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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 17 Nov 2020 04:32:12 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2020/Nov/17/t1605584476ym8swgbhz0utuof.htm/, Retrieved Tue, 23 Apr 2024 15:08:59 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 23 Apr 2024 15:08:59 +0200

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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	Big 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=&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=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	Big Analytics Cloud Computing Center

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0
beta	0
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

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

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
8	33.86	25.3944387755102	8.46556122448982
9	44.24	33.8647448979592	10.3752551020408
10	37.25	25.8993367346939	11.3506632653061
11	66.42	39.7996428571428	26.6203571428572
12	58.36	34.2699489795918	24.0900510204082
13	38.56	24.6745408163265	13.8854591836735
14	30.61	64.5362755102041	-33.9262755102041
15	92.07	44.356581632653	47.713418367347
16	36.82	52.826887755102	-16.006887755102
17	63.12	44.8614795918367	18.2585204081633
18	54.14	58.7617857142857	-4.62178571428569
19	43.82	53.2320918367347	-9.41209183673467
20	43.48	43.6366836734694	-0.156683673469367
21	61.24	83.4984183673469	-22.2584183673469
22	39.03	63.3187244897959	-24.2887244897959
23	72.94	71.7890306122449	1.15096938775511
24	54.44	63.8236224489796	-9.38362244897958

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
8 & 33.86 & 25.3944387755102 & 8.46556122448982 \tabularnewline
9 & 44.24 & 33.8647448979592 & 10.3752551020408 \tabularnewline
10 & 37.25 & 25.8993367346939 & 11.3506632653061 \tabularnewline
11 & 66.42 & 39.7996428571428 & 26.6203571428572 \tabularnewline
12 & 58.36 & 34.2699489795918 & 24.0900510204082 \tabularnewline
13 & 38.56 & 24.6745408163265 & 13.8854591836735 \tabularnewline
14 & 30.61 & 64.5362755102041 & -33.9262755102041 \tabularnewline
15 & 92.07 & 44.356581632653 & 47.713418367347 \tabularnewline
16 & 36.82 & 52.826887755102 & -16.006887755102 \tabularnewline
17 & 63.12 & 44.8614795918367 & 18.2585204081633 \tabularnewline
18 & 54.14 & 58.7617857142857 & -4.62178571428569 \tabularnewline
19 & 43.82 & 53.2320918367347 & -9.41209183673467 \tabularnewline
20 & 43.48 & 43.6366836734694 & -0.156683673469367 \tabularnewline
21 & 61.24 & 83.4984183673469 & -22.2584183673469 \tabularnewline
22 & 39.03 & 63.3187244897959 & -24.2887244897959 \tabularnewline
23 & 72.94 & 71.7890306122449 & 1.15096938775511 \tabularnewline
24 & 54.44 & 63.8236224489796 & -9.38362244897958 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]8[/C][C]33.86[/C][C]25.3944387755102[/C][C]8.46556122448982[/C][/ROW]
[ROW][C]9[/C][C]44.24[/C][C]33.8647448979592[/C][C]10.3752551020408[/C][/ROW]
[ROW][C]10[/C][C]37.25[/C][C]25.8993367346939[/C][C]11.3506632653061[/C][/ROW]
[ROW][C]11[/C][C]66.42[/C][C]39.7996428571428[/C][C]26.6203571428572[/C][/ROW]
[ROW][C]12[/C][C]58.36[/C][C]34.2699489795918[/C][C]24.0900510204082[/C][/ROW]
[ROW][C]13[/C][C]38.56[/C][C]24.6745408163265[/C][C]13.8854591836735[/C][/ROW]
[ROW][C]14[/C][C]30.61[/C][C]64.5362755102041[/C][C]-33.9262755102041[/C][/ROW]
[ROW][C]15[/C][C]92.07[/C][C]44.356581632653[/C][C]47.713418367347[/C][/ROW]
[ROW][C]16[/C][C]36.82[/C][C]52.826887755102[/C][C]-16.006887755102[/C][/ROW]
[ROW][C]17[/C][C]63.12[/C][C]44.8614795918367[/C][C]18.2585204081633[/C][/ROW]
[ROW][C]18[/C][C]54.14[/C][C]58.7617857142857[/C][C]-4.62178571428569[/C][/ROW]
[ROW][C]19[/C][C]43.82[/C][C]53.2320918367347[/C][C]-9.41209183673467[/C][/ROW]
[ROW][C]20[/C][C]43.48[/C][C]43.6366836734694[/C][C]-0.156683673469367[/C][/ROW]
[ROW][C]21[/C][C]61.24[/C][C]83.4984183673469[/C][C]-22.2584183673469[/C][/ROW]
[ROW][C]22[/C][C]39.03[/C][C]63.3187244897959[/C][C]-24.2887244897959[/C][/ROW]
[ROW][C]23[/C][C]72.94[/C][C]71.7890306122449[/C][C]1.15096938775511[/C][/ROW]
[ROW][C]24[/C][C]54.44[/C][C]63.8236224489796[/C][C]-9.38362244897958[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
8	33.86	25.3944387755102	8.46556122448982
9	44.24	33.8647448979592	10.3752551020408
10	37.25	25.8993367346939	11.3506632653061
11	66.42	39.7996428571428	26.6203571428572
12	58.36	34.2699489795918	24.0900510204082
13	38.56	24.6745408163265	13.8854591836735
14	30.61	64.5362755102041	-33.9262755102041
15	92.07	44.356581632653	47.713418367347
16	36.82	52.826887755102	-16.006887755102
17	63.12	44.8614795918367	18.2585204081633
18	54.14	58.7617857142857	-4.62178571428569
19	43.82	53.2320918367347	-9.41209183673467
20	43.48	43.6366836734694	-0.156683673469367
21	61.24	83.4984183673469	-22.2584183673469
22	39.03	63.3187244897959	-24.2887244897959
23	72.94	71.7890306122449	1.15096938775511
24	54.44	63.8236224489796	-9.38362244897958

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
25	77.7239285714286	36.7612622894819	118.686594853375
26	72.1942346938775	31.2315684119309	113.156900975824
27	62.5988265306122	21.6361602486656	103.561492812559
28	102.46056122449	61.4978949425432	143.423227506436
29	82.2808673469388	41.3182010649921	123.243533628885
30	90.7511734693878	49.7885071874411	131.713839751334
31	82.7857653061224	41.8230990241758	123.748431588069

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
25 & 77.7239285714286 & 36.7612622894819 & 118.686594853375 \tabularnewline
26 & 72.1942346938775 & 31.2315684119309 & 113.156900975824 \tabularnewline
27 & 62.5988265306122 & 21.6361602486656 & 103.561492812559 \tabularnewline
28 & 102.46056122449 & 61.4978949425432 & 143.423227506436 \tabularnewline
29 & 82.2808673469388 & 41.3182010649921 & 123.243533628885 \tabularnewline
30 & 90.7511734693878 & 49.7885071874411 & 131.713839751334 \tabularnewline
31 & 82.7857653061224 & 41.8230990241758 & 123.748431588069 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]25[/C][C]77.7239285714286[/C][C]36.7612622894819[/C][C]118.686594853375[/C][/ROW]
[ROW][C]26[/C][C]72.1942346938775[/C][C]31.2315684119309[/C][C]113.156900975824[/C][/ROW]
[ROW][C]27[/C][C]62.5988265306122[/C][C]21.6361602486656[/C][C]103.561492812559[/C][/ROW]
[ROW][C]28[/C][C]102.46056122449[/C][C]61.4978949425432[/C][C]143.423227506436[/C][/ROW]
[ROW][C]29[/C][C]82.2808673469388[/C][C]41.3182010649921[/C][C]123.243533628885[/C][/ROW]
[ROW][C]30[/C][C]90.7511734693878[/C][C]49.7885071874411[/C][C]131.713839751334[/C][/ROW]
[ROW][C]31[/C][C]82.7857653061224[/C][C]41.8230990241758[/C][C]123.748431588069[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
25	77.7239285714286	36.7612622894819	118.686594853375
26	72.1942346938775	31.2315684119309	113.156900975824
27	62.5988265306122	21.6361602486656	103.561492812559
28	102.46056122449	61.4978949425432	143.423227506436
29	82.2808673469388	41.3182010649921	123.243533628885
30	90.7511734693878	49.7885071874411	131.713839751334
31	82.7857653061224	41.8230990241758	123.748431588069

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 7 ; par2 = Triple ; par3 = additive ; par4 = 7 ;

Parameters (R input):

par1 = 7 ; par2 = Triple ; par3 = additive ; par4 = 7 ;

R code (references can be found in the software module):

par4 <- '7'
par3 <- 'additive'
par2 <- 'Triple'
par1 <- '7'
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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code