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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 12:51:28 -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/t13977535255r5ektr1c2qma09.htm/, Retrieved Fri, 17 May 2024 02:32:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234467, Retrieved Fri, 17 May 2024 02:32:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact143

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 16:51:28] [0886edc6b443bd4bec60935c27dcdd54] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
147695
94225
257237
37829
61780
124448
88600

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'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234467&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234467&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234467&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'Gwilym Jenkins' @ jenkins.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.237271492651614
beta1
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.237271492651614 \tabularnewline
beta & 1 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234467&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]0.237271492651614[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234467&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234467&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
alpha0.237271492651614
beta1
gammaFALSE






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
325723740755216482
43782990015.0145444135-52186.0145444135
56178063145.5146836366-1365.5146836366
612444848010.272974903276437.7270250968
78860069472.016145676719127.9838543233

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 257237 & 40755 & 216482 \tabularnewline
4 & 37829 & 90015.0145444135 & -52186.0145444135 \tabularnewline
5 & 61780 & 63145.5146836366 & -1365.5146836366 \tabularnewline
6 & 124448 & 48010.2729749032 & 76437.7270250968 \tabularnewline
7 & 88600 & 69472.0161456767 & 19127.9838543233 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234467&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]257237[/C][C]40755[/C][C]216482[/C][/ROW]
[ROW][C]4[/C][C]37829[/C][C]90015.0145444135[/C][C]-52186.0145444135[/C][/ROW]
[ROW][C]5[/C][C]61780[/C][C]63145.5146836366[/C][C]-1365.5146836366[/C][/ROW]
[ROW][C]6[/C][C]124448[/C][C]48010.2729749032[/C][C]76437.7270250968[/C][/ROW]
[ROW][C]7[/C][C]88600[/C][C]69472.0161456767[/C][C]19127.9838543233[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234467&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234467&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
325723740755216482
43782990015.0145444135-52186.0145444135
56178063145.5146836366-1365.5146836366
612444848010.272974903276437.7270250968
78860069472.016145676719127.9838543233






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
881874.3162913713-119997.815719186283746.448301929
989738.0911565347-133710.837440508313187.019753578
1097601.8660216981-168063.002206475363266.734249872
11105465.640886862-222079.907465435433011.189239158
12113329.415752025-292432.520362794519091.351866844

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
8 & 81874.3162913713 & -119997.815719186 & 283746.448301929 \tabularnewline
9 & 89738.0911565347 & -133710.837440508 & 313187.019753578 \tabularnewline
10 & 97601.8660216981 & -168063.002206475 & 363266.734249872 \tabularnewline
11 & 105465.640886862 & -222079.907465435 & 433011.189239158 \tabularnewline
12 & 113329.415752025 & -292432.520362794 & 519091.351866844 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234467&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]81874.3162913713[/C][C]-119997.815719186[/C][C]283746.448301929[/C][/ROW]
[ROW][C]9[/C][C]89738.0911565347[/C][C]-133710.837440508[/C][C]313187.019753578[/C][/ROW]
[ROW][C]10[/C][C]97601.8660216981[/C][C]-168063.002206475[/C][C]363266.734249872[/C][/ROW]
[ROW][C]11[/C][C]105465.640886862[/C][C]-222079.907465435[/C][C]433011.189239158[/C][/ROW]
[ROW][C]12[/C][C]113329.415752025[/C][C]-292432.520362794[/C][C]519091.351866844[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234467&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234467&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
881874.3162913713-119997.815719186283746.448301929
989738.0911565347-133710.837440508313187.019753578
1097601.8660216981-168063.002206475363266.734249872
11105465.640886862-222079.907465435433011.189239158
12113329.415752025-292432.520362794519091.351866844


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')