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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

Fri, 09 Dec 2011 06:37:33 -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/2011/Dec/09/t1323430687lrffjyun893xdm0.htm/, Retrieved Thu, 02 May 2024 19:14:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=153267, Retrieved Thu, 02 May 2024 19:14:59 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

134

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

-       [Variance Reduction Matrix] [] [2011-12-09 11:37:33] [5988e21ec0676b551e455a86717edc1d] [Current]
- R  D    [Variance Reduction Matrix] [] [2011-12-09 11:54:01] [f2faabc3a2466a29562900bc59f67898] 
- RM D    [Standard Deviation-Mean Plot] [] [2011-12-09 12:00:54] [f2faabc3a2466a29562900bc59f67898] 
- RM D    [Standard Deviation-Mean Plot] [] [2011-12-09 12:01:36] [f2faabc3a2466a29562900bc59f67898] 
- RMPD    [ARIMA Backward Selection] [] [2011-12-09 12:17:21] [f2faabc3a2466a29562900bc59f67898] 
- RMPD    [ARIMA Forecasting] [] [2011-12-09 12:23:21] [f2faabc3a2466a29562900bc59f67898] 

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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	0 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153267&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153267&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153267&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	0 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Variance Reduction Matrix
V(Y[t],d=0,D=0)	30797648.7781421	Range	25303	Trim Var.	18058471.3113208
V(Y[t],d=1,D=0)	38246138.1387006	Range	29984	Trim Var.	19463113.1254368
V(Y[t],d=2,D=0)	101874492.440678	Range	56102	Trim Var.	51687905.6560232
V(Y[t],d=3,D=0)	332659170.285541	Range	91105	Trim Var.	183585533.868778
V(Y[t],d=0,D=1)	11827909.837585	Range	13003	Trim Var.	7706127.77962348
V(Y[t],d=1,D=1)	9163815.74423759	Range	12295	Trim Var.	5990556.79268293
V(Y[t],d=2,D=1)	27789085.2146161	Range	22955	Trim Var.	17315204.6487805
V(Y[t],d=3,D=1)	93191276.3714976	Range	41164	Trim Var.	55324761.973718
V(Y[t],d=0,D=2)	43385475.2222222	Range	23794	Trim Var.	32001369.905303
V(Y[t],d=1,D=2)	20201076.8539683	Range	19889	Trim Var.	12036305.3508065
V(Y[t],d=2,D=2)	60047781.1058824	Range	34184	Trim Var.	35613051.2473118
V(Y[t],d=3,D=2)	202740376.107843	Range	63377	Trim Var.	121215851.264368

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 30797648.7781421 & Range & 25303 & Trim Var. & 18058471.3113208 \tabularnewline
V(Y[t],d=1,D=0) & 38246138.1387006 & Range & 29984 & Trim Var. & 19463113.1254368 \tabularnewline
V(Y[t],d=2,D=0) & 101874492.440678 & Range & 56102 & Trim Var. & 51687905.6560232 \tabularnewline
V(Y[t],d=3,D=0) & 332659170.285541 & Range & 91105 & Trim Var. & 183585533.868778 \tabularnewline
V(Y[t],d=0,D=1) & 11827909.837585 & Range & 13003 & Trim Var. & 7706127.77962348 \tabularnewline
V(Y[t],d=1,D=1) & 9163815.74423759 & Range & 12295 & Trim Var. & 5990556.79268293 \tabularnewline
V(Y[t],d=2,D=1) & 27789085.2146161 & Range & 22955 & Trim Var. & 17315204.6487805 \tabularnewline
V(Y[t],d=3,D=1) & 93191276.3714976 & Range & 41164 & Trim Var. & 55324761.973718 \tabularnewline
V(Y[t],d=0,D=2) & 43385475.2222222 & Range & 23794 & Trim Var. & 32001369.905303 \tabularnewline
V(Y[t],d=1,D=2) & 20201076.8539683 & Range & 19889 & Trim Var. & 12036305.3508065 \tabularnewline
V(Y[t],d=2,D=2) & 60047781.1058824 & Range & 34184 & Trim Var. & 35613051.2473118 \tabularnewline
V(Y[t],d=3,D=2) & 202740376.107843 & Range & 63377 & Trim Var. & 121215851.264368 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153267&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]30797648.7781421[/C][C]Range[/C][C]25303[/C][C]Trim Var.[/C][C]18058471.3113208[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]38246138.1387006[/C][C]Range[/C][C]29984[/C][C]Trim Var.[/C][C]19463113.1254368[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]101874492.440678[/C][C]Range[/C][C]56102[/C][C]Trim Var.[/C][C]51687905.6560232[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]332659170.285541[/C][C]Range[/C][C]91105[/C][C]Trim Var.[/C][C]183585533.868778[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]11827909.837585[/C][C]Range[/C][C]13003[/C][C]Trim Var.[/C][C]7706127.77962348[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]9163815.74423759[/C][C]Range[/C][C]12295[/C][C]Trim Var.[/C][C]5990556.79268293[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]27789085.2146161[/C][C]Range[/C][C]22955[/C][C]Trim Var.[/C][C]17315204.6487805[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]93191276.3714976[/C][C]Range[/C][C]41164[/C][C]Trim Var.[/C][C]55324761.973718[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]43385475.2222222[/C][C]Range[/C][C]23794[/C][C]Trim Var.[/C][C]32001369.905303[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]20201076.8539683[/C][C]Range[/C][C]19889[/C][C]Trim Var.[/C][C]12036305.3508065[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]60047781.1058824[/C][C]Range[/C][C]34184[/C][C]Trim Var.[/C][C]35613051.2473118[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]202740376.107843[/C][C]Range[/C][C]63377[/C][C]Trim Var.[/C][C]121215851.264368[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153267&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153267&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)	30797648.7781421	Range	25303	Trim Var.	18058471.3113208
V(Y[t],d=1,D=0)	38246138.1387006	Range	29984	Trim Var.	19463113.1254368
V(Y[t],d=2,D=0)	101874492.440678	Range	56102	Trim Var.	51687905.6560232
V(Y[t],d=3,D=0)	332659170.285541	Range	91105	Trim Var.	183585533.868778
V(Y[t],d=0,D=1)	11827909.837585	Range	13003	Trim Var.	7706127.77962348
V(Y[t],d=1,D=1)	9163815.74423759	Range	12295	Trim Var.	5990556.79268293
V(Y[t],d=2,D=1)	27789085.2146161	Range	22955	Trim Var.	17315204.6487805
V(Y[t],d=3,D=1)	93191276.3714976	Range	41164	Trim Var.	55324761.973718
V(Y[t],d=0,D=2)	43385475.2222222	Range	23794	Trim Var.	32001369.905303
V(Y[t],d=1,D=2)	20201076.8539683	Range	19889	Trim Var.	12036305.3508065
V(Y[t],d=2,D=2)	60047781.1058824	Range	34184	Trim Var.	35613051.2473118
V(Y[t],d=3,D=2)	202740376.107843	Range	63377	Trim Var.	121215851.264368

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