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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 12 Nov 2013 08:52:33 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Nov/12/t1384264375osyoovzm1cymo0c.htm/, Retrieved Thu, 02 May 2024 22:05:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=224389, Retrieved Thu, 02 May 2024 22:05:28 +0000

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-     [Multiple Regression] [HPC Retail Sales] [2008-03-08 13:40:54] [1c0f2c85e8a48e42648374b3bcceca26]
- RMPD    [Exponential Smoothing] [sjlpkhpqisuf] [2013-11-12 13:52:33] [e931f330ae8eb739e69629b6955c783c] [Current]

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-6
-7
-12
-16
-18
-19
-20
-24
-17
-23
-25
-24
-17

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	'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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224389&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]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224389&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224389&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	'George Udny Yule' @ yule.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.921244149227802
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.921244149227802 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224389&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]0.921244149227802[/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=224389&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224389&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	0.921244149227802
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	-7	-6	-1
3	-12	-6.9212441492278	-5.0787558507722
4	-16	-11.6000182621082	-4.39998173789184
5	-18	-15.6534756948502	-2.34652430514981
6	-19	-17.8151974819903	-1.18480251800971
7	-20	-18.9066898696971	-1.0933101303029
8	-24	-19.9138954305301	-4.08610456946987
9	-17	-23.6781953582872	6.67819535828724
10	-23	-17.5259469570649	-5.47405304293515
11	-25	-22.5688862954315	-2.4311137045685
12	-24	-24.8085355718728	0.80853557187276
13	-17	-24.0636769068424	7.06367690684242

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & -7 & -6 & -1 \tabularnewline
3 & -12 & -6.9212441492278 & -5.0787558507722 \tabularnewline
4 & -16 & -11.6000182621082 & -4.39998173789184 \tabularnewline
5 & -18 & -15.6534756948502 & -2.34652430514981 \tabularnewline
6 & -19 & -17.8151974819903 & -1.18480251800971 \tabularnewline
7 & -20 & -18.9066898696971 & -1.0933101303029 \tabularnewline
8 & -24 & -19.9138954305301 & -4.08610456946987 \tabularnewline
9 & -17 & -23.6781953582872 & 6.67819535828724 \tabularnewline
10 & -23 & -17.5259469570649 & -5.47405304293515 \tabularnewline
11 & -25 & -22.5688862954315 & -2.4311137045685 \tabularnewline
12 & -24 & -24.8085355718728 & 0.80853557187276 \tabularnewline
13 & -17 & -24.0636769068424 & 7.06367690684242 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224389&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]-7[/C][C]-6[/C][C]-1[/C][/ROW]
[ROW][C]3[/C][C]-12[/C][C]-6.9212441492278[/C][C]-5.0787558507722[/C][/ROW]
[ROW][C]4[/C][C]-16[/C][C]-11.6000182621082[/C][C]-4.39998173789184[/C][/ROW]
[ROW][C]5[/C][C]-18[/C][C]-15.6534756948502[/C][C]-2.34652430514981[/C][/ROW]
[ROW][C]6[/C][C]-19[/C][C]-17.8151974819903[/C][C]-1.18480251800971[/C][/ROW]
[ROW][C]7[/C][C]-20[/C][C]-18.9066898696971[/C][C]-1.0933101303029[/C][/ROW]
[ROW][C]8[/C][C]-24[/C][C]-19.9138954305301[/C][C]-4.08610456946987[/C][/ROW]
[ROW][C]9[/C][C]-17[/C][C]-23.6781953582872[/C][C]6.67819535828724[/C][/ROW]
[ROW][C]10[/C][C]-23[/C][C]-17.5259469570649[/C][C]-5.47405304293515[/C][/ROW]
[ROW][C]11[/C][C]-25[/C][C]-22.5688862954315[/C][C]-2.4311137045685[/C][/ROW]
[ROW][C]12[/C][C]-24[/C][C]-24.8085355718728[/C][C]0.80853557187276[/C][/ROW]
[ROW][C]13[/C][C]-17[/C][C]-24.0636769068424[/C][C]7.06367690684242[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224389&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224389&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	-7	-6	-1
3	-12	-6.9212441492278	-5.0787558507722
4	-16	-11.6000182621082	-4.39998173789184
5	-18	-15.6534756948502	-2.34652430514981
6	-19	-17.8151974819903	-1.18480251800971
7	-20	-18.9066898696971	-1.0933101303029
8	-24	-19.9138954305301	-4.08610456946987
9	-17	-23.6781953582872	6.67819535828724
10	-23	-17.5259469570649	-5.47405304293515
11	-25	-22.5688862954315	-2.4311137045685
12	-24	-24.8085355718728	0.80853557187276
13	-17	-24.0636769068424	7.06367690684242

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
14	-17.5563058843783	-25.6776437553135	-9.43496801344309
15	-17.5563058843783	-28.5986103262383	-6.5140014425183
16	-17.5563058843783	-30.8945533689452	-4.21805839981137
17	-17.5563058843783	-32.8496117576155	-2.26300001114112
18	-17.5563058843783	-34.5816271179182	-0.530984650838374
19	-17.5563058843783	-36.1530239195064	1.04041215074984
20	-17.5563058843783	-37.6016115755095	2.48899980675286
21	-17.5563058843783	-38.9523484816375	3.83973671288089
22	-17.5563058843783	-40.2227347472708	5.11012297851417
23	-17.5563058843783	-41.4256032340993	6.31299146534273
24	-17.5563058843783	-42.570696033695	7.45808426493844
25	-17.5563058843783	-43.6656159693857	8.5530042006291

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
14 & -17.5563058843783 & -25.6776437553135 & -9.43496801344309 \tabularnewline
15 & -17.5563058843783 & -28.5986103262383 & -6.5140014425183 \tabularnewline
16 & -17.5563058843783 & -30.8945533689452 & -4.21805839981137 \tabularnewline
17 & -17.5563058843783 & -32.8496117576155 & -2.26300001114112 \tabularnewline
18 & -17.5563058843783 & -34.5816271179182 & -0.530984650838374 \tabularnewline
19 & -17.5563058843783 & -36.1530239195064 & 1.04041215074984 \tabularnewline
20 & -17.5563058843783 & -37.6016115755095 & 2.48899980675286 \tabularnewline
21 & -17.5563058843783 & -38.9523484816375 & 3.83973671288089 \tabularnewline
22 & -17.5563058843783 & -40.2227347472708 & 5.11012297851417 \tabularnewline
23 & -17.5563058843783 & -41.4256032340993 & 6.31299146534273 \tabularnewline
24 & -17.5563058843783 & -42.570696033695 & 7.45808426493844 \tabularnewline
25 & -17.5563058843783 & -43.6656159693857 & 8.5530042006291 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224389&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]14[/C][C]-17.5563058843783[/C][C]-25.6776437553135[/C][C]-9.43496801344309[/C][/ROW]
[ROW][C]15[/C][C]-17.5563058843783[/C][C]-28.5986103262383[/C][C]-6.5140014425183[/C][/ROW]
[ROW][C]16[/C][C]-17.5563058843783[/C][C]-30.8945533689452[/C][C]-4.21805839981137[/C][/ROW]
[ROW][C]17[/C][C]-17.5563058843783[/C][C]-32.8496117576155[/C][C]-2.26300001114112[/C][/ROW]
[ROW][C]18[/C][C]-17.5563058843783[/C][C]-34.5816271179182[/C][C]-0.530984650838374[/C][/ROW]
[ROW][C]19[/C][C]-17.5563058843783[/C][C]-36.1530239195064[/C][C]1.04041215074984[/C][/ROW]
[ROW][C]20[/C][C]-17.5563058843783[/C][C]-37.6016115755095[/C][C]2.48899980675286[/C][/ROW]
[ROW][C]21[/C][C]-17.5563058843783[/C][C]-38.9523484816375[/C][C]3.83973671288089[/C][/ROW]
[ROW][C]22[/C][C]-17.5563058843783[/C][C]-40.2227347472708[/C][C]5.11012297851417[/C][/ROW]
[ROW][C]23[/C][C]-17.5563058843783[/C][C]-41.4256032340993[/C][C]6.31299146534273[/C][/ROW]
[ROW][C]24[/C][C]-17.5563058843783[/C][C]-42.570696033695[/C][C]7.45808426493844[/C][/ROW]
[ROW][C]25[/C][C]-17.5563058843783[/C][C]-43.6656159693857[/C][C]8.5530042006291[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224389&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224389&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
14	-17.5563058843783	-25.6776437553135	-9.43496801344309
15	-17.5563058843783	-28.5986103262383	-6.5140014425183
16	-17.5563058843783	-30.8945533689452	-4.21805839981137
17	-17.5563058843783	-32.8496117576155	-2.26300001114112
18	-17.5563058843783	-34.5816271179182	-0.530984650838374
19	-17.5563058843783	-36.1530239195064	1.04041215074984
20	-17.5563058843783	-37.6016115755095	2.48899980675286
21	-17.5563058843783	-38.9523484816375	3.83973671288089
22	-17.5563058843783	-40.2227347472708	5.11012297851417
23	-17.5563058843783	-41.4256032340993	6.31299146534273
24	-17.5563058843783	-42.570696033695	7.45808426493844
25	-17.5563058843783	-43.6656159693857	8.5530042006291

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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code