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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_variancereduction.wasp
Title produced by softwareVariance Reduction Matrix
Date of computationWed, 29 Dec 2010 18:59:19 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/29/t1293649779u7jsluccljce2r6.htm/, Retrieved Fri, 03 May 2024 14:07:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117044, Retrieved Fri, 03 May 2024 14:07:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact150

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [Partial autocorre...] [2008-12-09 20:18:51] [12d343c4448a5f9e527bb31caeac580b]
-   P   [(Partial) Autocorrelation Function] [Partial autocorre...] [2008-12-09 20:27:26] [12d343c4448a5f9e527bb31caeac580b]
- RMPD    [(Partial) Autocorrelation Function] [] [2009-12-17 10:05:30] [fa44bc1b850de3469c0e3e9a5981c418]
- RMPD        [Variance Reduction Matrix] [variance reductio...] [2010-12-29 18:59:19] [95610e892c4b5c84ff80f4c898567a9d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0.3
-0.1
-1
-1.2
-0.8
-1.7
-1.1
-0.4
0.6
0.6
1.9
2.3
2.6
3.1
4.7
5.5
5.4
5.9
5.8
5.2
4.2
4.4
3.6
3.5
3.1
2.9
2.2
1.5
1.1
1.4
1.3
1.3
1.8
1.8
1.8
1.7
1.6
1.5
1.2
1.2
1.6
1.6
1.9
2.2
2
1.7
2.4
2.6
2.9
2.6
2.5
3.2
3.1
3.1
2.9
2.5
2.8
3.1
2.6
2.3

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117044&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 Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117044&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117044&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Variance Reduction Matrix
V(Y[t],d=0,D=0)2.87528531073446Range7.6Trim Var.1.78182040531097
V(Y[t],d=1,D=0)0.270555230859147Range2.6Trim Var.0.151436865021771
V(Y[t],d=2,D=0)0.38683908045977Range2.8Trim Var.0.254374057315234
V(Y[t],d=3,D=0)1.15431077694236Range5Trim Var.0.70678431372549
V(Y[t],d=0,D=1)0.270555230859147Range2.6Trim Var.0.151436865021771
V(Y[t],d=1,D=1)0.38683908045977Range2.8Trim Var.0.254374057315234
V(Y[t],d=2,D=1)1.15431077694236Range5Trim Var.0.70678431372549
V(Y[t],d=3,D=1)3.80362337662338Range9.2Trim Var.2.17571020408163
V(Y[t],d=0,D=2)0.38683908045977Range2.8Trim Var.0.254374057315234
V(Y[t],d=1,D=2)1.15431077694236Range5Trim Var.0.70678431372549
V(Y[t],d=2,D=2)3.80362337662338Range9.2Trim Var.2.17571020408163
V(Y[t],d=3,D=2)13.2821346801347Range16.6Trim Var.7.72353741496599

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 2.87528531073446 & Range & 7.6 & Trim Var. & 1.78182040531097 \tabularnewline
V(Y[t],d=1,D=0) & 0.270555230859147 & Range & 2.6 & Trim Var. & 0.151436865021771 \tabularnewline
V(Y[t],d=2,D=0) & 0.38683908045977 & Range & 2.8 & Trim Var. & 0.254374057315234 \tabularnewline
V(Y[t],d=3,D=0) & 1.15431077694236 & Range & 5 & Trim Var. & 0.70678431372549 \tabularnewline
V(Y[t],d=0,D=1) & 0.270555230859147 & Range & 2.6 & Trim Var. & 0.151436865021771 \tabularnewline
V(Y[t],d=1,D=1) & 0.38683908045977 & Range & 2.8 & Trim Var. & 0.254374057315234 \tabularnewline
V(Y[t],d=2,D=1) & 1.15431077694236 & Range & 5 & Trim Var. & 0.70678431372549 \tabularnewline
V(Y[t],d=3,D=1) & 3.80362337662338 & Range & 9.2 & Trim Var. & 2.17571020408163 \tabularnewline
V(Y[t],d=0,D=2) & 0.38683908045977 & Range & 2.8 & Trim Var. & 0.254374057315234 \tabularnewline
V(Y[t],d=1,D=2) & 1.15431077694236 & Range & 5 & Trim Var. & 0.70678431372549 \tabularnewline
V(Y[t],d=2,D=2) & 3.80362337662338 & Range & 9.2 & Trim Var. & 2.17571020408163 \tabularnewline
V(Y[t],d=3,D=2) & 13.2821346801347 & Range & 16.6 & Trim Var. & 7.72353741496599 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117044&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]2.87528531073446[/C][C]Range[/C][C]7.6[/C][C]Trim Var.[/C][C]1.78182040531097[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.270555230859147[/C][C]Range[/C][C]2.6[/C][C]Trim Var.[/C][C]0.151436865021771[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.38683908045977[/C][C]Range[/C][C]2.8[/C][C]Trim Var.[/C][C]0.254374057315234[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]1.15431077694236[/C][C]Range[/C][C]5[/C][C]Trim Var.[/C][C]0.70678431372549[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.270555230859147[/C][C]Range[/C][C]2.6[/C][C]Trim Var.[/C][C]0.151436865021771[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.38683908045977[/C][C]Range[/C][C]2.8[/C][C]Trim Var.[/C][C]0.254374057315234[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]1.15431077694236[/C][C]Range[/C][C]5[/C][C]Trim Var.[/C][C]0.70678431372549[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]3.80362337662338[/C][C]Range[/C][C]9.2[/C][C]Trim Var.[/C][C]2.17571020408163[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]0.38683908045977[/C][C]Range[/C][C]2.8[/C][C]Trim Var.[/C][C]0.254374057315234[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]1.15431077694236[/C][C]Range[/C][C]5[/C][C]Trim Var.[/C][C]0.70678431372549[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]3.80362337662338[/C][C]Range[/C][C]9.2[/C][C]Trim Var.[/C][C]2.17571020408163[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]13.2821346801347[/C][C]Range[/C][C]16.6[/C][C]Trim Var.[/C][C]7.72353741496599[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117044&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117044&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Variance Reduction Matrix
V(Y[t],d=0,D=0)2.87528531073446Range7.6Trim Var.1.78182040531097
V(Y[t],d=1,D=0)0.270555230859147Range2.6Trim Var.0.151436865021771
V(Y[t],d=2,D=0)0.38683908045977Range2.8Trim Var.0.254374057315234
V(Y[t],d=3,D=0)1.15431077694236Range5Trim Var.0.70678431372549
V(Y[t],d=0,D=1)0.270555230859147Range2.6Trim Var.0.151436865021771
V(Y[t],d=1,D=1)0.38683908045977Range2.8Trim Var.0.254374057315234
V(Y[t],d=2,D=1)1.15431077694236Range5Trim Var.0.70678431372549
V(Y[t],d=3,D=1)3.80362337662338Range9.2Trim Var.2.17571020408163
V(Y[t],d=0,D=2)0.38683908045977Range2.8Trim Var.0.254374057315234
V(Y[t],d=1,D=2)1.15431077694236Range5Trim Var.0.70678431372549
V(Y[t],d=2,D=2)3.80362337662338Range9.2Trim Var.2.17571020408163
V(Y[t],d=3,D=2)13.2821346801347Range16.6Trim Var.7.72353741496599


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 1 ;
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()