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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

Sat, 01 Dec 2012 07:45:23 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/01/t1354366084d1c2wz30rb3sr2c.htm/, Retrieved Sun, 28 Apr 2024 20:27:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=195273, Retrieved Sun, 28 Apr 2024 20:27:57 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

136

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

-     [Univariate Data Series] [Paper - exogene v...] [2010-12-01 16:02:49] [6f0e7a2d1a07390e3505a2db8288f975]
- RMP   [(Partial) Autocorrelation Function] [ACF 1] [2012-12-01 12:28:25] [aa4758794357e809405bf1fb1497cdc4]
- RMP       [Variance Reduction Matrix] [VRM] [2012-12-01 12:45:23] [4289cf790da1cc09a0cb8798de13fde3] [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	'Sir Maurice George Kendall' @ kendall.wessa.net

\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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195273&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195273&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195273&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	'Sir Maurice George Kendall' @ kendall.wessa.net

Variance Reduction Matrix
V(Y[t],d=0,D=0)	263028.810087719	Range	2541	Trim Var.	163350.332147743
V(Y[t],d=1,D=0)	371533.678163494	Range	2491	Trim Var.	279013.314285714
V(Y[t],d=2,D=0)	1221386.91191947	Range	4365	Trim Var.	944696.792885829
V(Y[t],d=3,D=0)	4274802.5514259	Range	8326	Trim Var.	3262423.93417573
V(Y[t],d=0,D=1)	96417.5058806655	Range	1432	Trim Var.	61711.7654572381
V(Y[t],d=1,D=1)	150008.806935057	Range	1737	Trim Var.	100983.426940639
V(Y[t],d=2,D=1)	421283.723727793	Range	2887	Trim Var.	280544.758802817
V(Y[t],d=3,D=1)	1323947.06944444	Range	5371	Trim Var.	867719.323541248
V(Y[t],d=0,D=2)	202272.956964006	Range	1915	Trim Var.	133451.271577381
V(Y[t],d=1,D=2)	332658.507847083	Range	2774	Trim Var.	183615.142857143
V(Y[t],d=2,D=2)	835845.84699793	Range	4266	Trim Var.	501589.724219989
V(Y[t],d=3,D=2)	2467169.89428815	Range	7011	Trim Var.	1480435.08743169

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 263028.810087719 & Range & 2541 & Trim Var. & 163350.332147743 \tabularnewline
V(Y[t],d=1,D=0) & 371533.678163494 & Range & 2491 & Trim Var. & 279013.314285714 \tabularnewline
V(Y[t],d=2,D=0) & 1221386.91191947 & Range & 4365 & Trim Var. & 944696.792885829 \tabularnewline
V(Y[t],d=3,D=0) & 4274802.5514259 & Range & 8326 & Trim Var. & 3262423.93417573 \tabularnewline
V(Y[t],d=0,D=1) & 96417.5058806655 & Range & 1432 & Trim Var. & 61711.7654572381 \tabularnewline
V(Y[t],d=1,D=1) & 150008.806935057 & Range & 1737 & Trim Var. & 100983.426940639 \tabularnewline
V(Y[t],d=2,D=1) & 421283.723727793 & Range & 2887 & Trim Var. & 280544.758802817 \tabularnewline
V(Y[t],d=3,D=1) & 1323947.06944444 & Range & 5371 & Trim Var. & 867719.323541248 \tabularnewline
V(Y[t],d=0,D=2) & 202272.956964006 & Range & 1915 & Trim Var. & 133451.271577381 \tabularnewline
V(Y[t],d=1,D=2) & 332658.507847083 & Range & 2774 & Trim Var. & 183615.142857143 \tabularnewline
V(Y[t],d=2,D=2) & 835845.84699793 & Range & 4266 & Trim Var. & 501589.724219989 \tabularnewline
V(Y[t],d=3,D=2) & 2467169.89428815 & Range & 7011 & Trim Var. & 1480435.08743169 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195273&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]263028.810087719[/C][C]Range[/C][C]2541[/C][C]Trim Var.[/C][C]163350.332147743[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]371533.678163494[/C][C]Range[/C][C]2491[/C][C]Trim Var.[/C][C]279013.314285714[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1221386.91191947[/C][C]Range[/C][C]4365[/C][C]Trim Var.[/C][C]944696.792885829[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]4274802.5514259[/C][C]Range[/C][C]8326[/C][C]Trim Var.[/C][C]3262423.93417573[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]96417.5058806655[/C][C]Range[/C][C]1432[/C][C]Trim Var.[/C][C]61711.7654572381[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]150008.806935057[/C][C]Range[/C][C]1737[/C][C]Trim Var.[/C][C]100983.426940639[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]421283.723727793[/C][C]Range[/C][C]2887[/C][C]Trim Var.[/C][C]280544.758802817[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]1323947.06944444[/C][C]Range[/C][C]5371[/C][C]Trim Var.[/C][C]867719.323541248[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]202272.956964006[/C][C]Range[/C][C]1915[/C][C]Trim Var.[/C][C]133451.271577381[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]332658.507847083[/C][C]Range[/C][C]2774[/C][C]Trim Var.[/C][C]183615.142857143[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]835845.84699793[/C][C]Range[/C][C]4266[/C][C]Trim Var.[/C][C]501589.724219989[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]2467169.89428815[/C][C]Range[/C][C]7011[/C][C]Trim Var.[/C][C]1480435.08743169[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195273&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195273&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)	263028.810087719	Range	2541	Trim Var.	163350.332147743
V(Y[t],d=1,D=0)	371533.678163494	Range	2491	Trim Var.	279013.314285714
V(Y[t],d=2,D=0)	1221386.91191947	Range	4365	Trim Var.	944696.792885829
V(Y[t],d=3,D=0)	4274802.5514259	Range	8326	Trim Var.	3262423.93417573
V(Y[t],d=0,D=1)	96417.5058806655	Range	1432	Trim Var.	61711.7654572381
V(Y[t],d=1,D=1)	150008.806935057	Range	1737	Trim Var.	100983.426940639
V(Y[t],d=2,D=1)	421283.723727793	Range	2887	Trim Var.	280544.758802817
V(Y[t],d=3,D=1)	1323947.06944444	Range	5371	Trim Var.	867719.323541248
V(Y[t],d=0,D=2)	202272.956964006	Range	1915	Trim Var.	133451.271577381
V(Y[t],d=1,D=2)	332658.507847083	Range	2774	Trim Var.	183615.142857143
V(Y[t],d=2,D=2)	835845.84699793	Range	4266	Trim Var.	501589.724219989
V(Y[t],d=3,D=2)	2467169.89428815	Range	7011	Trim Var.	1480435.08743169

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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