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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

Wed, 29 Dec 2010 13:42:23 +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/t1293630253ho9ecuht3myjr0o.htm/, Retrieved Fri, 03 May 2024 09:01:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116832, Retrieved Fri, 03 May 2024 09:01:04 +0000

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No (this computation is public)

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Estimated Impact

117

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

-       [Variance Reduction Matrix] [Paper] [2010-12-29 13:42:23] [d5e0edb7e0239841e94676417b2a1e2e] [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	'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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116832&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116832&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116832&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	'George Udny Yule' @ 72.249.76.132

Variance Reduction Matrix
V(Y[t],d=0,D=0)	2832307.76901408	Range	5727	Trim Var.	2231443.11981567
V(Y[t],d=1,D=0)	166830.630434783	Range	2067	Trim Var.	93668.609465891
V(Y[t],d=2,D=0)	260801.914748508	Range	2520	Trim Var.	153825.614207650
V(Y[t],d=3,D=0)	687209.833845478	Range	4256	Trim Var.	334864.294915254
V(Y[t],d=0,D=1)	4220800.4956166	Range	6953	Trim Var.	3372981.15239477
V(Y[t],d=1,D=1)	141222.359346642	Range	1803	Trim Var.	94906.9121417798
V(Y[t],d=2,D=1)	197968.446115288	Range	2211	Trim Var.	117596.743529412
V(Y[t],d=3,D=1)	613627.079220779	Range	3684	Trim Var.	394290.515918367
V(Y[t],d=0,D=2)	8469815.96854764	Range	9564	Trim Var.	6834628.49878049
V(Y[t],d=1,D=2)	411786.417874396	Range	3008	Trim Var.	212920.717307692
V(Y[t],d=2,D=2)	620872.163636364	Range	3858	Trim Var.	331528.859649123
V(Y[t],d=3,D=2)	1932720.62737844	Range	6316	Trim Var.	1067255.53698435

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 2832307.76901408 & Range & 5727 & Trim Var. & 2231443.11981567 \tabularnewline
V(Y[t],d=1,D=0) & 166830.630434783 & Range & 2067 & Trim Var. & 93668.609465891 \tabularnewline
V(Y[t],d=2,D=0) & 260801.914748508 & Range & 2520 & Trim Var. & 153825.614207650 \tabularnewline
V(Y[t],d=3,D=0) & 687209.833845478 & Range & 4256 & Trim Var. & 334864.294915254 \tabularnewline
V(Y[t],d=0,D=1) & 4220800.4956166 & Range & 6953 & Trim Var. & 3372981.15239477 \tabularnewline
V(Y[t],d=1,D=1) & 141222.359346642 & Range & 1803 & Trim Var. & 94906.9121417798 \tabularnewline
V(Y[t],d=2,D=1) & 197968.446115288 & Range & 2211 & Trim Var. & 117596.743529412 \tabularnewline
V(Y[t],d=3,D=1) & 613627.079220779 & Range & 3684 & Trim Var. & 394290.515918367 \tabularnewline
V(Y[t],d=0,D=2) & 8469815.96854764 & Range & 9564 & Trim Var. & 6834628.49878049 \tabularnewline
V(Y[t],d=1,D=2) & 411786.417874396 & Range & 3008 & Trim Var. & 212920.717307692 \tabularnewline
V(Y[t],d=2,D=2) & 620872.163636364 & Range & 3858 & Trim Var. & 331528.859649123 \tabularnewline
V(Y[t],d=3,D=2) & 1932720.62737844 & Range & 6316 & Trim Var. & 1067255.53698435 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116832&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]2832307.76901408[/C][C]Range[/C][C]5727[/C][C]Trim Var.[/C][C]2231443.11981567[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]166830.630434783[/C][C]Range[/C][C]2067[/C][C]Trim Var.[/C][C]93668.609465891[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]260801.914748508[/C][C]Range[/C][C]2520[/C][C]Trim Var.[/C][C]153825.614207650[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]687209.833845478[/C][C]Range[/C][C]4256[/C][C]Trim Var.[/C][C]334864.294915254[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]4220800.4956166[/C][C]Range[/C][C]6953[/C][C]Trim Var.[/C][C]3372981.15239477[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]141222.359346642[/C][C]Range[/C][C]1803[/C][C]Trim Var.[/C][C]94906.9121417798[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]197968.446115288[/C][C]Range[/C][C]2211[/C][C]Trim Var.[/C][C]117596.743529412[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]613627.079220779[/C][C]Range[/C][C]3684[/C][C]Trim Var.[/C][C]394290.515918367[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]8469815.96854764[/C][C]Range[/C][C]9564[/C][C]Trim Var.[/C][C]6834628.49878049[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]411786.417874396[/C][C]Range[/C][C]3008[/C][C]Trim Var.[/C][C]212920.717307692[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]620872.163636364[/C][C]Range[/C][C]3858[/C][C]Trim Var.[/C][C]331528.859649123[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]1932720.62737844[/C][C]Range[/C][C]6316[/C][C]Trim Var.[/C][C]1067255.53698435[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116832&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116832&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)	2832307.76901408	Range	5727	Trim Var.	2231443.11981567
V(Y[t],d=1,D=0)	166830.630434783	Range	2067	Trim Var.	93668.609465891
V(Y[t],d=2,D=0)	260801.914748508	Range	2520	Trim Var.	153825.614207650
V(Y[t],d=3,D=0)	687209.833845478	Range	4256	Trim Var.	334864.294915254
V(Y[t],d=0,D=1)	4220800.4956166	Range	6953	Trim Var.	3372981.15239477
V(Y[t],d=1,D=1)	141222.359346642	Range	1803	Trim Var.	94906.9121417798
V(Y[t],d=2,D=1)	197968.446115288	Range	2211	Trim Var.	117596.743529412
V(Y[t],d=3,D=1)	613627.079220779	Range	3684	Trim Var.	394290.515918367
V(Y[t],d=0,D=2)	8469815.96854764	Range	9564	Trim Var.	6834628.49878049
V(Y[t],d=1,D=2)	411786.417874396	Range	3008	Trim Var.	212920.717307692
V(Y[t],d=2,D=2)	620872.163636364	Range	3858	Trim Var.	331528.859649123
V(Y[t],d=3,D=2)	1932720.62737844	Range	6316	Trim Var.	1067255.53698435

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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