Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 12 Nov 2013 08:58:20 -0500

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/2013/Nov/12/t13842647184g0vg41ol3y441e.htm/, Retrieved Thu, 02 May 2024 14:53:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=224395, Retrieved Thu, 02 May 2024 14:53:57 +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)

-     [Multiple Regression] [HPC Retail Sales] [2008-03-08 13:40:54] [1c0f2c85e8a48e42648374b3bcceca26]
- RMPD    [Exponential Smoothing] [ws885] [2013-11-12 13:58:20] [e931f330ae8eb739e69629b6955c783c] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224395&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224395&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224395&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	2 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.713070296404289
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.713070296404289 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224395&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]0.713070296404289[/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=224395&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224395&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	0.713070296404289
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	40	38	2
3	39	39.4261405928086	-0.426140592808579
4	48	39.1222723939847	8.87772760601533
5	54	45.4527162494026	8.54728375059744
6	55	51.5475304068926	3.45246959310736
7	56	54.0093839229765	1.9906160770235
8	63	55.4288331190468	7.57116688095321
9	52	60.8276073309744	-8.82760733097443
10	59	54.5329027549358	4.46709724506418
11	57	57.7182571115405	-0.718257111540517
12	62	57.2060893001198	4.79391069988016
13	50	60.6244846238191	-10.6244846238191

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 40 & 38 & 2 \tabularnewline
3 & 39 & 39.4261405928086 & -0.426140592808579 \tabularnewline
4 & 48 & 39.1222723939847 & 8.87772760601533 \tabularnewline
5 & 54 & 45.4527162494026 & 8.54728375059744 \tabularnewline
6 & 55 & 51.5475304068926 & 3.45246959310736 \tabularnewline
7 & 56 & 54.0093839229765 & 1.9906160770235 \tabularnewline
8 & 63 & 55.4288331190468 & 7.57116688095321 \tabularnewline
9 & 52 & 60.8276073309744 & -8.82760733097443 \tabularnewline
10 & 59 & 54.5329027549358 & 4.46709724506418 \tabularnewline
11 & 57 & 57.7182571115405 & -0.718257111540517 \tabularnewline
12 & 62 & 57.2060893001198 & 4.79391069988016 \tabularnewline
13 & 50 & 60.6244846238191 & -10.6244846238191 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224395&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]40[/C][C]38[/C][C]2[/C][/ROW]
[ROW][C]3[/C][C]39[/C][C]39.4261405928086[/C][C]-0.426140592808579[/C][/ROW]
[ROW][C]4[/C][C]48[/C][C]39.1222723939847[/C][C]8.87772760601533[/C][/ROW]
[ROW][C]5[/C][C]54[/C][C]45.4527162494026[/C][C]8.54728375059744[/C][/ROW]
[ROW][C]6[/C][C]55[/C][C]51.5475304068926[/C][C]3.45246959310736[/C][/ROW]
[ROW][C]7[/C][C]56[/C][C]54.0093839229765[/C][C]1.9906160770235[/C][/ROW]
[ROW][C]8[/C][C]63[/C][C]55.4288331190468[/C][C]7.57116688095321[/C][/ROW]
[ROW][C]9[/C][C]52[/C][C]60.8276073309744[/C][C]-8.82760733097443[/C][/ROW]
[ROW][C]10[/C][C]59[/C][C]54.5329027549358[/C][C]4.46709724506418[/C][/ROW]
[ROW][C]11[/C][C]57[/C][C]57.7182571115405[/C][C]-0.718257111540517[/C][/ROW]
[ROW][C]12[/C][C]62[/C][C]57.2060893001198[/C][C]4.79391069988016[/C][/ROW]
[ROW][C]13[/C][C]50[/C][C]60.6244846238191[/C][C]-10.6244846238191[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224395&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224395&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	40	38	2
3	39	39.4261405928086	-0.426140592808579
4	48	39.1222723939847	8.87772760601533
5	54	45.4527162494026	8.54728375059744
6	55	51.5475304068926	3.45246959310736
7	56	54.0093839229765	1.9906160770235
8	63	55.4288331190468	7.57116688095321
9	52	60.8276073309744	-8.82760733097443
10	59	54.5329027549358	4.46709724506418
11	57	57.7182571115405	-0.718257111540517
12	62	57.2060893001198	4.79391069988016
13	50	60.6244846238191	-10.6244846238191

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
14	53.0484802239696	40.845642092602	65.2513183553372
15	53.0484802239696	38.0609841998676	68.0359762480716
16	53.0484802239696	35.7181364395958	70.3788240083434
17	53.0484802239696	33.6563015352122	72.440658912727
18	53.0484802239696	31.7935426115274	74.3034178364118
19	53.0484802239696	30.0813700112998	76.0155904366394
20	53.0484802239696	28.4882699208587	77.6086905270805
21	53.0484802239696	26.9923924757072	79.104567972232
22	53.0484802239696	25.5778506833628	80.5191097645764
23	53.0484802239696	24.2326639771691	81.8642964707701
24	53.0484802239696	22.9475326544746	83.1494277934646
25	53.0484802239696	21.7150663787851	84.3818940691541

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
14 & 53.0484802239696 & 40.845642092602 & 65.2513183553372 \tabularnewline
15 & 53.0484802239696 & 38.0609841998676 & 68.0359762480716 \tabularnewline
16 & 53.0484802239696 & 35.7181364395958 & 70.3788240083434 \tabularnewline
17 & 53.0484802239696 & 33.6563015352122 & 72.440658912727 \tabularnewline
18 & 53.0484802239696 & 31.7935426115274 & 74.3034178364118 \tabularnewline
19 & 53.0484802239696 & 30.0813700112998 & 76.0155904366394 \tabularnewline
20 & 53.0484802239696 & 28.4882699208587 & 77.6086905270805 \tabularnewline
21 & 53.0484802239696 & 26.9923924757072 & 79.104567972232 \tabularnewline
22 & 53.0484802239696 & 25.5778506833628 & 80.5191097645764 \tabularnewline
23 & 53.0484802239696 & 24.2326639771691 & 81.8642964707701 \tabularnewline
24 & 53.0484802239696 & 22.9475326544746 & 83.1494277934646 \tabularnewline
25 & 53.0484802239696 & 21.7150663787851 & 84.3818940691541 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224395&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]53.0484802239696[/C][C]40.845642092602[/C][C]65.2513183553372[/C][/ROW]
[ROW][C]15[/C][C]53.0484802239696[/C][C]38.0609841998676[/C][C]68.0359762480716[/C][/ROW]
[ROW][C]16[/C][C]53.0484802239696[/C][C]35.7181364395958[/C][C]70.3788240083434[/C][/ROW]
[ROW][C]17[/C][C]53.0484802239696[/C][C]33.6563015352122[/C][C]72.440658912727[/C][/ROW]
[ROW][C]18[/C][C]53.0484802239696[/C][C]31.7935426115274[/C][C]74.3034178364118[/C][/ROW]
[ROW][C]19[/C][C]53.0484802239696[/C][C]30.0813700112998[/C][C]76.0155904366394[/C][/ROW]
[ROW][C]20[/C][C]53.0484802239696[/C][C]28.4882699208587[/C][C]77.6086905270805[/C][/ROW]
[ROW][C]21[/C][C]53.0484802239696[/C][C]26.9923924757072[/C][C]79.104567972232[/C][/ROW]
[ROW][C]22[/C][C]53.0484802239696[/C][C]25.5778506833628[/C][C]80.5191097645764[/C][/ROW]
[ROW][C]23[/C][C]53.0484802239696[/C][C]24.2326639771691[/C][C]81.8642964707701[/C][/ROW]
[ROW][C]24[/C][C]53.0484802239696[/C][C]22.9475326544746[/C][C]83.1494277934646[/C][/ROW]
[ROW][C]25[/C][C]53.0484802239696[/C][C]21.7150663787851[/C][C]84.3818940691541[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224395&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224395&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	53.0484802239696	40.845642092602	65.2513183553372
15	53.0484802239696	38.0609841998676	68.0359762480716
16	53.0484802239696	35.7181364395958	70.3788240083434
17	53.0484802239696	33.6563015352122	72.440658912727
18	53.0484802239696	31.7935426115274	74.3034178364118
19	53.0484802239696	30.0813700112998	76.0155904366394
20	53.0484802239696	28.4882699208587	77.6086905270805
21	53.0484802239696	26.9923924757072	79.104567972232
22	53.0484802239696	25.5778506833628	80.5191097645764
23	53.0484802239696	24.2326639771691	81.8642964707701
24	53.0484802239696	22.9475326544746	83.1494277934646
25	53.0484802239696	21.7150663787851	84.3818940691541

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 ;

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