Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 10 Jan 2016 14:43:56 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Jan/10/t1452437175n1ig9uqq3c7yjvu.htm/, Retrieved Sat, 04 May 2024 23:04:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=287881, Retrieved Sat, 04 May 2024 23:04:02 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Exponential Smoothing] [] [2016-01-10 14:43:56] [d41d8cd98f00b204e9800998ecf8427e] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

3,25
1,85
1,45
2,8
4,05
2,15
1,9
3,45
4,45
2,2
2
3,75
4,6
2,25
2,3
4,3

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ yule.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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287881&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287881&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287881&T=0

As an alternative you can also use a 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 Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.0176224703645908
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0176224703645908 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287881&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]0.0176224703645908[/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=287881&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287881&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.0176224703645908
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	1.85	3.25	-1.4
3	1.45	3.22532854148957	-1.77532854148957
4	2.8	3.19404286687976	-0.394042866879761
5	4.05	3.18709885813579	0.862901141864206
6	2.15	3.20230530793587	-1.05230530793587
7	1.9	3.18376108883227	-1.28376108883227
8	3.45	3.16113804708911	0.288861952910895
9	4.45	3.16622850829374	1.28377149170626
10	2.2	3.18885173336124	-0.988851733361236
11	2	3.1714257229951	-1.1714257229951
12	3.75	3.1507823079073	0.599217692092697
13	4.6	3.16134200392814	1.43865799607185
14	2.25	3.1866947118287	-0.936694711828703
15	2.3	3.17018783702883	-0.870187837028833
16	4.3	3.15485297765916	1.14514702234084

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1.85 & 3.25 & -1.4 \tabularnewline
3 & 1.45 & 3.22532854148957 & -1.77532854148957 \tabularnewline
4 & 2.8 & 3.19404286687976 & -0.394042866879761 \tabularnewline
5 & 4.05 & 3.18709885813579 & 0.862901141864206 \tabularnewline
6 & 2.15 & 3.20230530793587 & -1.05230530793587 \tabularnewline
7 & 1.9 & 3.18376108883227 & -1.28376108883227 \tabularnewline
8 & 3.45 & 3.16113804708911 & 0.288861952910895 \tabularnewline
9 & 4.45 & 3.16622850829374 & 1.28377149170626 \tabularnewline
10 & 2.2 & 3.18885173336124 & -0.988851733361236 \tabularnewline
11 & 2 & 3.1714257229951 & -1.1714257229951 \tabularnewline
12 & 3.75 & 3.1507823079073 & 0.599217692092697 \tabularnewline
13 & 4.6 & 3.16134200392814 & 1.43865799607185 \tabularnewline
14 & 2.25 & 3.1866947118287 & -0.936694711828703 \tabularnewline
15 & 2.3 & 3.17018783702883 & -0.870187837028833 \tabularnewline
16 & 4.3 & 3.15485297765916 & 1.14514702234084 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287881&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]1.85[/C][C]3.25[/C][C]-1.4[/C][/ROW]
[ROW][C]3[/C][C]1.45[/C][C]3.22532854148957[/C][C]-1.77532854148957[/C][/ROW]
[ROW][C]4[/C][C]2.8[/C][C]3.19404286687976[/C][C]-0.394042866879761[/C][/ROW]
[ROW][C]5[/C][C]4.05[/C][C]3.18709885813579[/C][C]0.862901141864206[/C][/ROW]
[ROW][C]6[/C][C]2.15[/C][C]3.20230530793587[/C][C]-1.05230530793587[/C][/ROW]
[ROW][C]7[/C][C]1.9[/C][C]3.18376108883227[/C][C]-1.28376108883227[/C][/ROW]
[ROW][C]8[/C][C]3.45[/C][C]3.16113804708911[/C][C]0.288861952910895[/C][/ROW]
[ROW][C]9[/C][C]4.45[/C][C]3.16622850829374[/C][C]1.28377149170626[/C][/ROW]
[ROW][C]10[/C][C]2.2[/C][C]3.18885173336124[/C][C]-0.988851733361236[/C][/ROW]
[ROW][C]11[/C][C]2[/C][C]3.1714257229951[/C][C]-1.1714257229951[/C][/ROW]
[ROW][C]12[/C][C]3.75[/C][C]3.1507823079073[/C][C]0.599217692092697[/C][/ROW]
[ROW][C]13[/C][C]4.6[/C][C]3.16134200392814[/C][C]1.43865799607185[/C][/ROW]
[ROW][C]14[/C][C]2.25[/C][C]3.1866947118287[/C][C]-0.936694711828703[/C][/ROW]
[ROW][C]15[/C][C]2.3[/C][C]3.17018783702883[/C][C]-0.870187837028833[/C][/ROW]
[ROW][C]16[/C][C]4.3[/C][C]3.15485297765916[/C][C]1.14514702234084[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287881&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287881&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	1.85	3.25	-1.4
3	1.45	3.22532854148957	-1.77532854148957
4	2.8	3.19404286687976	-0.394042866879761
5	4.05	3.18709885813579	0.862901141864206
6	2.15	3.20230530793587	-1.05230530793587
7	1.9	3.18376108883227	-1.28376108883227
8	3.45	3.16113804708911	0.288861952910895
9	4.45	3.16622850829374	1.28377149170626
10	2.2	3.18885173336124	-0.988851733361236
11	2	3.1714257229951	-1.1714257229951
12	3.75	3.1507823079073	0.599217692092697
13	4.6	3.16134200392814	1.43865799607185
14	2.25	3.1866947118287	-0.936694711828703
15	2.3	3.17018783702883	-0.870187837028833
16	4.3	3.15485297765916	1.14514702234084

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
17	3.17503329712346	1.01418161466347	5.33588497958346
18	3.17503329712346	1.01384611288478	5.33622048136215
19	3.17503329712346	1.01351066318116	5.33655593106577
20	3.17503329712346	1.01317526552837	5.33689132871856

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
17 & 3.17503329712346 & 1.01418161466347 & 5.33588497958346 \tabularnewline
18 & 3.17503329712346 & 1.01384611288478 & 5.33622048136215 \tabularnewline
19 & 3.17503329712346 & 1.01351066318116 & 5.33655593106577 \tabularnewline
20 & 3.17503329712346 & 1.01317526552837 & 5.33689132871856 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287881&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]3.17503329712346[/C][C]1.01418161466347[/C][C]5.33588497958346[/C][/ROW]
[ROW][C]18[/C][C]3.17503329712346[/C][C]1.01384611288478[/C][C]5.33622048136215[/C][/ROW]
[ROW][C]19[/C][C]3.17503329712346[/C][C]1.01351066318116[/C][C]5.33655593106577[/C][/ROW]
[ROW][C]20[/C][C]3.17503329712346[/C][C]1.01317526552837[/C][C]5.33689132871856[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287881&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287881&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
17	3.17503329712346	1.01418161466347	5.33588497958346
18	3.17503329712346	1.01384611288478	5.33622048136215
19	3.17503329712346	1.01351066318116	5.33655593106577
20	3.17503329712346	1.01317526552837	5.33689132871856

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 4 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 4 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code