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Author*The author of this computation has been verified*
R Software Modulerwasp_decomposeloess.wasp
Title produced by softwareDecomposition by Loess
Date of computationSat, 17 Dec 2016 14:33:02 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/17/t1481981845s0yxsdi7cx1umxi.htm/, Retrieved Thu, 02 May 2024 08:00:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300784, Retrieved Thu, 02 May 2024 08:00:36 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact87
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Decomposition by Loess] [] [2016-12-17 13:33:02] [6e17bb30248b72d8119c893128a7a697] [Current]
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Dataseries X:
3228
3480.8
3621.8
3667.6
3458.4
3594.2
3780.8
3807.8
3595.4
3798
3966
3985.4
3755.4
3972
4189.6
4142.8




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300784&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]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300784&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300784&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 time2 seconds
R ServerBig Analytics Cloud Computing Center







Seasonal Decomposition by Loess - Parameters
ComponentWindowDegreeJump
Seasonal161017
Trend711
Low-pass511

\begin{tabular}{lllllllll}
\hline
Seasonal Decomposition by Loess - Parameters \tabularnewline
Component & Window & Degree & Jump \tabularnewline
Seasonal & 161 & 0 & 17 \tabularnewline
Trend & 7 & 1 & 1 \tabularnewline
Low-pass & 5 & 1 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300784&T=1

[TABLE]
[ROW][C]Seasonal Decomposition by Loess - Parameters[/C][/ROW]
[ROW][C]Component[/C][C]Window[/C][C]Degree[/C][C]Jump[/C][/ROW]
[ROW][C]Seasonal[/C][C]161[/C][C]0[/C][C]17[/C][/ROW]
[ROW][C]Trend[/C][C]7[/C][C]1[/C][C]1[/C][/ROW]
[ROW][C]Low-pass[/C][C]5[/C][C]1[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300784&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300784&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Seasonal Decomposition by Loess - Parameters
ComponentWindowDegreeJump
Seasonal161017
Trend711
Low-pass511







Seasonal Decomposition by Loess - Time Series Components
tObservedFittedSeasonalTrendRemainder
132283216.86975105248-190.0505536891123429.18080263663-11.1302489475211
23480.83509.84058733075-25.66518511638533477.4245977856429.0405873307454
33621.83596.21894552725121.0904142456193526.29064022713-25.5810544727497
43667.63668.7397809161794.62528255658333571.834936527251.13978091617128
53458.43498.73540785789-190.0505536891123608.1151458312240.3354078578895
63594.23572.01121651481-25.66518511638533642.05396860158-22.1887834851923
73780.83765.85346720755121.0904142456193674.65611854683-14.9465327924459
83807.83801.2581631840594.62528255658333719.71655425937-6.54183681594895
93595.43610.76458596465-190.0505536891123770.0859677244615.3645859646531
1037983806.69140141261-25.66518511638533814.973783703788.69140141260914
1139663955.57720374669121.0904142456193855.33238200769-10.4227962533068
123985.43979.1607933533894.62528255658333897.01392409004-6.23920664662
133755.43753.77794090725-190.0505536891123947.07261278187-1.62205909275463
1439723977.15236676041-25.66518511638533992.512818355975.15236676041377
154189.64223.69995889275121.0904142456194034.4096268616334.0999588927502
164142.84115.2829900354494.62528255658334075.69172740797-27.5170099645575

\begin{tabular}{lllllllll}
\hline
Seasonal Decomposition by Loess - Time Series Components \tabularnewline
t & Observed & Fitted & Seasonal & Trend & Remainder \tabularnewline
1 & 3228 & 3216.86975105248 & -190.050553689112 & 3429.18080263663 & -11.1302489475211 \tabularnewline
2 & 3480.8 & 3509.84058733075 & -25.6651851163853 & 3477.42459778564 & 29.0405873307454 \tabularnewline
3 & 3621.8 & 3596.21894552725 & 121.090414245619 & 3526.29064022713 & -25.5810544727497 \tabularnewline
4 & 3667.6 & 3668.73978091617 & 94.6252825565833 & 3571.83493652725 & 1.13978091617128 \tabularnewline
5 & 3458.4 & 3498.73540785789 & -190.050553689112 & 3608.11514583122 & 40.3354078578895 \tabularnewline
6 & 3594.2 & 3572.01121651481 & -25.6651851163853 & 3642.05396860158 & -22.1887834851923 \tabularnewline
7 & 3780.8 & 3765.85346720755 & 121.090414245619 & 3674.65611854683 & -14.9465327924459 \tabularnewline
8 & 3807.8 & 3801.25816318405 & 94.6252825565833 & 3719.71655425937 & -6.54183681594895 \tabularnewline
9 & 3595.4 & 3610.76458596465 & -190.050553689112 & 3770.08596772446 & 15.3645859646531 \tabularnewline
10 & 3798 & 3806.69140141261 & -25.6651851163853 & 3814.97378370378 & 8.69140141260914 \tabularnewline
11 & 3966 & 3955.57720374669 & 121.090414245619 & 3855.33238200769 & -10.4227962533068 \tabularnewline
12 & 3985.4 & 3979.16079335338 & 94.6252825565833 & 3897.01392409004 & -6.23920664662 \tabularnewline
13 & 3755.4 & 3753.77794090725 & -190.050553689112 & 3947.07261278187 & -1.62205909275463 \tabularnewline
14 & 3972 & 3977.15236676041 & -25.6651851163853 & 3992.51281835597 & 5.15236676041377 \tabularnewline
15 & 4189.6 & 4223.69995889275 & 121.090414245619 & 4034.40962686163 & 34.0999588927502 \tabularnewline
16 & 4142.8 & 4115.28299003544 & 94.6252825565833 & 4075.69172740797 & -27.5170099645575 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300784&T=2

[TABLE]
[ROW][C]Seasonal Decomposition by Loess - Time Series Components[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Seasonal[/C][C]Trend[/C][C]Remainder[/C][/ROW]
[ROW][C]1[/C][C]3228[/C][C]3216.86975105248[/C][C]-190.050553689112[/C][C]3429.18080263663[/C][C]-11.1302489475211[/C][/ROW]
[ROW][C]2[/C][C]3480.8[/C][C]3509.84058733075[/C][C]-25.6651851163853[/C][C]3477.42459778564[/C][C]29.0405873307454[/C][/ROW]
[ROW][C]3[/C][C]3621.8[/C][C]3596.21894552725[/C][C]121.090414245619[/C][C]3526.29064022713[/C][C]-25.5810544727497[/C][/ROW]
[ROW][C]4[/C][C]3667.6[/C][C]3668.73978091617[/C][C]94.6252825565833[/C][C]3571.83493652725[/C][C]1.13978091617128[/C][/ROW]
[ROW][C]5[/C][C]3458.4[/C][C]3498.73540785789[/C][C]-190.050553689112[/C][C]3608.11514583122[/C][C]40.3354078578895[/C][/ROW]
[ROW][C]6[/C][C]3594.2[/C][C]3572.01121651481[/C][C]-25.6651851163853[/C][C]3642.05396860158[/C][C]-22.1887834851923[/C][/ROW]
[ROW][C]7[/C][C]3780.8[/C][C]3765.85346720755[/C][C]121.090414245619[/C][C]3674.65611854683[/C][C]-14.9465327924459[/C][/ROW]
[ROW][C]8[/C][C]3807.8[/C][C]3801.25816318405[/C][C]94.6252825565833[/C][C]3719.71655425937[/C][C]-6.54183681594895[/C][/ROW]
[ROW][C]9[/C][C]3595.4[/C][C]3610.76458596465[/C][C]-190.050553689112[/C][C]3770.08596772446[/C][C]15.3645859646531[/C][/ROW]
[ROW][C]10[/C][C]3798[/C][C]3806.69140141261[/C][C]-25.6651851163853[/C][C]3814.97378370378[/C][C]8.69140141260914[/C][/ROW]
[ROW][C]11[/C][C]3966[/C][C]3955.57720374669[/C][C]121.090414245619[/C][C]3855.33238200769[/C][C]-10.4227962533068[/C][/ROW]
[ROW][C]12[/C][C]3985.4[/C][C]3979.16079335338[/C][C]94.6252825565833[/C][C]3897.01392409004[/C][C]-6.23920664662[/C][/ROW]
[ROW][C]13[/C][C]3755.4[/C][C]3753.77794090725[/C][C]-190.050553689112[/C][C]3947.07261278187[/C][C]-1.62205909275463[/C][/ROW]
[ROW][C]14[/C][C]3972[/C][C]3977.15236676041[/C][C]-25.6651851163853[/C][C]3992.51281835597[/C][C]5.15236676041377[/C][/ROW]
[ROW][C]15[/C][C]4189.6[/C][C]4223.69995889275[/C][C]121.090414245619[/C][C]4034.40962686163[/C][C]34.0999588927502[/C][/ROW]
[ROW][C]16[/C][C]4142.8[/C][C]4115.28299003544[/C][C]94.6252825565833[/C][C]4075.69172740797[/C][C]-27.5170099645575[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300784&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300784&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Seasonal Decomposition by Loess - Time Series Components
tObservedFittedSeasonalTrendRemainder
132283216.86975105248-190.0505536891123429.18080263663-11.1302489475211
23480.83509.84058733075-25.66518511638533477.4245977856429.0405873307454
33621.83596.21894552725121.0904142456193526.29064022713-25.5810544727497
43667.63668.7397809161794.62528255658333571.834936527251.13978091617128
53458.43498.73540785789-190.0505536891123608.1151458312240.3354078578895
63594.23572.01121651481-25.66518511638533642.05396860158-22.1887834851923
73780.83765.85346720755121.0904142456193674.65611854683-14.9465327924459
83807.83801.2581631840594.62528255658333719.71655425937-6.54183681594895
93595.43610.76458596465-190.0505536891123770.0859677244615.3645859646531
1037983806.69140141261-25.66518511638533814.973783703788.69140141260914
1139663955.57720374669121.0904142456193855.33238200769-10.4227962533068
123985.43979.1607933533894.62528255658333897.01392409004-6.23920664662
133755.43753.77794090725-190.0505536891123947.07261278187-1.62205909275463
1439723977.15236676041-25.66518511638533992.512818355975.15236676041377
154189.64223.69995889275121.0904142456194034.4096268616334.0999588927502
164142.84115.2829900354494.62528255658334075.69172740797-27.5170099645575



Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 4 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
Parameters (R input):
par1 = 4 ; par2 = periodic ; par3 = 0 ; par4 = ; par5 = 1 ; par6 = ; par7 = 1 ; par8 = FALSE ;
R code (references can be found in the software module):
par8 <- 'FALSE'
par7 <- '1'
par6 <- ''
par5 <- '1'
par4 <- ''
par3 <- '0'
par2 <- 'periodic'
par1 <- '4'
par1 <- as.numeric(par1) #seasonal period
if (par2 != 'periodic') par2 <- as.numeric(par2) #s.window
par3 <- as.numeric(par3) #s.degree
if (par4 == '') par4 <- NULL else par4 <- as.numeric(par4)#t.window
par5 <- as.numeric(par5)#t.degree
if (par6 != '') par6 <- as.numeric(par6)#l.window
par7 <- as.numeric(par7)#l.degree
if (par8 == 'FALSE') par8 <- FALSE else par9 <- TRUE #robust
nx <- length(x)
x <- ts(x,frequency=par1)
if (par6 != '') {
m <- stl(x,s.window=par2, s.degree=par3, t.window=par4, t.degre=par5, l.window=par6, l.degree=par7, robust=par8)
} else {
m <- stl(x,s.window=par2, s.degree=par3, t.window=par4, t.degre=par5, l.degree=par7, robust=par8)
}
m$time.series
m$win
m$deg
m$jump
m$inner
m$outer
bitmap(file='test1.png')
plot(m,main=main)
dev.off()
mylagmax <- nx/2
bitmap(file='test2.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(x),lag.max = mylagmax,main='Observed')
acf(as.numeric(m$time.series[,'trend']),na.action=na.pass,lag.max = mylagmax,main='Trend')
acf(as.numeric(m$time.series[,'seasonal']),na.action=na.pass,lag.max = mylagmax,main='Seasonal')
acf(as.numeric(m$time.series[,'remainder']),na.action=na.pass,lag.max = mylagmax,main='Remainder')
par(op)
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
spectrum(as.numeric(x),main='Observed')
spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'trend']),'trend']),main='Trend')
spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'seasonal']),'seasonal']),main='Seasonal')
spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'remainder']),'remainder']),main='Remainder')
par(op)
dev.off()
bitmap(file='test4.png')
op <- par(mfrow = c(2,2))
cpgram(as.numeric(x),main='Observed')
cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'trend']),'trend']),main='Trend')
cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'seasonal']),'seasonal']),main='Seasonal')
cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'remainder']),'remainder']),main='Remainder')
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Seasonal Decomposition by Loess - Parameters',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Component',header=TRUE)
a<-table.element(a,'Window',header=TRUE)
a<-table.element(a,'Degree',header=TRUE)
a<-table.element(a,'Jump',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Seasonal',header=TRUE)
a<-table.element(a,m$win['s'])
a<-table.element(a,m$deg['s'])
a<-table.element(a,m$jump['s'])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Trend',header=TRUE)
a<-table.element(a,m$win['t'])
a<-table.element(a,m$deg['t'])
a<-table.element(a,m$jump['t'])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Low-pass',header=TRUE)
a<-table.element(a,m$win['l'])
a<-table.element(a,m$deg['l'])
a<-table.element(a,m$jump['l'])
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,'Seasonal Decomposition by Loess - Time Series Components',6,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,'Seasonal',header=TRUE)
a<-table.element(a,'Trend',header=TRUE)
a<-table.element(a,'Remainder',header=TRUE)
a<-table.row.end(a)
for (i in 1:nx) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]+m$time.series[i,'remainder'])
a<-table.element(a,m$time.series[i,'seasonal'])
a<-table.element(a,m$time.series[i,'trend'])
a<-table.element(a,m$time.series[i,'remainder'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')