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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, 14 Nov 2013 07:20:25 -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/2013/Nov/14/t13844316358m7r69xrcn04dd8.htm/, Retrieved Mon, 29 Apr 2024 13:11:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=225299, Retrieved Mon, 29 Apr 2024 13:11:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact58

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [zdqs] [2013-11-14 12:20:25] [e931f330ae8eb739e69629b6955c783c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1045620
1050293
1030185
1015746
999514
990204
962206
947314
958768

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225299&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]3 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=225299&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225299&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 time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933083789849
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933083789849 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225299&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]0.999933083789849[/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=225299&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225299&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
alpha0.999933083789849
betaFALSE
gammaFALSE






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2105029310456204673
310301851050292.68730055-20107.6873005501
410157461030186.34553023-14440.345530229
59995141015746.9662932-16232.9662931962
6990204999515.086248584-9311.08624858386
7962206990204.623062604-27998.6230626041
8947314962207.873561745-14893.8735617448
9958768947314.99664157311453.0033584267

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1050293 & 1045620 & 4673 \tabularnewline
3 & 1030185 & 1050292.68730055 & -20107.6873005501 \tabularnewline
4 & 1015746 & 1030186.34553023 & -14440.345530229 \tabularnewline
5 & 999514 & 1015746.9662932 & -16232.9662931962 \tabularnewline
6 & 990204 & 999515.086248584 & -9311.08624858386 \tabularnewline
7 & 962206 & 990204.623062604 & -27998.6230626041 \tabularnewline
8 & 947314 & 962207.873561745 & -14893.8735617448 \tabularnewline
9 & 958768 & 947314.996641573 & 11453.0033584267 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225299&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]1050293[/C][C]1045620[/C][C]4673[/C][/ROW]
[ROW][C]3[/C][C]1030185[/C][C]1050292.68730055[/C][C]-20107.6873005501[/C][/ROW]
[ROW][C]4[/C][C]1015746[/C][C]1030186.34553023[/C][C]-14440.345530229[/C][/ROW]
[ROW][C]5[/C][C]999514[/C][C]1015746.9662932[/C][C]-16232.9662931962[/C][/ROW]
[ROW][C]6[/C][C]990204[/C][C]999515.086248584[/C][C]-9311.08624858386[/C][/ROW]
[ROW][C]7[/C][C]962206[/C][C]990204.623062604[/C][C]-27998.6230626041[/C][/ROW]
[ROW][C]8[/C][C]947314[/C][C]962207.873561745[/C][C]-14893.8735617448[/C][/ROW]
[ROW][C]9[/C][C]958768[/C][C]947314.996641573[/C][C]11453.0033584267[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225299&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225299&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
2105029310456204673
310301851050292.68730055-20107.6873005501
410157461030186.34553023-14440.345530229
59995141015746.9662932-16232.9662931962
6990204999515.086248584-9311.08624858386
7962206990204.623062604-27998.6230626041
8947314962207.873561745-14893.8735617448
9958768947314.99664157311453.0033584267






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10958767.23360842933333.455473689984201.011743151
11958767.23360842922799.643055451994734.82416139
12958767.23360842914716.602850561002817.86436628
13958767.23360842907902.2302156681009632.23700117
14958767.23360842901898.6212627331015635.84595411
15958767.23360842896470.9289820351021063.53823481
16958767.23360842891479.6413637671026054.82585307
17958767.23360842886833.8576966641030700.60952018
18958767.23360842882470.4376728021035064.02954404
19958767.23360842878343.4089665841039191.05825026
20958767.23360842874418.0660369491043116.40117989
21958767.23360842870667.4460378511046867.02117899

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
10 & 958767.23360842 & 933333.455473689 & 984201.011743151 \tabularnewline
11 & 958767.23360842 & 922799.643055451 & 994734.82416139 \tabularnewline
12 & 958767.23360842 & 914716.60285056 & 1002817.86436628 \tabularnewline
13 & 958767.23360842 & 907902.230215668 & 1009632.23700117 \tabularnewline
14 & 958767.23360842 & 901898.621262733 & 1015635.84595411 \tabularnewline
15 & 958767.23360842 & 896470.928982035 & 1021063.53823481 \tabularnewline
16 & 958767.23360842 & 891479.641363767 & 1026054.82585307 \tabularnewline
17 & 958767.23360842 & 886833.857696664 & 1030700.60952018 \tabularnewline
18 & 958767.23360842 & 882470.437672802 & 1035064.02954404 \tabularnewline
19 & 958767.23360842 & 878343.408966584 & 1039191.05825026 \tabularnewline
20 & 958767.23360842 & 874418.066036949 & 1043116.40117989 \tabularnewline
21 & 958767.23360842 & 870667.446037851 & 1046867.02117899 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225299&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]10[/C][C]958767.23360842[/C][C]933333.455473689[/C][C]984201.011743151[/C][/ROW]
[ROW][C]11[/C][C]958767.23360842[/C][C]922799.643055451[/C][C]994734.82416139[/C][/ROW]
[ROW][C]12[/C][C]958767.23360842[/C][C]914716.60285056[/C][C]1002817.86436628[/C][/ROW]
[ROW][C]13[/C][C]958767.23360842[/C][C]907902.230215668[/C][C]1009632.23700117[/C][/ROW]
[ROW][C]14[/C][C]958767.23360842[/C][C]901898.621262733[/C][C]1015635.84595411[/C][/ROW]
[ROW][C]15[/C][C]958767.23360842[/C][C]896470.928982035[/C][C]1021063.53823481[/C][/ROW]
[ROW][C]16[/C][C]958767.23360842[/C][C]891479.641363767[/C][C]1026054.82585307[/C][/ROW]
[ROW][C]17[/C][C]958767.23360842[/C][C]886833.857696664[/C][C]1030700.60952018[/C][/ROW]
[ROW][C]18[/C][C]958767.23360842[/C][C]882470.437672802[/C][C]1035064.02954404[/C][/ROW]
[ROW][C]19[/C][C]958767.23360842[/C][C]878343.408966584[/C][C]1039191.05825026[/C][/ROW]
[ROW][C]20[/C][C]958767.23360842[/C][C]874418.066036949[/C][C]1043116.40117989[/C][/ROW]
[ROW][C]21[/C][C]958767.23360842[/C][C]870667.446037851[/C][C]1046867.02117899[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225299&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225299&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
10958767.23360842933333.455473689984201.011743151
11958767.23360842922799.643055451994734.82416139
12958767.23360842914716.602850561002817.86436628
13958767.23360842907902.2302156681009632.23700117
14958767.23360842901898.6212627331015635.84595411
15958767.23360842896470.9289820351021063.53823481
16958767.23360842891479.6413637671026054.82585307
17958767.23360842886833.8576966641030700.60952018
18958767.23360842882470.4376728021035064.02954404
19958767.23360842878343.4089665841039191.05825026
20958767.23360842874418.0660369491043116.40117989
21958767.23360842870667.4460378511046867.02117899


Figures (Output of Computation)

Input Parameters & R Code

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')