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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 23 Jul 2012 13:06:59 -0400

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/2012/Jul/23/t1343064077wjb4lo3nvd9jw1j.htm/, Retrieved Sun, 28 Apr 2024 17:24:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=168831, Retrieved Sun, 28 Apr 2024 17:24:42 +0000

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Original text written by user:

risk forecasting for health pilot

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No (this computation is public)

User-defined keywords

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Estimated Impact

178

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

-       [Exponential Smoothing] [healtchare] [2012-07-23 17:06:59] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Histogram

Boxplots

4.2
2.6
2.0
2.8
4.8
4.9
5.6
2.7
1.9
6.8
4.6
4.0
2.8
9.0
3.8

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168831&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168831&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168831&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	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	6.61069613518961e-05
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 6.61069613518961e-05 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168831&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]6.61069613518961e-05[/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=168831&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168831&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	6.61069613518961e-05
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	2.6	4.2	-1.6
3	2	4.19989422886184	-2.19989422886184
4	2.8	4.19974880053907	-1.39974880053907
5	4.8	4.19965626739921	0.600343732600788
6	4.9	4.19969595429914	0.700304045700859
7	5.6	4.19974224927163	1.40025775072837
8	2.7	4.19983481605664	-1.49983481605664
9	1.9	4.19973566653442	-2.29973566653442
10	6.8	4.19958363799759	2.60041636200241
11	4.6	4.19975554362153	0.400244456378468
12	4	4.19978200256634	-0.199782002566341
13	2.8	4.19976879558522	-1.39976879558522
14	9	4.19967626112355	4.80032373887645
15	3.8	4.19999359593943	-0.399993595939431

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 2.6 & 4.2 & -1.6 \tabularnewline
3 & 2 & 4.19989422886184 & -2.19989422886184 \tabularnewline
4 & 2.8 & 4.19974880053907 & -1.39974880053907 \tabularnewline
5 & 4.8 & 4.19965626739921 & 0.600343732600788 \tabularnewline
6 & 4.9 & 4.19969595429914 & 0.700304045700859 \tabularnewline
7 & 5.6 & 4.19974224927163 & 1.40025775072837 \tabularnewline
8 & 2.7 & 4.19983481605664 & -1.49983481605664 \tabularnewline
9 & 1.9 & 4.19973566653442 & -2.29973566653442 \tabularnewline
10 & 6.8 & 4.19958363799759 & 2.60041636200241 \tabularnewline
11 & 4.6 & 4.19975554362153 & 0.400244456378468 \tabularnewline
12 & 4 & 4.19978200256634 & -0.199782002566341 \tabularnewline
13 & 2.8 & 4.19976879558522 & -1.39976879558522 \tabularnewline
14 & 9 & 4.19967626112355 & 4.80032373887645 \tabularnewline
15 & 3.8 & 4.19999359593943 & -0.399993595939431 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168831&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]2.6[/C][C]4.2[/C][C]-1.6[/C][/ROW]
[ROW][C]3[/C][C]2[/C][C]4.19989422886184[/C][C]-2.19989422886184[/C][/ROW]
[ROW][C]4[/C][C]2.8[/C][C]4.19974880053907[/C][C]-1.39974880053907[/C][/ROW]
[ROW][C]5[/C][C]4.8[/C][C]4.19965626739921[/C][C]0.600343732600788[/C][/ROW]
[ROW][C]6[/C][C]4.9[/C][C]4.19969595429914[/C][C]0.700304045700859[/C][/ROW]
[ROW][C]7[/C][C]5.6[/C][C]4.19974224927163[/C][C]1.40025775072837[/C][/ROW]
[ROW][C]8[/C][C]2.7[/C][C]4.19983481605664[/C][C]-1.49983481605664[/C][/ROW]
[ROW][C]9[/C][C]1.9[/C][C]4.19973566653442[/C][C]-2.29973566653442[/C][/ROW]
[ROW][C]10[/C][C]6.8[/C][C]4.19958363799759[/C][C]2.60041636200241[/C][/ROW]
[ROW][C]11[/C][C]4.6[/C][C]4.19975554362153[/C][C]0.400244456378468[/C][/ROW]
[ROW][C]12[/C][C]4[/C][C]4.19978200256634[/C][C]-0.199782002566341[/C][/ROW]
[ROW][C]13[/C][C]2.8[/C][C]4.19976879558522[/C][C]-1.39976879558522[/C][/ROW]
[ROW][C]14[/C][C]9[/C][C]4.19967626112355[/C][C]4.80032373887645[/C][/ROW]
[ROW][C]15[/C][C]3.8[/C][C]4.19999359593943[/C][C]-0.399993595939431[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168831&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168831&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	2.6	4.2	-1.6
3	2	4.19989422886184	-2.19989422886184
4	2.8	4.19974880053907	-1.39974880053907
5	4.8	4.19965626739921	0.600343732600788
6	4.9	4.19969595429914	0.700304045700859
7	5.6	4.19974224927163	1.40025775072837
8	2.7	4.19983481605664	-1.49983481605664
9	1.9	4.19973566653442	-2.29973566653442
10	6.8	4.19958363799759	2.60041636200241
11	4.6	4.19975554362153	0.400244456378468
12	4	4.19978200256634	-0.199782002566341
13	2.8	4.19976879558522	-1.39976879558522
14	9	4.19967626112355	4.80032373887645
15	3.8	4.19999359593943	-0.399993595939431

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
16	4.19996715357824	0.286989074759388	8.1129452323971
17	4.19996715357824	0.286989066209276	8.11294524094721
18	4.19996715357824	0.286989057659164	8.11294524949732
19	4.19996715357824	0.286989049109052	8.11294525804743
20	4.19996715357824	0.28698904055894	8.11294526659755
21	4.19996715357824	0.286989032008828	8.11294527514766
22	4.19996715357824	0.286989023458716	8.11294528369777
23	4.19996715357824	0.286989014908603	8.11294529224788
24	4.19996715357824	0.286989006358492	8.11294530079799
25	4.19996715357824	0.28698899780838	8.11294530934811
26	4.19996715357824	0.286988989258268	8.11294531789822
27	4.19996715357824	0.286988980708156	8.11294532644833

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
16 & 4.19996715357824 & 0.286989074759388 & 8.1129452323971 \tabularnewline
17 & 4.19996715357824 & 0.286989066209276 & 8.11294524094721 \tabularnewline
18 & 4.19996715357824 & 0.286989057659164 & 8.11294524949732 \tabularnewline
19 & 4.19996715357824 & 0.286989049109052 & 8.11294525804743 \tabularnewline
20 & 4.19996715357824 & 0.28698904055894 & 8.11294526659755 \tabularnewline
21 & 4.19996715357824 & 0.286989032008828 & 8.11294527514766 \tabularnewline
22 & 4.19996715357824 & 0.286989023458716 & 8.11294528369777 \tabularnewline
23 & 4.19996715357824 & 0.286989014908603 & 8.11294529224788 \tabularnewline
24 & 4.19996715357824 & 0.286989006358492 & 8.11294530079799 \tabularnewline
25 & 4.19996715357824 & 0.28698899780838 & 8.11294530934811 \tabularnewline
26 & 4.19996715357824 & 0.286988989258268 & 8.11294531789822 \tabularnewline
27 & 4.19996715357824 & 0.286988980708156 & 8.11294532644833 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168831&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]16[/C][C]4.19996715357824[/C][C]0.286989074759388[/C][C]8.1129452323971[/C][/ROW]
[ROW][C]17[/C][C]4.19996715357824[/C][C]0.286989066209276[/C][C]8.11294524094721[/C][/ROW]
[ROW][C]18[/C][C]4.19996715357824[/C][C]0.286989057659164[/C][C]8.11294524949732[/C][/ROW]
[ROW][C]19[/C][C]4.19996715357824[/C][C]0.286989049109052[/C][C]8.11294525804743[/C][/ROW]
[ROW][C]20[/C][C]4.19996715357824[/C][C]0.28698904055894[/C][C]8.11294526659755[/C][/ROW]
[ROW][C]21[/C][C]4.19996715357824[/C][C]0.286989032008828[/C][C]8.11294527514766[/C][/ROW]
[ROW][C]22[/C][C]4.19996715357824[/C][C]0.286989023458716[/C][C]8.11294528369777[/C][/ROW]
[ROW][C]23[/C][C]4.19996715357824[/C][C]0.286989014908603[/C][C]8.11294529224788[/C][/ROW]
[ROW][C]24[/C][C]4.19996715357824[/C][C]0.286989006358492[/C][C]8.11294530079799[/C][/ROW]
[ROW][C]25[/C][C]4.19996715357824[/C][C]0.28698899780838[/C][C]8.11294530934811[/C][/ROW]
[ROW][C]26[/C][C]4.19996715357824[/C][C]0.286988989258268[/C][C]8.11294531789822[/C][/ROW]
[ROW][C]27[/C][C]4.19996715357824[/C][C]0.286988980708156[/C][C]8.11294532644833[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168831&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168831&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
16	4.19996715357824	0.286989074759388	8.1129452323971
17	4.19996715357824	0.286989066209276	8.11294524094721
18	4.19996715357824	0.286989057659164	8.11294524949732
19	4.19996715357824	0.286989049109052	8.11294525804743
20	4.19996715357824	0.28698904055894	8.11294526659755
21	4.19996715357824	0.286989032008828	8.11294527514766
22	4.19996715357824	0.286989023458716	8.11294528369777
23	4.19996715357824	0.286989014908603	8.11294529224788
24	4.19996715357824	0.286989006358492	8.11294530079799
25	4.19996715357824	0.28698899780838	8.11294530934811
26	4.19996715357824	0.286988989258268	8.11294531789822
27	4.19996715357824	0.286988980708156	8.11294532644833

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 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; 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