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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

Tue, 28 Dec 2010 16:20:38 +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/28/t1293553097polvvoucja6eiqw.htm/, Retrieved Sat, 04 May 2024 21:56:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116402, Retrieved Sat, 04 May 2024 21:56:11 +0000

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No (this computation is public)

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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] [] [2010-12-28 16:20:38] [a8b9961884f5001e2816791dd4ebd90c] [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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116402&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116402&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116402&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Variance Reduction Matrix
V(Y[t],d=0,D=0)	601550.046165884	Range	3590	Trim Var.	353833.795386905
V(Y[t],d=1,D=0)	528938.711871227	Range	3956	Trim Var.	244723.187916027
V(Y[t],d=2,D=0)	1241706.43146998	Range	5281	Trim Var.	745499.06530936
V(Y[t],d=3,D=0)	3909971.49872123	Range	9423	Trim Var.	2275416.52786885
V(Y[t],d=0,D=1)	290565.419209040	Range	2789	Trim Var.	147726.506289308
V(Y[t],d=1,D=1)	344305.538281707	Range	2902	Trim Var.	201078.002177068
V(Y[t],d=2,D=1)	812837.869630974	Range	4960	Trim Var.	421655.391779789
V(Y[t],d=3,D=1)	2484929.78822055	Range	8215	Trim Var.	1271616.28313725
V(Y[t],d=0,D=2)	963965.615248227	Range	4833	Trim Var.	436201.837398374
V(Y[t],d=1,D=2)	1056860.77705828	Range	4960	Trim Var.	510167.83902439
V(Y[t],d=2,D=2)	2337006.83285024	Range	8617	Trim Var.	1099811.40448718
V(Y[t],d=3,D=2)	7016010.4949495	Range	14529	Trim Var.	2861402.30499325

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 601550.046165884 & Range & 3590 & Trim Var. & 353833.795386905 \tabularnewline
V(Y[t],d=1,D=0) & 528938.711871227 & Range & 3956 & Trim Var. & 244723.187916027 \tabularnewline
V(Y[t],d=2,D=0) & 1241706.43146998 & Range & 5281 & Trim Var. & 745499.06530936 \tabularnewline
V(Y[t],d=3,D=0) & 3909971.49872123 & Range & 9423 & Trim Var. & 2275416.52786885 \tabularnewline
V(Y[t],d=0,D=1) & 290565.419209040 & Range & 2789 & Trim Var. & 147726.506289308 \tabularnewline
V(Y[t],d=1,D=1) & 344305.538281707 & Range & 2902 & Trim Var. & 201078.002177068 \tabularnewline
V(Y[t],d=2,D=1) & 812837.869630974 & Range & 4960 & Trim Var. & 421655.391779789 \tabularnewline
V(Y[t],d=3,D=1) & 2484929.78822055 & Range & 8215 & Trim Var. & 1271616.28313725 \tabularnewline
V(Y[t],d=0,D=2) & 963965.615248227 & Range & 4833 & Trim Var. & 436201.837398374 \tabularnewline
V(Y[t],d=1,D=2) & 1056860.77705828 & Range & 4960 & Trim Var. & 510167.83902439 \tabularnewline
V(Y[t],d=2,D=2) & 2337006.83285024 & Range & 8617 & Trim Var. & 1099811.40448718 \tabularnewline
V(Y[t],d=3,D=2) & 7016010.4949495 & Range & 14529 & Trim Var. & 2861402.30499325 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116402&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]601550.046165884[/C][C]Range[/C][C]3590[/C][C]Trim Var.[/C][C]353833.795386905[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]528938.711871227[/C][C]Range[/C][C]3956[/C][C]Trim Var.[/C][C]244723.187916027[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1241706.43146998[/C][C]Range[/C][C]5281[/C][C]Trim Var.[/C][C]745499.06530936[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]3909971.49872123[/C][C]Range[/C][C]9423[/C][C]Trim Var.[/C][C]2275416.52786885[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]290565.419209040[/C][C]Range[/C][C]2789[/C][C]Trim Var.[/C][C]147726.506289308[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]344305.538281707[/C][C]Range[/C][C]2902[/C][C]Trim Var.[/C][C]201078.002177068[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]812837.869630974[/C][C]Range[/C][C]4960[/C][C]Trim Var.[/C][C]421655.391779789[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]2484929.78822055[/C][C]Range[/C][C]8215[/C][C]Trim Var.[/C][C]1271616.28313725[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]963965.615248227[/C][C]Range[/C][C]4833[/C][C]Trim Var.[/C][C]436201.837398374[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]1056860.77705828[/C][C]Range[/C][C]4960[/C][C]Trim Var.[/C][C]510167.83902439[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]2337006.83285024[/C][C]Range[/C][C]8617[/C][C]Trim Var.[/C][C]1099811.40448718[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]7016010.4949495[/C][C]Range[/C][C]14529[/C][C]Trim Var.[/C][C]2861402.30499325[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116402&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116402&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)	601550.046165884	Range	3590	Trim Var.	353833.795386905
V(Y[t],d=1,D=0)	528938.711871227	Range	3956	Trim Var.	244723.187916027
V(Y[t],d=2,D=0)	1241706.43146998	Range	5281	Trim Var.	745499.06530936
V(Y[t],d=3,D=0)	3909971.49872123	Range	9423	Trim Var.	2275416.52786885
V(Y[t],d=0,D=1)	290565.419209040	Range	2789	Trim Var.	147726.506289308
V(Y[t],d=1,D=1)	344305.538281707	Range	2902	Trim Var.	201078.002177068
V(Y[t],d=2,D=1)	812837.869630974	Range	4960	Trim Var.	421655.391779789
V(Y[t],d=3,D=1)	2484929.78822055	Range	8215	Trim Var.	1271616.28313725
V(Y[t],d=0,D=2)	963965.615248227	Range	4833	Trim Var.	436201.837398374
V(Y[t],d=1,D=2)	1056860.77705828	Range	4960	Trim Var.	510167.83902439
V(Y[t],d=2,D=2)	2337006.83285024	Range	8617	Trim Var.	1099811.40448718
V(Y[t],d=3,D=2)	7016010.4949495	Range	14529	Trim Var.	2861402.30499325

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