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Description of Statistical Computation

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, 17 Apr 2014 04:24:23 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Apr/17/t1397723099m2ybvjpy327iayr.htm/, Retrieved Fri, 17 May 2024 01:44:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234466, Retrieved Fri, 17 May 2024 01:44:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact155

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Double exponentia...] [2014-04-17 08:24:23] [0886edc6b443bd4bec60935c27dcdd54] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
73911
20581
49828
90196
41013
124787
73544

Tables (Output of Computation)





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=234466&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=234466&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234466&T=0

As an alternative you can also use a QR Code:  
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
alpha0.551350522962104
beta0.99126257533721
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.551350522962104 \tabularnewline
beta & 0.99126257533721 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234466&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]0.551350522962104[/C][/ROW]
[ROW][C]beta[/C][C]0.99126257533721[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234466&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234466&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.551350522962104
beta0.99126257533721
gammaFALSE






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
349828-3274982577
4901964580.939179025185615.0608209749
54101390377.3827427556-49364.3827427556
612478774773.56843824150013.431561759
773544141295.761780212-67751.761780212

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 49828 & -32749 & 82577 \tabularnewline
4 & 90196 & 4580.9391790251 & 85615.0608209749 \tabularnewline
5 & 41013 & 90377.3827427556 & -49364.3827427556 \tabularnewline
6 & 124787 & 74773.568438241 & 50013.431561759 \tabularnewline
7 & 73544 & 141295.761780212 & -67751.761780212 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234466&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]49828[/C][C]-32749[/C][C]82577[/C][/ROW]
[ROW][C]4[/C][C]90196[/C][C]4580.9391790251[/C][C]85615.0608209749[/C][/ROW]
[ROW][C]5[/C][C]41013[/C][C]90377.3827427556[/C][C]-49364.3827427556[/C][/ROW]
[ROW][C]6[/C][C]124787[/C][C]74773.568438241[/C][C]50013.431561759[/C][/ROW]
[ROW][C]7[/C][C]73544[/C][C]141295.761780212[/C][C]-67751.761780212[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234466&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234466&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
349828-3274982577
4901964580.939179025185615.0608209749
54101390377.3827427556-49364.3827427556
612478774773.56843824150013.431561759
773544141295.761780212-67751.761780212






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8105859.471127175-38279.7741635873249998.716417937
9107778.149763261-106274.624819485321830.924346007
10109696.828399348-209676.68236454429070.339163236
11111615.507035434-337528.413185919560759.427256787
12113534.185671521-484314.162335405711382.533678446

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
8 & 105859.471127175 & -38279.7741635873 & 249998.716417937 \tabularnewline
9 & 107778.149763261 & -106274.624819485 & 321830.924346007 \tabularnewline
10 & 109696.828399348 & -209676.68236454 & 429070.339163236 \tabularnewline
11 & 111615.507035434 & -337528.413185919 & 560759.427256787 \tabularnewline
12 & 113534.185671521 & -484314.162335405 & 711382.533678446 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234466&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]8[/C][C]105859.471127175[/C][C]-38279.7741635873[/C][C]249998.716417937[/C][/ROW]
[ROW][C]9[/C][C]107778.149763261[/C][C]-106274.624819485[/C][C]321830.924346007[/C][/ROW]
[ROW][C]10[/C][C]109696.828399348[/C][C]-209676.68236454[/C][C]429070.339163236[/C][/ROW]
[ROW][C]11[/C][C]111615.507035434[/C][C]-337528.413185919[/C][C]560759.427256787[/C][/ROW]
[ROW][C]12[/C][C]113534.185671521[/C][C]-484314.162335405[/C][C]711382.533678446[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234466&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234466&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8105859.471127175-38279.7741635873249998.716417937
9107778.149763261-106274.624819485321830.924346007
10109696.828399348-209676.68236454429070.339163236
11111615.507035434-337528.413185919560759.427256787
12113534.185671521-484314.162335405711382.533678446


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 5 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 5 ; par2 = Double ; 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')