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*The author of this computation has been verified*

R Software Module

rwasp_variancereduction.wasp

Title produced by software

Variance Reduction Matrix

Date of computation

Sun, 19 Dec 2010 16:06:59 +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/19/t12927752063bczdodcvzcfh63.htm/, Retrieved Sun, 05 May 2024 03:44:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112557, Retrieved Sun, 05 May 2024 03:44:51 +0000

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No (this computation is public)

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Estimated Impact

121

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

-       [Variance Reduction Matrix] [] [2010-12-19 16:06:59] [020d6ac062bd52f65e15713212085515] [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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112557&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112557&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112557&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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Variance Reduction Matrix
V(Y[t],d=0,D=0)	354025.168361582	Range	2364	Trim Var.	261338.295248078
V(Y[t],d=1,D=0)	290314.801870251	Range	2405	Trim Var.	195337.625544267
V(Y[t],d=2,D=0)	539530.120992135	Range	2918	Trim Var.	397890.298642534
V(Y[t],d=3,D=0)	1414658.30827068	Range	4614	Trim Var.	1017973.45254902
V(Y[t],d=0,D=1)	171857.233599291	Range	1783	Trim Var.	102129.719512195
V(Y[t],d=1,D=1)	190603.77613321	Range	1893	Trim Var.	120597.319512195
V(Y[t],d=2,D=1)	475617.654589372	Range	2799	Trim Var.	314452.686538462
V(Y[t],d=3,D=1)	1470509.29090909	Range	4746	Trim Var.	940101.956815115
V(Y[t],d=0,D=2)	403605.844444444	Range	3019	Trim Var.	218545.458669355
V(Y[t],d=1,D=2)	512370.322689076	Range	2977	Trim Var.	333206.866666667
V(Y[t],d=2,D=2)	1317264.79946524	Range	4242	Trim Var.	947027.481609195
V(Y[t],d=3,D=2)	4157848.49621212	Range	8062	Trim Var.	2822179.43349754

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 354025.168361582 & Range & 2364 & Trim Var. & 261338.295248078 \tabularnewline
V(Y[t],d=1,D=0) & 290314.801870251 & Range & 2405 & Trim Var. & 195337.625544267 \tabularnewline
V(Y[t],d=2,D=0) & 539530.120992135 & Range & 2918 & Trim Var. & 397890.298642534 \tabularnewline
V(Y[t],d=3,D=0) & 1414658.30827068 & Range & 4614 & Trim Var. & 1017973.45254902 \tabularnewline
V(Y[t],d=0,D=1) & 171857.233599291 & Range & 1783 & Trim Var. & 102129.719512195 \tabularnewline
V(Y[t],d=1,D=1) & 190603.77613321 & Range & 1893 & Trim Var. & 120597.319512195 \tabularnewline
V(Y[t],d=2,D=1) & 475617.654589372 & Range & 2799 & Trim Var. & 314452.686538462 \tabularnewline
V(Y[t],d=3,D=1) & 1470509.29090909 & Range & 4746 & Trim Var. & 940101.956815115 \tabularnewline
V(Y[t],d=0,D=2) & 403605.844444444 & Range & 3019 & Trim Var. & 218545.458669355 \tabularnewline
V(Y[t],d=1,D=2) & 512370.322689076 & Range & 2977 & Trim Var. & 333206.866666667 \tabularnewline
V(Y[t],d=2,D=2) & 1317264.79946524 & Range & 4242 & Trim Var. & 947027.481609195 \tabularnewline
V(Y[t],d=3,D=2) & 4157848.49621212 & Range & 8062 & Trim Var. & 2822179.43349754 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112557&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]354025.168361582[/C][C]Range[/C][C]2364[/C][C]Trim Var.[/C][C]261338.295248078[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]290314.801870251[/C][C]Range[/C][C]2405[/C][C]Trim Var.[/C][C]195337.625544267[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]539530.120992135[/C][C]Range[/C][C]2918[/C][C]Trim Var.[/C][C]397890.298642534[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]1414658.30827068[/C][C]Range[/C][C]4614[/C][C]Trim Var.[/C][C]1017973.45254902[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]171857.233599291[/C][C]Range[/C][C]1783[/C][C]Trim Var.[/C][C]102129.719512195[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]190603.77613321[/C][C]Range[/C][C]1893[/C][C]Trim Var.[/C][C]120597.319512195[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]475617.654589372[/C][C]Range[/C][C]2799[/C][C]Trim Var.[/C][C]314452.686538462[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]1470509.29090909[/C][C]Range[/C][C]4746[/C][C]Trim Var.[/C][C]940101.956815115[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]403605.844444444[/C][C]Range[/C][C]3019[/C][C]Trim Var.[/C][C]218545.458669355[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]512370.322689076[/C][C]Range[/C][C]2977[/C][C]Trim Var.[/C][C]333206.866666667[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]1317264.79946524[/C][C]Range[/C][C]4242[/C][C]Trim Var.[/C][C]947027.481609195[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]4157848.49621212[/C][C]Range[/C][C]8062[/C][C]Trim Var.[/C][C]2822179.43349754[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112557&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112557&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)	354025.168361582	Range	2364	Trim Var.	261338.295248078
V(Y[t],d=1,D=0)	290314.801870251	Range	2405	Trim Var.	195337.625544267
V(Y[t],d=2,D=0)	539530.120992135	Range	2918	Trim Var.	397890.298642534
V(Y[t],d=3,D=0)	1414658.30827068	Range	4614	Trim Var.	1017973.45254902
V(Y[t],d=0,D=1)	171857.233599291	Range	1783	Trim Var.	102129.719512195
V(Y[t],d=1,D=1)	190603.77613321	Range	1893	Trim Var.	120597.319512195
V(Y[t],d=2,D=1)	475617.654589372	Range	2799	Trim Var.	314452.686538462
V(Y[t],d=3,D=1)	1470509.29090909	Range	4746	Trim Var.	940101.956815115
V(Y[t],d=0,D=2)	403605.844444444	Range	3019	Trim Var.	218545.458669355
V(Y[t],d=1,D=2)	512370.322689076	Range	2977	Trim Var.	333206.866666667
V(Y[t],d=2,D=2)	1317264.79946524	Range	4242	Trim Var.	947027.481609195
V(Y[t],d=3,D=2)	4157848.49621212	Range	8062	Trim Var.	2822179.43349754

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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Input Parameters & R Code