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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 13:23:51 +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/t1293629278i3g9o1sj2uyrsgw.htm/, Retrieved Fri, 03 May 2024 04:32:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116811, Retrieved Fri, 03 May 2024 04:32:06 +0000

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Estimated Impact

115

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

-       [Variance Reduction Matrix] [] [2010-12-29 13:23:51] [5e4b6b538311b7e958647ef5010fb0e5] [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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116811&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116811&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116811&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Variance Reduction Matrix
V(Y[t],d=0,D=0)	2804095.63122415	Range	7212	Trim Var.	2274262.92471737
V(Y[t],d=1,D=0)	1411808.38894009	Range	6618	Trim Var.	853890.773850485
V(Y[t],d=2,D=0)	2339266.39911722	Range	10067	Trim Var.	1376473.31259917
V(Y[t],d=3,D=0)	6832962.84141727	Range	18151	Trim Var.	3930569.44300129
V(Y[t],d=0,D=1)	243458.22999223	Range	4428	Trim Var.	68907.6338582677
V(Y[t],d=1,D=1)	610998.7035359	Range	7551	Trim Var.	149949.037495313
V(Y[t],d=2,D=1)	1987773.2690041	Range	12466	Trim Var.	501155.783936508
V(Y[t],d=3,D=1)	6803560.42006079	Range	24665	Trim Var.	1758738.02296774
V(Y[t],d=0,D=2)	583220.816736063	Range	7001	Trim Var.	165459.994495147
V(Y[t],d=1,D=2)	1509734.69242513	Range	12322	Trim Var.	360658.761420572
V(Y[t],d=2,D=2)	4840894.27215265	Range	20740	Trim Var.	1207966.69175412
V(Y[t],d=3,D=2)	16440908.1007752	Range	39981	Trim Var.	4210221.53440122

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 2804095.63122415 & Range & 7212 & Trim Var. & 2274262.92471737 \tabularnewline
V(Y[t],d=1,D=0) & 1411808.38894009 & Range & 6618 & Trim Var. & 853890.773850485 \tabularnewline
V(Y[t],d=2,D=0) & 2339266.39911722 & Range & 10067 & Trim Var. & 1376473.31259917 \tabularnewline
V(Y[t],d=3,D=0) & 6832962.84141727 & Range & 18151 & Trim Var. & 3930569.44300129 \tabularnewline
V(Y[t],d=0,D=1) & 243458.22999223 & Range & 4428 & Trim Var. & 68907.6338582677 \tabularnewline
V(Y[t],d=1,D=1) & 610998.7035359 & Range & 7551 & Trim Var. & 149949.037495313 \tabularnewline
V(Y[t],d=2,D=1) & 1987773.2690041 & Range & 12466 & Trim Var. & 501155.783936508 \tabularnewline
V(Y[t],d=3,D=1) & 6803560.42006079 & Range & 24665 & Trim Var. & 1758738.02296774 \tabularnewline
V(Y[t],d=0,D=2) & 583220.816736063 & Range & 7001 & Trim Var. & 165459.994495147 \tabularnewline
V(Y[t],d=1,D=2) & 1509734.69242513 & Range & 12322 & Trim Var. & 360658.761420572 \tabularnewline
V(Y[t],d=2,D=2) & 4840894.27215265 & Range & 20740 & Trim Var. & 1207966.69175412 \tabularnewline
V(Y[t],d=3,D=2) & 16440908.1007752 & Range & 39981 & Trim Var. & 4210221.53440122 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116811&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]2804095.63122415[/C][C]Range[/C][C]7212[/C][C]Trim Var.[/C][C]2274262.92471737[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1411808.38894009[/C][C]Range[/C][C]6618[/C][C]Trim Var.[/C][C]853890.773850485[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]2339266.39911722[/C][C]Range[/C][C]10067[/C][C]Trim Var.[/C][C]1376473.31259917[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]6832962.84141727[/C][C]Range[/C][C]18151[/C][C]Trim Var.[/C][C]3930569.44300129[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]243458.22999223[/C][C]Range[/C][C]4428[/C][C]Trim Var.[/C][C]68907.6338582677[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]610998.7035359[/C][C]Range[/C][C]7551[/C][C]Trim Var.[/C][C]149949.037495313[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]1987773.2690041[/C][C]Range[/C][C]12466[/C][C]Trim Var.[/C][C]501155.783936508[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]6803560.42006079[/C][C]Range[/C][C]24665[/C][C]Trim Var.[/C][C]1758738.02296774[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]583220.816736063[/C][C]Range[/C][C]7001[/C][C]Trim Var.[/C][C]165459.994495147[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]1509734.69242513[/C][C]Range[/C][C]12322[/C][C]Trim Var.[/C][C]360658.761420572[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]4840894.27215265[/C][C]Range[/C][C]20740[/C][C]Trim Var.[/C][C]1207966.69175412[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]16440908.1007752[/C][C]Range[/C][C]39981[/C][C]Trim Var.[/C][C]4210221.53440122[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116811&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116811&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)	2804095.63122415	Range	7212	Trim Var.	2274262.92471737
V(Y[t],d=1,D=0)	1411808.38894009	Range	6618	Trim Var.	853890.773850485
V(Y[t],d=2,D=0)	2339266.39911722	Range	10067	Trim Var.	1376473.31259917
V(Y[t],d=3,D=0)	6832962.84141727	Range	18151	Trim Var.	3930569.44300129
V(Y[t],d=0,D=1)	243458.22999223	Range	4428	Trim Var.	68907.6338582677
V(Y[t],d=1,D=1)	610998.7035359	Range	7551	Trim Var.	149949.037495313
V(Y[t],d=2,D=1)	1987773.2690041	Range	12466	Trim Var.	501155.783936508
V(Y[t],d=3,D=1)	6803560.42006079	Range	24665	Trim Var.	1758738.02296774
V(Y[t],d=0,D=2)	583220.816736063	Range	7001	Trim Var.	165459.994495147
V(Y[t],d=1,D=2)	1509734.69242513	Range	12322	Trim Var.	360658.761420572
V(Y[t],d=2,D=2)	4840894.27215265	Range	20740	Trim Var.	1207966.69175412
V(Y[t],d=3,D=2)	16440908.1007752	Range	39981	Trim Var.	4210221.53440122

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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Tree of Dependent Computations

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Tables (Output of Computation)

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Input Parameters & R Code