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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 computationFri, 23 Dec 2016 14:10:10 +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/23/t1482498631ggg37igm6kuwucd.htm/, Retrieved Tue, 07 May 2024 15:37:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302928, Retrieved Tue, 07 May 2024 15:37:41 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [niet flippen stom...] [2016-12-23 13:10:10] [d92250bd36540c2281a4ec15b45df1dd] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4511.15
4497.61
4497.61
4524.68
4569.79
4596.85
4614.9
4632.94
4660.02
4714.15
4772.79
4817.9
4872.04
4926.17
4971.28
5020.9
5066.02
5088.57
5084.06
5066.02

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=302928&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=302928&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302928&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
alpha1
beta0.467657063306984
gamma0.023757986713303

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.467657063306984 \tabularnewline
gamma & 0.023757986713303 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302928&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.467657063306984[/C][/ROW]
[ROW][C]gamma[/C][C]0.023757986713303[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302928&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302928&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
alpha1
beta0.467657063306984
gamma0.023757986713303






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
74614.94540.3127976190574.5872023809497
84632.944663.69694631147-30.7569463114723
94660.024673.76157645649-13.7415764564921
104714.154709.434397832314.71560216769376
114772.794784.19468249377-11.4046824937741
124817.94814.562868837453.33713116254512
134872.044847.7118351301324.3281648698667
144926.174909.8365732688216.3334267311766
154971.284978.013348981-6.73334898100074
165020.95034.99361743699-14.093617436989
175066.025096.44763769504-30.4276376950347
185088.575104.39960467387-15.8296046738751
195084.065106.02511157211-21.9651115721108
205066.025087.85047199909-21.8304719990883

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
7 & 4614.9 & 4540.31279761905 & 74.5872023809497 \tabularnewline
8 & 4632.94 & 4663.69694631147 & -30.7569463114723 \tabularnewline
9 & 4660.02 & 4673.76157645649 & -13.7415764564921 \tabularnewline
10 & 4714.15 & 4709.43439783231 & 4.71560216769376 \tabularnewline
11 & 4772.79 & 4784.19468249377 & -11.4046824937741 \tabularnewline
12 & 4817.9 & 4814.56286883745 & 3.33713116254512 \tabularnewline
13 & 4872.04 & 4847.71183513013 & 24.3281648698667 \tabularnewline
14 & 4926.17 & 4909.83657326882 & 16.3334267311766 \tabularnewline
15 & 4971.28 & 4978.013348981 & -6.73334898100074 \tabularnewline
16 & 5020.9 & 5034.99361743699 & -14.093617436989 \tabularnewline
17 & 5066.02 & 5096.44763769504 & -30.4276376950347 \tabularnewline
18 & 5088.57 & 5104.39960467387 & -15.8296046738751 \tabularnewline
19 & 5084.06 & 5106.02511157211 & -21.9651115721108 \tabularnewline
20 & 5066.02 & 5087.85047199909 & -21.8304719990883 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302928&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]7[/C][C]4614.9[/C][C]4540.31279761905[/C][C]74.5872023809497[/C][/ROW]
[ROW][C]8[/C][C]4632.94[/C][C]4663.69694631147[/C][C]-30.7569463114723[/C][/ROW]
[ROW][C]9[/C][C]4660.02[/C][C]4673.76157645649[/C][C]-13.7415764564921[/C][/ROW]
[ROW][C]10[/C][C]4714.15[/C][C]4709.43439783231[/C][C]4.71560216769376[/C][/ROW]
[ROW][C]11[/C][C]4772.79[/C][C]4784.19468249377[/C][C]-11.4046824937741[/C][/ROW]
[ROW][C]12[/C][C]4817.9[/C][C]4814.56286883745[/C][C]3.33713116254512[/C][/ROW]
[ROW][C]13[/C][C]4872.04[/C][C]4847.71183513013[/C][C]24.3281648698667[/C][/ROW]
[ROW][C]14[/C][C]4926.17[/C][C]4909.83657326882[/C][C]16.3334267311766[/C][/ROW]
[ROW][C]15[/C][C]4971.28[/C][C]4978.013348981[/C][C]-6.73334898100074[/C][/ROW]
[ROW][C]16[/C][C]5020.9[/C][C]5034.99361743699[/C][C]-14.093617436989[/C][/ROW]
[ROW][C]17[/C][C]5066.02[/C][C]5096.44763769504[/C][C]-30.4276376950347[/C][/ROW]
[ROW][C]18[/C][C]5088.57[/C][C]5104.39960467387[/C][C]-15.8296046738751[/C][/ROW]
[ROW][C]19[/C][C]5084.06[/C][C]5106.02511157211[/C][C]-21.9651115721108[/C][/ROW]
[ROW][C]20[/C][C]5066.02[/C][C]5087.85047199909[/C][C]-21.8304719990883[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302928&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302928&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
74614.94540.3127976190574.5872023809497
84632.944663.69694631147-30.7569463114723
94660.024673.76157645649-13.7415764564921
104714.154709.434397832314.71560216769376
114772.794784.19468249377-11.4046824937741
124817.94814.562868837453.33713116254512
134872.044847.7118351301324.3281648698667
144926.174909.8365732688216.3334267311766
154971.284978.013348981-6.73334898100074
165020.95034.99361743699-14.093617436989
175066.025096.44763769504-30.4276376950347
185088.575104.39960467387-15.8296046738751
195084.065106.02511157211-21.9651115721108
205066.025087.85047199909-21.8304719990883






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
215066.009630906725011.746509529255120.27275228419
225081.018428480114984.649550049375177.38730691085
235114.45222605354971.920265017675256.98418708934
245124.947690293564931.76999837915318.12538220802
255121.921487866954873.764925004655370.07805072925
265115.502785440344808.264321404625422.74124947605
275115.492416347064745.293902466765485.69093022736
285130.501213920454693.667133139535567.33529470137
295163.935011493844656.968904251735670.90111873594
305174.43047573394593.993798987595754.8671524802
315171.404273307284514.298302901035828.51024371354
325164.985570880674428.136106921055901.8350348403

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
21 & 5066.00963090672 & 5011.74650952925 & 5120.27275228419 \tabularnewline
22 & 5081.01842848011 & 4984.64955004937 & 5177.38730691085 \tabularnewline
23 & 5114.4522260535 & 4971.92026501767 & 5256.98418708934 \tabularnewline
24 & 5124.94769029356 & 4931.7699983791 & 5318.12538220802 \tabularnewline
25 & 5121.92148786695 & 4873.76492500465 & 5370.07805072925 \tabularnewline
26 & 5115.50278544034 & 4808.26432140462 & 5422.74124947605 \tabularnewline
27 & 5115.49241634706 & 4745.29390246676 & 5485.69093022736 \tabularnewline
28 & 5130.50121392045 & 4693.66713313953 & 5567.33529470137 \tabularnewline
29 & 5163.93501149384 & 4656.96890425173 & 5670.90111873594 \tabularnewline
30 & 5174.4304757339 & 4593.99379898759 & 5754.8671524802 \tabularnewline
31 & 5171.40427330728 & 4514.29830290103 & 5828.51024371354 \tabularnewline
32 & 5164.98557088067 & 4428.13610692105 & 5901.8350348403 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302928&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]5066.00963090672[/C][C]5011.74650952925[/C][C]5120.27275228419[/C][/ROW]
[ROW][C]22[/C][C]5081.01842848011[/C][C]4984.64955004937[/C][C]5177.38730691085[/C][/ROW]
[ROW][C]23[/C][C]5114.4522260535[/C][C]4971.92026501767[/C][C]5256.98418708934[/C][/ROW]
[ROW][C]24[/C][C]5124.94769029356[/C][C]4931.7699983791[/C][C]5318.12538220802[/C][/ROW]
[ROW][C]25[/C][C]5121.92148786695[/C][C]4873.76492500465[/C][C]5370.07805072925[/C][/ROW]
[ROW][C]26[/C][C]5115.50278544034[/C][C]4808.26432140462[/C][C]5422.74124947605[/C][/ROW]
[ROW][C]27[/C][C]5115.49241634706[/C][C]4745.29390246676[/C][C]5485.69093022736[/C][/ROW]
[ROW][C]28[/C][C]5130.50121392045[/C][C]4693.66713313953[/C][C]5567.33529470137[/C][/ROW]
[ROW][C]29[/C][C]5163.93501149384[/C][C]4656.96890425173[/C][C]5670.90111873594[/C][/ROW]
[ROW][C]30[/C][C]5174.4304757339[/C][C]4593.99379898759[/C][C]5754.8671524802[/C][/ROW]
[ROW][C]31[/C][C]5171.40427330728[/C][C]4514.29830290103[/C][C]5828.51024371354[/C][/ROW]
[ROW][C]32[/C][C]5164.98557088067[/C][C]4428.13610692105[/C][C]5901.8350348403[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302928&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302928&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
215066.009630906725011.746509529255120.27275228419
225081.018428480114984.649550049375177.38730691085
235114.45222605354971.920265017675256.98418708934
245124.947690293564931.76999837915318.12538220802
255121.921487866954873.764925004655370.07805072925
265115.502785440344808.264321404625422.74124947605
275115.492416347064745.293902466765485.69093022736
285130.501213920454693.667133139535567.33529470137
295163.935011493844656.968904251735670.90111873594
305174.43047573394593.993798987595754.8671524802
315171.404273307284514.298302901035828.51024371354
325164.985570880674428.136106921055901.8350348403


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 6 ; par6 = 2 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
Parameters (R input):
par1 = 6 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
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')