Free Statistics

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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 16 Oct 2020 08:00:36 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2020/Oct/16/t1602828071vplrc41fhibrtn1.htm/, Retrieved Fri, 26 Apr 2024 23:24:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=319269, Retrieved Fri, 26 Apr 2024 23:24:04 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact131
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2020-10-16 06:00:36] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
17/10/19	0.57%
18/10/19	-1.68%
21/10/19	1.60%
22/10/19	-1.12%
23/10/19	-0.20%
24/10/19	1.06%
25/10/19	-1.09%
28/10/19	0.89%
29/10/19	-0.81%
30/10/19	0.98%
31/10/19	-0.19%
1/11/19	0.83%
4/11/19	0.74%
5/11/19	-0.16%
6/11/19	-0.33%
7/11/19	-0.42%
8/11/19	-0.13%
11/11/19	-0.80%
12/11/19	0.36%
13/11/19	-1.40%
14/11/19	0.08%
15/11/19	-0.86%
18/11/19	0.75%
19/11/19	0.01%
20/11/19	-0.41%
21/11/19	-0.62%
22/11/19	0.63%
25/11/19	1.61%
26/11/19	1.30%
27/11/19	1.20%
29/11/19	-0.97%
2/12/19	-1.07%
3/12/19	-0.65%
4/12/19	-0.52%
5/12/19	-1.15%
6/12/19	0.64%
9/12/19	-0.12%
10/12/19	-0.59%
11/12/19	0.55%
12/12/19	0.66%
13/12/19	0.03%
16/12/19	0.47%
17/12/19	1.21%
18/12/19	-0.37%
19/12/19	0.46%
20/12/19	-0.32%
23/12/19	0.36%
24/12/19	-0.21%
26/12/19	4.45%
27/12/19	0.06%
30/12/19	-1.23%
31/12/19	0.05%
2/1/20	2.72%
3/1/20	-1.21%
6/1/20	1.49%
7/1/20	0.21%
8/1/20	-0.78%
9/1/20	0.48%
10/1/20	-0.94%
13/1/20	0.43%
14/1/20	-1.16%
15/1/20	-0.40%
16/1/20	0.85%
17/1/20	-0.70%
21/1/20	1.46%
22/1/20	-0.24%
23/1/20	-0.15%
24/1/20	-1.22%
27/1/20	-1.79%
28/1/20	1.36%
29/1/20	0.26%
30/1/20	0.68%
31/1/20	7.38%
3/2/20	-0.23%
4/2/20	2.27%
5/2/20	-0.48%
6/2/20	0.51%
7/2/20	1.42%
10/2/20	2.63%
11/2/20	0.79%
12/2/20	0.43%
13/2/20	-0.47%
14/2/20	-0.70%
18/2/20	0.97%
19/2/20	0.67%
20/2/20	-0.79%
21/2/20	-2.65%
24/2/20	-4.14%
25/2/20	-1.82%
26/2/20	0.35%
27/2/20	-4.81%
28/2/20	-0.03%
2/3/20	3.73%
3/3/20	-2.30%
4/3/20	3.50%
5/3/20	-2.62%
6/3/20	-1.19%
9/3/20	-5.29%
10/3/20	5.07%
11/3/20	-3.75%
12/3/20	-7.92%
13/3/20	6.46%
16/3/20	-5.37%
17/3/20	7.03%
18/3/20	1.23%
19/3/20	2.78%
20/3/20	-1.85%
23/3/20	3.07%
24/3/20	1.96%
25/3/20	-2.80%
26/3/20	3.69%
27/3/20	-2.83%
30/3/20	3.36%
31/3/20	-0.72%
1/4/20	-2.16%
2/4/20	0.58%
3/4/20	-0.64%
6/4/20	4.77%
7/4/20	0.70%
8/4/20	1.56%
9/4/20	-0.01%
13/4/20	6.17%
14/4/20	5.28%
15/4/20	1.07%
16/4/20	4.36%
17/4/20	-1.38%
20/4/20	0.78%
21/4/20	-2.74%
22/4/20	1.52%
23/4/20	1.52%
24/4/20	0.45%
27/4/20	-1.42%
28/4/20	-2.61%
29/4/20	2.53%
30/4/20	4.27%
1/5/20	-7.60%
4/5/20	1.31%
5/5/20	0.08%
6/5/20	1.44%
7/5/20	0.70%
8/5/20	0.51%
11/5/20	1.24%
12/5/20	-2.16%
13/5/20	0.47%
14/5/20	0.88%
15/5/20	0.88%
18/5/20	0.68%
19/5/20	0.95%
20/5/20	1.98%
21/5/20	-2.05%
22/5/20	-0.40%
26/5/20	-0.62%
27/5/20	-0.47%
28/5/20	-0.39%
29/5/20	1.72%
1/6/20	1.17%
2/6/20	0.06%
3/6/20	0.24%
4/6/20	-0.72%
5/6/20	0.91%
8/6/20	1.65%
9/6/20	3.04%
10/6/20	1.79%
11/6/20	-3.38%
12/6/20	-0.51%
15/6/20	1.09%
16/6/20	1.66%
17/6/20	0.98%
18/6/20	0.49%
19/6/20	0.79%
22/6/20	1.45%
23/6/20	1.86%
24/6/20	-1.09%
25/6/20	0.74%
26/6/20	-2.24%
29/6/20	-0.46%
30/6/20	2.93%
1/7/20	4.35%
2/7/20	0.40%
6/7/20	5.77%
7/7/20	-1.86%
8/7/20	2.70%
9/7/20	3.29%
10/7/20	0.55%
13/7/20	-3.00%
14/7/20	-0.64%
15/7/20	-2.44%
16/7/20	-0.30%
17/7/20	-1.26%
20/7/20	7.93%
21/7/20	-1.83%
22/7/20	-1.22%
23/7/20	-3.66%
24/7/20	0.75%
27/7/20	1.54%
28/7/20	-1.80%
29/7/20	1.11%
30/7/20	0.60%
31/7/20	3.70%
3/8/20	-1.67%
4/8/20	0.87%
5/8/20	2.11%
6/8/20	0.62%
7/8/20	-1.78%
10/8/20	-0.61%
11/8/20	-2.14%
12/8/20	2.65%
13/8/20	-0.04%
14/8/20	-0.41%
17/8/20	1.09%
18/8/20	4.09%
19/8/20	-1.57%
20/8/20	1.13%
21/8/20	-0.38%
24/8/20	0.69%
25/8/20	1.18%
26/8/20	2.85%
27/8/20	-1.22%
28/8/20	0.05%
31/8/20	1.45%
1/9/20	1.40%
2/9/20	0.92%
3/9/20	-4.63%
4/9/20	-2.18%
8/9/20	-4.39%
9/9/20	3.77%
10/9/20	-2.86%
11/9/20	-1.85%
14/9/20	-0.43%
15/9/20	1.71%
16/9/20	-2.47%
17/9/20	-2.25%
18/9/20	-1.79%
21/9/20	0.19%
22/9/20	5.69%
23/9/20	-4.13%
24/9/20	0.66%
25/9/20	2.49%
28/9/20	2.55%
29/9/20	-0.92%
30/9/20	0.12%
1/10/20	2.30%
2/10/20	-2.99%
5/10/20	2.37%
6/10/20	-3.10%
7/10/20	3.09%
8/10/20	-0.16%
9/10/20	3.01%
12/10/20	4.75%
13/10/20	0.02%
14/10/20	-2.32%
15/10/20	-0.75%




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R ServerBig 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 time0 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319269&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]0 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=319269&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319269&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 Outputview raw output of R engine
Computing time0 seconds
R ServerBig Analytics Cloud Computing Center



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
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')