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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_variancereduction.wasp
Title produced by softwareVariance Reduction Matrix
Date of computationTue, 23 Jan 2018 16:22:53 +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/2018/Jan/23/t1516720980n3lxjmgkm5cgzip.htm/, Retrieved Wed, 08 May 2024 19:25:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=311166, Retrieved Wed, 08 May 2024 19:25:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact36

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Variance Reduction Matrix] [] [2018-01-23 15:22:53] [ff652b20bb7e11759c12f409641293b0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
26
20
19
20
25
22
26
22
19
24
26
13
22
21
7
17
25
25
19
23
22
21
18
22
18
23
20
15
21
18
19
22
16
18
20
24
24
18
21
17
22
16
21
24
24
16
16
18
20
24
17
19
20
15
22
23
16
19
19
21
24
22
18
24
24
22
23
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20
18
25
16
20
15
19
19
16
17
28
25
20
16
23
21
23
18
20
9
25
20
21
22
27
18
16
22
20
20

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=311166&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=311166&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=311166&T=0

As an alternative you can also use a QR Code:  
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 time1 seconds
R ServerBig Analytics Cloud Computing Center






Variance Reduction Matrix
V(Y[t],d=0,D=0)13.0309Range21Trim Var.7.1823
V(Y[t],d=1,D=0)26.4961Range30Trim Var.14.8118
V(Y[t],d=2,D=0)76.2487Range48Trim Var.45.0156
V(Y[t],d=3,D=0)246.861Range88Trim Var.143.907
V(Y[t],d=0,D=1)22.2161Range25Trim Var.12.889
V(Y[t],d=1,D=1)45.7331Range34Trim Var.24.2692
V(Y[t],d=2,D=1)132.699Range60Trim Var.68.8326
V(Y[t],d=3,D=1)422.978Range104Trim Var.240.103
V(Y[t],d=0,D=2)60.3282Range41Trim Var.36.2365
V(Y[t],d=1,D=2)111.708Range48Trim Var.71.0178
V(Y[t],d=2,D=2)312.363Range82Trim Var.198.285
V(Y[t],d=3,D=2)995.348Range138Trim Var.626.996

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 13.0309 & Range & 21 & Trim Var. & 7.1823 \tabularnewline
V(Y[t],d=1,D=0) & 26.4961 & Range & 30 & Trim Var. & 14.8118 \tabularnewline
V(Y[t],d=2,D=0) & 76.2487 & Range & 48 & Trim Var. & 45.0156 \tabularnewline
V(Y[t],d=3,D=0) & 246.861 & Range & 88 & Trim Var. & 143.907 \tabularnewline
V(Y[t],d=0,D=1) & 22.2161 & Range & 25 & Trim Var. & 12.889 \tabularnewline
V(Y[t],d=1,D=1) & 45.7331 & Range & 34 & Trim Var. & 24.2692 \tabularnewline
V(Y[t],d=2,D=1) & 132.699 & Range & 60 & Trim Var. & 68.8326 \tabularnewline
V(Y[t],d=3,D=1) & 422.978 & Range & 104 & Trim Var. & 240.103 \tabularnewline
V(Y[t],d=0,D=2) & 60.3282 & Range & 41 & Trim Var. & 36.2365 \tabularnewline
V(Y[t],d=1,D=2) & 111.708 & Range & 48 & Trim Var. & 71.0178 \tabularnewline
V(Y[t],d=2,D=2) & 312.363 & Range & 82 & Trim Var. & 198.285 \tabularnewline
V(Y[t],d=3,D=2) & 995.348 & Range & 138 & Trim Var. & 626.996 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=311166&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]13.0309[/C][C]Range[/C][C]21[/C][C]Trim Var.[/C][C]7.1823[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]26.4961[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]14.8118[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]76.2487[/C][C]Range[/C][C]48[/C][C]Trim Var.[/C][C]45.0156[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]246.861[/C][C]Range[/C][C]88[/C][C]Trim Var.[/C][C]143.907[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]22.2161[/C][C]Range[/C][C]25[/C][C]Trim Var.[/C][C]12.889[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]45.7331[/C][C]Range[/C][C]34[/C][C]Trim Var.[/C][C]24.2692[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]132.699[/C][C]Range[/C][C]60[/C][C]Trim Var.[/C][C]68.8326[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]422.978[/C][C]Range[/C][C]104[/C][C]Trim Var.[/C][C]240.103[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]60.3282[/C][C]Range[/C][C]41[/C][C]Trim Var.[/C][C]36.2365[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]111.708[/C][C]Range[/C][C]48[/C][C]Trim Var.[/C][C]71.0178[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]312.363[/C][C]Range[/C][C]82[/C][C]Trim Var.[/C][C]198.285[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]995.348[/C][C]Range[/C][C]138[/C][C]Trim Var.[/C][C]626.996[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=311166&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=311166&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Variance Reduction Matrix
V(Y[t],d=0,D=0)13.0309Range21Trim Var.7.1823
V(Y[t],d=1,D=0)26.4961Range30Trim Var.14.8118
V(Y[t],d=2,D=0)76.2487Range48Trim Var.45.0156
V(Y[t],d=3,D=0)246.861Range88Trim Var.143.907
V(Y[t],d=0,D=1)22.2161Range25Trim Var.12.889
V(Y[t],d=1,D=1)45.7331Range34Trim Var.24.2692
V(Y[t],d=2,D=1)132.699Range60Trim Var.68.8326
V(Y[t],d=3,D=1)422.978Range104Trim Var.240.103
V(Y[t],d=0,D=2)60.3282Range41Trim Var.36.2365
V(Y[t],d=1,D=2)111.708Range48Trim Var.71.0178
V(Y[t],d=2,D=2)312.363Range82Trim Var.198.285
V(Y[t],d=3,D=2)995.348Range138Trim Var.626.996


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
n.orig <- length(x)
x <- na.omit(x)
n <- length(x)
sx <- sort(x)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Variance Reduction Matrix',6,TRUE)
a<-table.row.end(a)
if(n.orig!=n) {
a<-table.row.start(a)
a<-table.element(a,'Warning: NAs were removed from the time series! The results shown below will only be correct if the NAs are all located at the start and/or end of the time series.',6,F)
a<-table.row.end(a)
}
for (bigd in 0:2) {
for (smalld in 0:3) {
mylabel <- 'V(Y[t],d='
mylabel <- paste(mylabel,as.character(smalld),sep='')
mylabel <- paste(mylabel,',D=',sep='')
mylabel <- paste(mylabel,as.character(bigd),sep='')
mylabel <- paste(mylabel,')',sep='')
a<-table.row.start(a)
a<-table.element(a,mylabel,header=TRUE)
myx <- x
if (smalld > 0) myx <- diff(myx,lag=1,differences=smalld)
if (bigd > 0) myx <- diff(myx,lag=par1,differences=bigd)
a<-table.element(a,signif(var(myx), digits=6))
a<-table.element(a,'Range',header=TRUE)
a<-table.element(a,signif(max(myx)-min(myx), digits=6))
a<-table.element(a,'Trim Var.',header=TRUE)
smyx <- sort(myx)
sn <- length(smyx)
a<-table.element(a,signif(var(smyx[smyx>quantile(smyx,0.05) & smyxa<-table.row.end(a)
}
}
a<-table.end(a)
table.save(a,file='mytable.tab')
bitmap(file='pic0.png')
op <- par(mfrow=c(2,2))
plot(x,type='l',xlab='time',ylab='value',main='d=0, D=0')
plot(diff(x,lag=1,differences=1),type='l',xlab='time',ylab='value',main='d=1, D=0')
plot(diff(x,lag=par1,differences=1),type='l',xlab='time',ylab='value',main='d=0, D=1')
plot(diff(diff(x,lag=1,differences=1),lag=par1,differences=1),type='l',xlab='time',ylab='value',main='d=1, D=1')
par(op)
dev.off()