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Author

*The author of this computation has been verified*

R Software Module

rwasp_variancereduction.wasp

Title produced by software

Variance Reduction Matrix

Date of computation

Wed, 29 Dec 2010 13:12:47 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/29/t1293628251q3ytc4jror9evr0.htm/, Retrieved Fri, 03 May 2024 06:00:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116795, Retrieved Fri, 03 May 2024 06:00:09 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

127

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Variance Reduction Matrix] [] [2010-12-22 21:18:53] [29e492448d11757ae0fad5ef6e7f8e86]
-    D    [Variance Reduction Matrix] [] [2010-12-29 13:12:47] [e180d4cd19004beeddc12e67012247dc] [Current]

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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	'George Udny Yule' @ 72.249.76.132

\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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116795&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116795&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116795&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	'George Udny Yule' @ 72.249.76.132

Variance Reduction Matrix
V(Y[t],d=0,D=0)	0.0576668053961393	Range	1.094926	Trim Var.	0.0413284050513392
V(Y[t],d=1,D=0)	0.0332012320687436	Range	0.947302	Trim Var.	0.0197865128954447
V(Y[t],d=2,D=0)	0.102362213815903	Range	1.451628	Trim Var.	0.0641619024452516
V(Y[t],d=3,D=0)	0.351393311422364	Range	2.809511	Trim Var.	0.221665691838349
V(Y[t],d=0,D=1)	0.0664523629992942	Range	1.068761	Trim Var.	0.0450905788742476
V(Y[t],d=1,D=1)	0.0607698669111542	Range	1.257701	Trim Var.	0.0338261131373265
V(Y[t],d=2,D=1)	0.188610631243745	Range	2.371738	Trim Var.	0.102464007757757
V(Y[t],d=3,D=1)	0.655700879723951	Range	4.392843	Trim Var.	0.340286666397597
V(Y[t],d=0,D=2)	0.139969119834466	Range	1.467312	Trim Var.	0.101859991416778
V(Y[t],d=1,D=2)	0.177967534868507	Range	2.311956	Trim Var.	0.0713404973614173
V(Y[t],d=2,D=2)	0.566247565481746	Range	4.219204	Trim Var.	0.205657477335524
V(Y[t],d=3,D=2)	2.01225559411631	Range	7.860215	Trim Var.	0.691061761646458

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.0576668053961393 & Range & 1.094926 & Trim Var. & 0.0413284050513392 \tabularnewline
V(Y[t],d=1,D=0) & 0.0332012320687436 & Range & 0.947302 & Trim Var. & 0.0197865128954447 \tabularnewline
V(Y[t],d=2,D=0) & 0.102362213815903 & Range & 1.451628 & Trim Var. & 0.0641619024452516 \tabularnewline
V(Y[t],d=3,D=0) & 0.351393311422364 & Range & 2.809511 & Trim Var. & 0.221665691838349 \tabularnewline
V(Y[t],d=0,D=1) & 0.0664523629992942 & Range & 1.068761 & Trim Var. & 0.0450905788742476 \tabularnewline
V(Y[t],d=1,D=1) & 0.0607698669111542 & Range & 1.257701 & Trim Var. & 0.0338261131373265 \tabularnewline
V(Y[t],d=2,D=1) & 0.188610631243745 & Range & 2.371738 & Trim Var. & 0.102464007757757 \tabularnewline
V(Y[t],d=3,D=1) & 0.655700879723951 & Range & 4.392843 & Trim Var. & 0.340286666397597 \tabularnewline
V(Y[t],d=0,D=2) & 0.139969119834466 & Range & 1.467312 & Trim Var. & 0.101859991416778 \tabularnewline
V(Y[t],d=1,D=2) & 0.177967534868507 & Range & 2.311956 & Trim Var. & 0.0713404973614173 \tabularnewline
V(Y[t],d=2,D=2) & 0.566247565481746 & Range & 4.219204 & Trim Var. & 0.205657477335524 \tabularnewline
V(Y[t],d=3,D=2) & 2.01225559411631 & Range & 7.860215 & Trim Var. & 0.691061761646458 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116795&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.0576668053961393[/C][C]Range[/C][C]1.094926[/C][C]Trim Var.[/C][C]0.0413284050513392[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.0332012320687436[/C][C]Range[/C][C]0.947302[/C][C]Trim Var.[/C][C]0.0197865128954447[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.102362213815903[/C][C]Range[/C][C]1.451628[/C][C]Trim Var.[/C][C]0.0641619024452516[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.351393311422364[/C][C]Range[/C][C]2.809511[/C][C]Trim Var.[/C][C]0.221665691838349[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.0664523629992942[/C][C]Range[/C][C]1.068761[/C][C]Trim Var.[/C][C]0.0450905788742476[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.0607698669111542[/C][C]Range[/C][C]1.257701[/C][C]Trim Var.[/C][C]0.0338261131373265[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.188610631243745[/C][C]Range[/C][C]2.371738[/C][C]Trim Var.[/C][C]0.102464007757757[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]0.655700879723951[/C][C]Range[/C][C]4.392843[/C][C]Trim Var.[/C][C]0.340286666397597[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]0.139969119834466[/C][C]Range[/C][C]1.467312[/C][C]Trim Var.[/C][C]0.101859991416778[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.177967534868507[/C][C]Range[/C][C]2.311956[/C][C]Trim Var.[/C][C]0.0713404973614173[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.566247565481746[/C][C]Range[/C][C]4.219204[/C][C]Trim Var.[/C][C]0.205657477335524[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]2.01225559411631[/C][C]Range[/C][C]7.860215[/C][C]Trim Var.[/C][C]0.691061761646458[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116795&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116795&T=1

As an alternative you can also use a QR Code:

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

Variance Reduction Matrix
V(Y[t],d=0,D=0)	0.0576668053961393	Range	1.094926	Trim Var.	0.0413284050513392
V(Y[t],d=1,D=0)	0.0332012320687436	Range	0.947302	Trim Var.	0.0197865128954447
V(Y[t],d=2,D=0)	0.102362213815903	Range	1.451628	Trim Var.	0.0641619024452516
V(Y[t],d=3,D=0)	0.351393311422364	Range	2.809511	Trim Var.	0.221665691838349
V(Y[t],d=0,D=1)	0.0664523629992942	Range	1.068761	Trim Var.	0.0450905788742476
V(Y[t],d=1,D=1)	0.0607698669111542	Range	1.257701	Trim Var.	0.0338261131373265
V(Y[t],d=2,D=1)	0.188610631243745	Range	2.371738	Trim Var.	0.102464007757757
V(Y[t],d=3,D=1)	0.655700879723951	Range	4.392843	Trim Var.	0.340286666397597
V(Y[t],d=0,D=2)	0.139969119834466	Range	1.467312	Trim Var.	0.101859991416778
V(Y[t],d=1,D=2)	0.177967534868507	Range	2.311956	Trim Var.	0.0713404973614173
V(Y[t],d=2,D=2)	0.566247565481746	Range	4.219204	Trim Var.	0.205657477335524
V(Y[t],d=3,D=2)	2.01225559411631	Range	7.860215	Trim Var.	0.691061761646458

Figure 1

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Postscript link

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Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 12 ;

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

par1 <- as.numeric(par1)
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)
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,var(myx))
a<-table.element(a,'Range',header=TRUE)
a<-table.element(a,max(myx)-min(myx))
a<-table.element(a,'Trim Var.',header=TRUE)
smyx <- sort(myx)
sn <- length(smyx)
a<-table.element(a,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()

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