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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 computationSat, 17 Dec 2016 14:55:41 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/17/t14819830269l6xes3vbbsk424.htm/, Retrieved Thu, 02 May 2024 11:55:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300790, Retrieved Thu, 02 May 2024 11:55:53 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact50

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [N1179 Exponential...] [2016-12-17 13:55:41] [2e11ca31a00cf8de75c33c1af2d59434] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3128
3444
3428
3803
3044
3427
3246
3505
3052
3613
3555
3675
3267
3601
3501
3855

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300790&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300790&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300790&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.538951432641687
beta0.495939404109885
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.538951432641687 \tabularnewline
beta & 0.495939404109885 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300790&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]0.538951432641687[/C][/ROW]
[ROW][C]beta[/C][C]0.495939404109885[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300790&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300790&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
alpha0.538951432641687
beta0.495939404109885
gammaFALSE






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
334283760-332
438033808.32875658326-5.32875658326202
530444031.29313910324-987.293139103243
634273461.13554044755-34.1355404475516
732463395.559600307-149.559600306999
835053227.80032311548277.199676884519
930523364.13550974581-312.135509745814
1036133099.41781047522513.58218952478
1135553416.99582047731138.004179522691
1236753569.04228187729105.957718122714
1332673732.13840433678-465.138404336784
1436013463.11588736369137.884112636315
1535013555.9478854375-54.9478854375034
1638553530.16593256933324.834067430671

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3428 & 3760 & -332 \tabularnewline
4 & 3803 & 3808.32875658326 & -5.32875658326202 \tabularnewline
5 & 3044 & 4031.29313910324 & -987.293139103243 \tabularnewline
6 & 3427 & 3461.13554044755 & -34.1355404475516 \tabularnewline
7 & 3246 & 3395.559600307 & -149.559600306999 \tabularnewline
8 & 3505 & 3227.80032311548 & 277.199676884519 \tabularnewline
9 & 3052 & 3364.13550974581 & -312.135509745814 \tabularnewline
10 & 3613 & 3099.41781047522 & 513.58218952478 \tabularnewline
11 & 3555 & 3416.99582047731 & 138.004179522691 \tabularnewline
12 & 3675 & 3569.04228187729 & 105.957718122714 \tabularnewline
13 & 3267 & 3732.13840433678 & -465.138404336784 \tabularnewline
14 & 3601 & 3463.11588736369 & 137.884112636315 \tabularnewline
15 & 3501 & 3555.9478854375 & -54.9478854375034 \tabularnewline
16 & 3855 & 3530.16593256933 & 324.834067430671 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300790&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]3428[/C][C]3760[/C][C]-332[/C][/ROW]
[ROW][C]4[/C][C]3803[/C][C]3808.32875658326[/C][C]-5.32875658326202[/C][/ROW]
[ROW][C]5[/C][C]3044[/C][C]4031.29313910324[/C][C]-987.293139103243[/C][/ROW]
[ROW][C]6[/C][C]3427[/C][C]3461.13554044755[/C][C]-34.1355404475516[/C][/ROW]
[ROW][C]7[/C][C]3246[/C][C]3395.559600307[/C][C]-149.559600306999[/C][/ROW]
[ROW][C]8[/C][C]3505[/C][C]3227.80032311548[/C][C]277.199676884519[/C][/ROW]
[ROW][C]9[/C][C]3052[/C][C]3364.13550974581[/C][C]-312.135509745814[/C][/ROW]
[ROW][C]10[/C][C]3613[/C][C]3099.41781047522[/C][C]513.58218952478[/C][/ROW]
[ROW][C]11[/C][C]3555[/C][C]3416.99582047731[/C][C]138.004179522691[/C][/ROW]
[ROW][C]12[/C][C]3675[/C][C]3569.04228187729[/C][C]105.957718122714[/C][/ROW]
[ROW][C]13[/C][C]3267[/C][C]3732.13840433678[/C][C]-465.138404336784[/C][/ROW]
[ROW][C]14[/C][C]3601[/C][C]3463.11588736369[/C][C]137.884112636315[/C][/ROW]
[ROW][C]15[/C][C]3501[/C][C]3555.9478854375[/C][C]-54.9478854375034[/C][/ROW]
[ROW][C]16[/C][C]3855[/C][C]3530.16593256933[/C][C]324.834067430671[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300790&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300790&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
334283760-332
438033808.32875658326-5.32875658326202
530444031.29313910324-987.293139103243
634273461.13554044755-34.1355404475516
732463395.559600307-149.559600306999
835053227.80032311548277.199676884519
930523364.13550974581-312.135509745814
1036133099.41781047522513.58218952478
1135553416.99582047731138.004179522691
1236753569.04228187729105.957718122714
1332673732.13840433678-465.138404336784
1436013463.11588736369137.884112636315
1535013555.9478854375-54.9478854375034
1638553530.16593256933324.834067430671






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
173795.892012643643052.540782151214539.24324313607
183886.548306705372931.690338962934841.40627444781
193977.20460076712732.789624290255221.61957724394
204067.860894828822473.505280593015662.21650906463
214158.517188890552165.802608507266151.23176927383
224249.173482952271817.23034139346681.11662451114

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
17 & 3795.89201264364 & 3052.54078215121 & 4539.24324313607 \tabularnewline
18 & 3886.54830670537 & 2931.69033896293 & 4841.40627444781 \tabularnewline
19 & 3977.2046007671 & 2732.78962429025 & 5221.61957724394 \tabularnewline
20 & 4067.86089482882 & 2473.50528059301 & 5662.21650906463 \tabularnewline
21 & 4158.51718889055 & 2165.80260850726 & 6151.23176927383 \tabularnewline
22 & 4249.17348295227 & 1817.2303413934 & 6681.11662451114 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300790&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]17[/C][C]3795.89201264364[/C][C]3052.54078215121[/C][C]4539.24324313607[/C][/ROW]
[ROW][C]18[/C][C]3886.54830670537[/C][C]2931.69033896293[/C][C]4841.40627444781[/C][/ROW]
[ROW][C]19[/C][C]3977.2046007671[/C][C]2732.78962429025[/C][C]5221.61957724394[/C][/ROW]
[ROW][C]20[/C][C]4067.86089482882[/C][C]2473.50528059301[/C][C]5662.21650906463[/C][/ROW]
[ROW][C]21[/C][C]4158.51718889055[/C][C]2165.80260850726[/C][C]6151.23176927383[/C][/ROW]
[ROW][C]22[/C][C]4249.17348295227[/C][C]1817.2303413934[/C][C]6681.11662451114[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300790&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300790&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
173795.892012643643052.540782151214539.24324313607
183886.548306705372931.690338962934841.40627444781
193977.20460076712732.789624290255221.61957724394
204067.860894828822473.505280593015662.21650906463
214158.517188890552165.802608507266151.23176927383
224249.173482952271817.23034139346681.11662451114


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 6 ;
R code (references can be found in the software module):
par4 <- '6'
par3 <- 'additive'
par2 <- 'Triple'
par1 <- '12'
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')