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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 computationSun, 11 Aug 2013 17:22:44 -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/2013/Aug/11/t1376256215z1b96zviwo9b23i.htm/, Retrieved Thu, 02 May 2024 08:18:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211015, Retrieved Thu, 02 May 2024 08:18:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact185

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-08-11 21:22:44] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
684.20

584.10

765.38

892.28

885.40

677.02

1006.63

1122.06

1163.39

993.20

1312.46

1545.31

1596.20

1260.41

1735.16

2029.66

2107.79

1650.30

2304.40

2639.42

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'George Udny Yule' @ yule.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211015&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211015&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211015&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'George Udny Yule' @ yule.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.175201784080109
beta1
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.175201784080109 \tabularnewline
beta & 1 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211015&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]0.175201784080109[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211015&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211015&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
alpha0.175201784080109
beta1
gamma1






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
5885.4816.739437568.6605625000002
6677.02618.94121859188858.0787814081123
71006.63922.49830887763284.1316911223685
81122.061109.7199378081112.3400621918934
91163.391204.37040563368-40.9804056336807
10993.2998.532748568981-5.33274856898061
111312.461321.25629517464-8.79629517464036
121545.311425.48989471617119.820105283828
131596.21506.3298534737389.8701465262693
141260.411387.08224309412-126.672243094118
151735.161698.6939433484236.4660566515834
162029.661937.8739867392991.7860132607116
172107.792005.12184849325102.668151506752
181650.31727.77712657823-77.4771265782292
192304.42209.4475815634894.9524184365164
202639.422541.6327602993797.7872397006349

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
5 & 885.4 & 816.7394375 & 68.6605625000002 \tabularnewline
6 & 677.02 & 618.941218591888 & 58.0787814081123 \tabularnewline
7 & 1006.63 & 922.498308877632 & 84.1316911223685 \tabularnewline
8 & 1122.06 & 1109.71993780811 & 12.3400621918934 \tabularnewline
9 & 1163.39 & 1204.37040563368 & -40.9804056336807 \tabularnewline
10 & 993.2 & 998.532748568981 & -5.33274856898061 \tabularnewline
11 & 1312.46 & 1321.25629517464 & -8.79629517464036 \tabularnewline
12 & 1545.31 & 1425.48989471617 & 119.820105283828 \tabularnewline
13 & 1596.2 & 1506.32985347373 & 89.8701465262693 \tabularnewline
14 & 1260.41 & 1387.08224309412 & -126.672243094118 \tabularnewline
15 & 1735.16 & 1698.69394334842 & 36.4660566515834 \tabularnewline
16 & 2029.66 & 1937.87398673929 & 91.7860132607116 \tabularnewline
17 & 2107.79 & 2005.12184849325 & 102.668151506752 \tabularnewline
18 & 1650.3 & 1727.77712657823 & -77.4771265782292 \tabularnewline
19 & 2304.4 & 2209.44758156348 & 94.9524184365164 \tabularnewline
20 & 2639.42 & 2541.63276029937 & 97.7872397006349 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211015&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]5[/C][C]885.4[/C][C]816.7394375[/C][C]68.6605625000002[/C][/ROW]
[ROW][C]6[/C][C]677.02[/C][C]618.941218591888[/C][C]58.0787814081123[/C][/ROW]
[ROW][C]7[/C][C]1006.63[/C][C]922.498308877632[/C][C]84.1316911223685[/C][/ROW]
[ROW][C]8[/C][C]1122.06[/C][C]1109.71993780811[/C][C]12.3400621918934[/C][/ROW]
[ROW][C]9[/C][C]1163.39[/C][C]1204.37040563368[/C][C]-40.9804056336807[/C][/ROW]
[ROW][C]10[/C][C]993.2[/C][C]998.532748568981[/C][C]-5.33274856898061[/C][/ROW]
[ROW][C]11[/C][C]1312.46[/C][C]1321.25629517464[/C][C]-8.79629517464036[/C][/ROW]
[ROW][C]12[/C][C]1545.31[/C][C]1425.48989471617[/C][C]119.820105283828[/C][/ROW]
[ROW][C]13[/C][C]1596.2[/C][C]1506.32985347373[/C][C]89.8701465262693[/C][/ROW]
[ROW][C]14[/C][C]1260.41[/C][C]1387.08224309412[/C][C]-126.672243094118[/C][/ROW]
[ROW][C]15[/C][C]1735.16[/C][C]1698.69394334842[/C][C]36.4660566515834[/C][/ROW]
[ROW][C]16[/C][C]2029.66[/C][C]1937.87398673929[/C][C]91.7860132607116[/C][/ROW]
[ROW][C]17[/C][C]2107.79[/C][C]2005.12184849325[/C][C]102.668151506752[/C][/ROW]
[ROW][C]18[/C][C]1650.3[/C][C]1727.77712657823[/C][C]-77.4771265782292[/C][/ROW]
[ROW][C]19[/C][C]2304.4[/C][C]2209.44758156348[/C][C]94.9524184365164[/C][/ROW]
[ROW][C]20[/C][C]2639.42[/C][C]2541.63276029937[/C][C]97.7872397006349[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211015&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211015&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
5885.4816.739437568.6605625000002
6677.02618.94121859188858.0787814081123
71006.63922.49830887763284.1316911223685
81122.061109.7199378081112.3400621918934
91163.391204.37040563368-40.9804056336807
10993.2998.532748568981-5.33274856898061
111312.461321.25629517464-8.79629517464036
121545.311425.48989471617119.820105283828
131596.21506.3298534737389.8701465262693
141260.411387.08224309412-126.672243094118
151735.161698.6939433484236.4660566515834
162029.661937.8739867392991.7860132607116
172107.792005.12184849325102.668151506752
181650.31727.77712657823-77.4771265782292
192304.42209.4475815634894.9524184365164
202639.422541.6327602993797.7872397006349






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
212657.08946032192515.609136007662798.56978463614
222233.367792290522083.453204405852383.28238017518
232904.600291146342737.255700499063071.94488179362
243239.620291146343045.108034490943434.13254780173

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
21 & 2657.0894603219 & 2515.60913600766 & 2798.56978463614 \tabularnewline
22 & 2233.36779229052 & 2083.45320440585 & 2383.28238017518 \tabularnewline
23 & 2904.60029114634 & 2737.25570049906 & 3071.94488179362 \tabularnewline
24 & 3239.62029114634 & 3045.10803449094 & 3434.13254780173 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211015&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]2657.0894603219[/C][C]2515.60913600766[/C][C]2798.56978463614[/C][/ROW]
[ROW][C]22[/C][C]2233.36779229052[/C][C]2083.45320440585[/C][C]2383.28238017518[/C][/ROW]
[ROW][C]23[/C][C]2904.60029114634[/C][C]2737.25570049906[/C][C]3071.94488179362[/C][/ROW]
[ROW][C]24[/C][C]3239.62029114634[/C][C]3045.10803449094[/C][C]3434.13254780173[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211015&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211015&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
212657.08946032192515.609136007662798.56978463614
222233.367792290522083.453204405852383.28238017518
232904.600291146342737.255700499063071.94488179362
243239.620291146343045.108034490943434.13254780173


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 4 ; par2 = Triple ; 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')