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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

Wed, 29 Dec 2010 16:06:13 +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/t1293638647ud35ahi5bh31kfa.htm/, Retrieved Fri, 03 May 2024 08:20:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116937, Retrieved Fri, 03 May 2024 08:20:30 +0000

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Estimated Impact

129

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

-       [Variance Reduction Matrix] [paper variantie r...] [2010-12-29 16:06:13] [be9f1751361e0e66b042227828c71db5] [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	2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116937&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]2 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=116937&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116937&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	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Variance Reduction Matrix
V(Y[t],d=0,D=0)	11164022.6228211	Range	11925	Trim Var.	8781358.41088569
V(Y[t],d=1,D=0)	73410.1433241192	Range	1403	Trim Var.	40532.7152868674
V(Y[t],d=2,D=0)	135922.976791567	Range	1981	Trim Var.	66444.8233122072
V(Y[t],d=3,D=0)	329013.871054279	Range	3316	Trim Var.	158730.443887497
V(Y[t],d=0,D=1)	187059.621518802	Range	2136	Trim Var.	114066.739287907
V(Y[t],d=1,D=1)	9566.14915521403	Range	779	Trim Var.	3108.09112352576
V(Y[t],d=2,D=1)	16419.5296019900	Range	896	Trim Var.	5210.09283786329
V(Y[t],d=3,D=1)	43445.9267336683	Range	1644	Trim Var.	17190.5016759777
V(Y[t],d=0,D=2)	120377.630476715	Range	1662	Trim Var.	82073.3793595545
V(Y[t],d=1,D=2)	22808.8904483431	Range	1175	Trim Var.	9487.79895579534
V(Y[t],d=2,D=2)	38667.9711809073	Range	1512	Trim Var.	16066.4133558749
V(Y[t],d=3,D=2)	103122.090681534	Range	2449	Trim Var.	45109.1975691474

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 11164022.6228211 & Range & 11925 & Trim Var. & 8781358.41088569 \tabularnewline
V(Y[t],d=1,D=0) & 73410.1433241192 & Range & 1403 & Trim Var. & 40532.7152868674 \tabularnewline
V(Y[t],d=2,D=0) & 135922.976791567 & Range & 1981 & Trim Var. & 66444.8233122072 \tabularnewline
V(Y[t],d=3,D=0) & 329013.871054279 & Range & 3316 & Trim Var. & 158730.443887497 \tabularnewline
V(Y[t],d=0,D=1) & 187059.621518802 & Range & 2136 & Trim Var. & 114066.739287907 \tabularnewline
V(Y[t],d=1,D=1) & 9566.14915521403 & Range & 779 & Trim Var. & 3108.09112352576 \tabularnewline
V(Y[t],d=2,D=1) & 16419.5296019900 & Range & 896 & Trim Var. & 5210.09283786329 \tabularnewline
V(Y[t],d=3,D=1) & 43445.9267336683 & Range & 1644 & Trim Var. & 17190.5016759777 \tabularnewline
V(Y[t],d=0,D=2) & 120377.630476715 & Range & 1662 & Trim Var. & 82073.3793595545 \tabularnewline
V(Y[t],d=1,D=2) & 22808.8904483431 & Range & 1175 & Trim Var. & 9487.79895579534 \tabularnewline
V(Y[t],d=2,D=2) & 38667.9711809073 & Range & 1512 & Trim Var. & 16066.4133558749 \tabularnewline
V(Y[t],d=3,D=2) & 103122.090681534 & Range & 2449 & Trim Var. & 45109.1975691474 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116937&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]11164022.6228211[/C][C]Range[/C][C]11925[/C][C]Trim Var.[/C][C]8781358.41088569[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]73410.1433241192[/C][C]Range[/C][C]1403[/C][C]Trim Var.[/C][C]40532.7152868674[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]135922.976791567[/C][C]Range[/C][C]1981[/C][C]Trim Var.[/C][C]66444.8233122072[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]329013.871054279[/C][C]Range[/C][C]3316[/C][C]Trim Var.[/C][C]158730.443887497[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]187059.621518802[/C][C]Range[/C][C]2136[/C][C]Trim Var.[/C][C]114066.739287907[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]9566.14915521403[/C][C]Range[/C][C]779[/C][C]Trim Var.[/C][C]3108.09112352576[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]16419.5296019900[/C][C]Range[/C][C]896[/C][C]Trim Var.[/C][C]5210.09283786329[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]43445.9267336683[/C][C]Range[/C][C]1644[/C][C]Trim Var.[/C][C]17190.5016759777[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]120377.630476715[/C][C]Range[/C][C]1662[/C][C]Trim Var.[/C][C]82073.3793595545[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]22808.8904483431[/C][C]Range[/C][C]1175[/C][C]Trim Var.[/C][C]9487.79895579534[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]38667.9711809073[/C][C]Range[/C][C]1512[/C][C]Trim Var.[/C][C]16066.4133558749[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]103122.090681534[/C][C]Range[/C][C]2449[/C][C]Trim Var.[/C][C]45109.1975691474[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116937&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116937&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)	11164022.6228211	Range	11925	Trim Var.	8781358.41088569
V(Y[t],d=1,D=0)	73410.1433241192	Range	1403	Trim Var.	40532.7152868674
V(Y[t],d=2,D=0)	135922.976791567	Range	1981	Trim Var.	66444.8233122072
V(Y[t],d=3,D=0)	329013.871054279	Range	3316	Trim Var.	158730.443887497
V(Y[t],d=0,D=1)	187059.621518802	Range	2136	Trim Var.	114066.739287907
V(Y[t],d=1,D=1)	9566.14915521403	Range	779	Trim Var.	3108.09112352576
V(Y[t],d=2,D=1)	16419.5296019900	Range	896	Trim Var.	5210.09283786329
V(Y[t],d=3,D=1)	43445.9267336683	Range	1644	Trim Var.	17190.5016759777
V(Y[t],d=0,D=2)	120377.630476715	Range	1662	Trim Var.	82073.3793595545
V(Y[t],d=1,D=2)	22808.8904483431	Range	1175	Trim Var.	9487.79895579534
V(Y[t],d=2,D=2)	38667.9711809073	Range	1512	Trim Var.	16066.4133558749
V(Y[t],d=3,D=2)	103122.090681534	Range	2449	Trim Var.	45109.1975691474

Figure 1

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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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