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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 20 Feb 2009 11:16:03 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Feb/20/t1235154097dj8vkyz6zke2vt3.htm/, Retrieved Sat, 11 May 2024 15:32:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=38084, Retrieved Sat, 11 May 2024 15:32:42 +0000
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Original text written by user:esto es una prueba
IsPrivate?No (this computation is public)
User-defined keywordsbarranca
Estimated Impact209

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [analisis de ingre...] [2009-02-20 18:16:03] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
72077
49560
46252
55204
47035
54511
73369
53409

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=38084&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=38084&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=38084&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 time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.629685196986489
beta1
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.629685196986489 \tabularnewline
beta & 1 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=38084&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]0.629685196986489[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=38084&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=38084&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
alpha0.629685196986489
beta1
gamma0






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3462522704319209
45520428717.245897826926486.7541021731
54703551652.5027954595-4617.50279545946
65451152094.29640404342416.70359595665
77336958487.188129727614881.8118702724
85340982100.0306536306-28691.0306536306

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 46252 & 27043 & 19209 \tabularnewline
4 & 55204 & 28717.2458978269 & 26486.7541021731 \tabularnewline
5 & 47035 & 51652.5027954595 & -4617.50279545946 \tabularnewline
6 & 54511 & 52094.2964040434 & 2416.70359595665 \tabularnewline
7 & 73369 & 58487.1881297276 & 14881.8118702724 \tabularnewline
8 & 53409 & 82100.0306536306 & -28691.0306536306 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=38084&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]46252[/C][C]27043[/C][C]19209[/C][/ROW]
[ROW][C]4[/C][C]55204[/C][C]28717.2458978269[/C][C]26486.7541021731[/C][/ROW]
[ROW][C]5[/C][C]47035[/C][C]51652.5027954595[/C][C]-4617.50279545946[/C][/ROW]
[ROW][C]6[/C][C]54511[/C][C]52094.2964040434[/C][C]2416.70359595665[/C][/ROW]
[ROW][C]7[/C][C]73369[/C][C]58487.1881297276[/C][C]14881.8118702724[/C][/ROW]
[ROW][C]8[/C][C]53409[/C][C]82100.0306536306[/C][C]-28691.0306536306[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=38084&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=38084&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
3462522704319209
45520428717.245897826926486.7541021731
54703551652.5027954595-4617.50279545946
65451152094.29640404342416.70359595665
77336958487.188129727614881.8118702724
85340982100.0306536306-28691.0306536306






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
960209.381960731721054.566189955599364.197731508
1056385.0505567096-6580.15174409519119350.252857514
1152560.7191526875-44575.9380985348149697.376403910
1248736.3877486654-89689.0383582924187161.813855623
1344912.0563446433-140448.620404781230272.733094067

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
9 & 60209.3819607317 & 21054.5661899555 & 99364.197731508 \tabularnewline
10 & 56385.0505567096 & -6580.15174409519 & 119350.252857514 \tabularnewline
11 & 52560.7191526875 & -44575.9380985348 & 149697.376403910 \tabularnewline
12 & 48736.3877486654 & -89689.0383582924 & 187161.813855623 \tabularnewline
13 & 44912.0563446433 & -140448.620404781 & 230272.733094067 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=38084&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]9[/C][C]60209.3819607317[/C][C]21054.5661899555[/C][C]99364.197731508[/C][/ROW]
[ROW][C]10[/C][C]56385.0505567096[/C][C]-6580.15174409519[/C][C]119350.252857514[/C][/ROW]
[ROW][C]11[/C][C]52560.7191526875[/C][C]-44575.9380985348[/C][C]149697.376403910[/C][/ROW]
[ROW][C]12[/C][C]48736.3877486654[/C][C]-89689.0383582924[/C][C]187161.813855623[/C][/ROW]
[ROW][C]13[/C][C]44912.0563446433[/C][C]-140448.620404781[/C][C]230272.733094067[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=38084&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=38084&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
960209.381960731721054.566189955599364.197731508
1056385.0505567096-6580.15174409519119350.252857514
1152560.7191526875-44575.9380985348149697.376403910
1248736.3877486654-89689.0383582924187161.813855623
1344912.0563446433-140448.620404781230272.733094067


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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')