743
371314.678132985871088.155986091881541.20027987986
381339.514285714291107.65171965071571.37685177787



Parameters (Session):
par4 = 12 ;
Parameters (R input):
par1 = 6 ; par2 = Triple ; par3 = additive ; par4 = 18 ;
R code (references can be found in the software module):
par4 <- '18'
par3 <- 'additive'
par2 <- 'Double'
par1 <- '6'
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')