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Author

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R Software Module

rwasp_variancereduction.wasp

Title produced by software

Variance Reduction Matrix

Date of computation

Wed, 21 Dec 2011 04:52:02 -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/21/t1324461147ub4y0x622hmdlm0.htm/, Retrieved Tue, 07 May 2024 15:56:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=158402, Retrieved Tue, 07 May 2024 15:56:57 +0000

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No (this computation is public)

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Estimated Impact

128

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

-     [Univariate Data Series] [web traffic] [2010-10-19 15:13:07] [b98453cac15ba1066b407e146608df68]
- RMP   [Variance Reduction Matrix] [Traffic] [2010-11-29 09:57:15] [b98453cac15ba1066b407e146608df68]
- RM      [Standard Deviation-Mean Plot] [Traffic] [2010-11-29 11:05:08] [b98453cac15ba1066b407e146608df68]
- RMP       [ARIMA Forecasting] [Traffic] [2010-11-29 21:10:32] [b98453cac15ba1066b407e146608df68]
- R PD        [ARIMA Forecasting] [] [2011-12-06 10:39:07] [aba4febe8a2e49e81bdc61a6c01f5c21]
-   PD          [ARIMA Forecasting] [] [2011-12-20 15:47:34] [aba4febe8a2e49e81bdc61a6c01f5c21]
- R               [ARIMA Forecasting] [ARIMA Forecasting CV] [2011-12-20 15:48:10] [aba4febe8a2e49e81bdc61a6c01f5c21]
- RMPD                [Variance Reduction Matrix] [Paper variance re...] [2011-12-21 09:52:02] [3627de22d386f4cb93d383ef7c1ade7f] [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	'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158402&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158402&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158402&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	'Gwilym Jenkins' @ jenkins.wessa.net

Variance Reduction Matrix
V(Y[t],d=0,D=0)	180574.21532246	Range	2354	Trim Var.	102054.619603212
V(Y[t],d=1,D=0)	322859.752859199	Range	4418	Trim Var.	162403.322030651
V(Y[t],d=2,D=0)	984780.374817882	Range	7290	Trim Var.	487964.878739316
V(Y[t],d=3,D=0)	3324766.42655279	Range	14084	Trim Var.	1646145.30158574
V(Y[t],d=0,D=1)	340474.349947717	Range	3581	Trim Var.	193967.321078431
V(Y[t],d=1,D=1)	682180.697571744	Range	5377	Trim Var.	342949.916196794
V(Y[t],d=2,D=1)	2112923.27713647	Range	9648	Trim Var.	1116665.25530244
V(Y[t],d=3,D=1)	7205679.72537638	Range	17267	Trim Var.	3974876.53975849
V(Y[t],d=0,D=2)	945876.58705036	Range	6066	Trim Var.	547018.290857143
V(Y[t],d=1,D=2)	2006467.50119904	Range	8795	Trim Var.	1101224.12606452
V(Y[t],d=2,D=2)	6183780.83999788	Range	13551	Trim Var.	3616282.682599
V(Y[t],d=3,D=2)	20944166.7628811	Range	23941	Trim Var.	12927082.1152872

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 180574.21532246 & Range & 2354 & Trim Var. & 102054.619603212 \tabularnewline
V(Y[t],d=1,D=0) & 322859.752859199 & Range & 4418 & Trim Var. & 162403.322030651 \tabularnewline
V(Y[t],d=2,D=0) & 984780.374817882 & Range & 7290 & Trim Var. & 487964.878739316 \tabularnewline
V(Y[t],d=3,D=0) & 3324766.42655279 & Range & 14084 & Trim Var. & 1646145.30158574 \tabularnewline
V(Y[t],d=0,D=1) & 340474.349947717 & Range & 3581 & Trim Var. & 193967.321078431 \tabularnewline
V(Y[t],d=1,D=1) & 682180.697571744 & Range & 5377 & Trim Var. & 342949.916196794 \tabularnewline
V(Y[t],d=2,D=1) & 2112923.27713647 & Range & 9648 & Trim Var. & 1116665.25530244 \tabularnewline
V(Y[t],d=3,D=1) & 7205679.72537638 & Range & 17267 & Trim Var. & 3974876.53975849 \tabularnewline
V(Y[t],d=0,D=2) & 945876.58705036 & Range & 6066 & Trim Var. & 547018.290857143 \tabularnewline
V(Y[t],d=1,D=2) & 2006467.50119904 & Range & 8795 & Trim Var. & 1101224.12606452 \tabularnewline
V(Y[t],d=2,D=2) & 6183780.83999788 & Range & 13551 & Trim Var. & 3616282.682599 \tabularnewline
V(Y[t],d=3,D=2) & 20944166.7628811 & Range & 23941 & Trim Var. & 12927082.1152872 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158402&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]180574.21532246[/C][C]Range[/C][C]2354[/C][C]Trim Var.[/C][C]102054.619603212[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]322859.752859199[/C][C]Range[/C][C]4418[/C][C]Trim Var.[/C][C]162403.322030651[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]984780.374817882[/C][C]Range[/C][C]7290[/C][C]Trim Var.[/C][C]487964.878739316[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]3324766.42655279[/C][C]Range[/C][C]14084[/C][C]Trim Var.[/C][C]1646145.30158574[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]340474.349947717[/C][C]Range[/C][C]3581[/C][C]Trim Var.[/C][C]193967.321078431[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]682180.697571744[/C][C]Range[/C][C]5377[/C][C]Trim Var.[/C][C]342949.916196794[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]2112923.27713647[/C][C]Range[/C][C]9648[/C][C]Trim Var.[/C][C]1116665.25530244[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]7205679.72537638[/C][C]Range[/C][C]17267[/C][C]Trim Var.[/C][C]3974876.53975849[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]945876.58705036[/C][C]Range[/C][C]6066[/C][C]Trim Var.[/C][C]547018.290857143[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]2006467.50119904[/C][C]Range[/C][C]8795[/C][C]Trim Var.[/C][C]1101224.12606452[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]6183780.83999788[/C][C]Range[/C][C]13551[/C][C]Trim Var.[/C][C]3616282.682599[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]20944166.7628811[/C][C]Range[/C][C]23941[/C][C]Trim Var.[/C][C]12927082.1152872[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158402&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158402&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)	180574.21532246	Range	2354	Trim Var.	102054.619603212
V(Y[t],d=1,D=0)	322859.752859199	Range	4418	Trim Var.	162403.322030651
V(Y[t],d=2,D=0)	984780.374817882	Range	7290	Trim Var.	487964.878739316
V(Y[t],d=3,D=0)	3324766.42655279	Range	14084	Trim Var.	1646145.30158574
V(Y[t],d=0,D=1)	340474.349947717	Range	3581	Trim Var.	193967.321078431
V(Y[t],d=1,D=1)	682180.697571744	Range	5377	Trim Var.	342949.916196794
V(Y[t],d=2,D=1)	2112923.27713647	Range	9648	Trim Var.	1116665.25530244
V(Y[t],d=3,D=1)	7205679.72537638	Range	17267	Trim Var.	3974876.53975849
V(Y[t],d=0,D=2)	945876.58705036	Range	6066	Trim Var.	547018.290857143
V(Y[t],d=1,D=2)	2006467.50119904	Range	8795	Trim Var.	1101224.12606452
V(Y[t],d=2,D=2)	6183780.83999788	Range	13551	Trim Var.	3616282.682599
V(Y[t],d=3,D=2)	20944166.7628811	Range	23941	Trim Var.	12927082.1152872

Figure 1

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Postscript link

PDF link

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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