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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 computationSun, 26 Dec 2010 14:00:28 +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/26/t12933720941vo15esi3cgiz74.htm/, Retrieved Mon, 06 May 2024 12:32:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115611, Retrieved Mon, 06 May 2024 12:32:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact140

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Variance Reduction Matrix] [] [2010-12-17 09:57:58] [d39e5c40c631ed6c22677d2e41dbfc7d]
-   PD    [Variance Reduction Matrix] [paper dow jones d...] [2010-12-26 14:00:28] [6df2229e3f2091de42c4a9cf9a617420] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10554,27
10532,54
10324,31
10695,25
10827,81
10872,48
10971,19
11145,65
11234,68
11333,88
10997,97
11036,89
11257,35
11533,59
11963,12
12185,15
12377,62
12512,89
12631,48
12268,53
12754,8
13407,75
13480,21
13673,28
13239,71
13557,69
13901,28
13200,58
13406,97
12538,12
12419,57
12193,88
12656,63
12812,48
12056,67
11322,38
11530,75
11114,08
9181,73
8614,55
8595,56
8396,2
7690,5
7235,47
7992,12
8398,37
8593
8679,75
9374,63
9634,97
9857,34
10238,83
10433,44
10471,24
10214,51
10677,52
11052,15
10500,19
10159,27
10222,24
10350,4

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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=115611&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=115611&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115611&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132






Variance Reduction Matrix
V(Y[t],d=0,D=0)2696364.92190290Range6665.81Trim Var.1775346.78963592
V(Y[t],d=1,D=0)206693.472627429Range2689Trim Var.106129.956215094
V(Y[t],d=2,D=0)315333.69806353Range2880.85Trim Var.183153.277441001
V(Y[t],d=3,D=0)844680.505012008Range4863.18Trim Var.467617.557393175
V(Y[t],d=0,D=1)6484010.03225Range8400.46Trim Var.5091627.56735161
V(Y[t],d=1,D=1)499293.117162722Range4430.66Trim Var.241729.140053949
V(Y[t],d=2,D=1)657294.68499223Range3950.75Trim Var.343275.374456097
V(Y[t],d=3,D=1)1799476.46214884Range6896.64000000001Trim Var.910485.004014808
V(Y[t],d=0,D=2)20416201.3273029Range15058.17Trim Var.16437568.7622104
V(Y[t],d=1,D=2)1600426.21108659Range6620.66Trim Var.848288.675753932
V(Y[t],d=2,D=2)2181387.14391261Range6861.76Trim Var.1236843.00712581
V(Y[t],d=3,D=2)6008929.05898146Range11294.37Trim Var.3431943.83733896

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 2696364.92190290 & Range & 6665.81 & Trim Var. & 1775346.78963592 \tabularnewline
V(Y[t],d=1,D=0) & 206693.472627429 & Range & 2689 & Trim Var. & 106129.956215094 \tabularnewline
V(Y[t],d=2,D=0) & 315333.69806353 & Range & 2880.85 & Trim Var. & 183153.277441001 \tabularnewline
V(Y[t],d=3,D=0) & 844680.505012008 & Range & 4863.18 & Trim Var. & 467617.557393175 \tabularnewline
V(Y[t],d=0,D=1) & 6484010.03225 & Range & 8400.46 & Trim Var. & 5091627.56735161 \tabularnewline
V(Y[t],d=1,D=1) & 499293.117162722 & Range & 4430.66 & Trim Var. & 241729.140053949 \tabularnewline
V(Y[t],d=2,D=1) & 657294.68499223 & Range & 3950.75 & Trim Var. & 343275.374456097 \tabularnewline
V(Y[t],d=3,D=1) & 1799476.46214884 & Range & 6896.64000000001 & Trim Var. & 910485.004014808 \tabularnewline
V(Y[t],d=0,D=2) & 20416201.3273029 & Range & 15058.17 & Trim Var. & 16437568.7622104 \tabularnewline
V(Y[t],d=1,D=2) & 1600426.21108659 & Range & 6620.66 & Trim Var. & 848288.675753932 \tabularnewline
V(Y[t],d=2,D=2) & 2181387.14391261 & Range & 6861.76 & Trim Var. & 1236843.00712581 \tabularnewline
V(Y[t],d=3,D=2) & 6008929.05898146 & Range & 11294.37 & Trim Var. & 3431943.83733896 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115611&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]2696364.92190290[/C][C]Range[/C][C]6665.81[/C][C]Trim Var.[/C][C]1775346.78963592[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]206693.472627429[/C][C]Range[/C][C]2689[/C][C]Trim Var.[/C][C]106129.956215094[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]315333.69806353[/C][C]Range[/C][C]2880.85[/C][C]Trim Var.[/C][C]183153.277441001[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]844680.505012008[/C][C]Range[/C][C]4863.18[/C][C]Trim Var.[/C][C]467617.557393175[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]6484010.03225[/C][C]Range[/C][C]8400.46[/C][C]Trim Var.[/C][C]5091627.56735161[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]499293.117162722[/C][C]Range[/C][C]4430.66[/C][C]Trim Var.[/C][C]241729.140053949[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]657294.68499223[/C][C]Range[/C][C]3950.75[/C][C]Trim Var.[/C][C]343275.374456097[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]1799476.46214884[/C][C]Range[/C][C]6896.64000000001[/C][C]Trim Var.[/C][C]910485.004014808[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]20416201.3273029[/C][C]Range[/C][C]15058.17[/C][C]Trim Var.[/C][C]16437568.7622104[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]1600426.21108659[/C][C]Range[/C][C]6620.66[/C][C]Trim Var.[/C][C]848288.675753932[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]2181387.14391261[/C][C]Range[/C][C]6861.76[/C][C]Trim Var.[/C][C]1236843.00712581[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]6008929.05898146[/C][C]Range[/C][C]11294.37[/C][C]Trim Var.[/C][C]3431943.83733896[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115611&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115611&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)2696364.92190290Range6665.81Trim Var.1775346.78963592
V(Y[t],d=1,D=0)206693.472627429Range2689Trim Var.106129.956215094
V(Y[t],d=2,D=0)315333.69806353Range2880.85Trim Var.183153.277441001
V(Y[t],d=3,D=0)844680.505012008Range4863.18Trim Var.467617.557393175
V(Y[t],d=0,D=1)6484010.03225Range8400.46Trim Var.5091627.56735161
V(Y[t],d=1,D=1)499293.117162722Range4430.66Trim Var.241729.140053949
V(Y[t],d=2,D=1)657294.68499223Range3950.75Trim Var.343275.374456097
V(Y[t],d=3,D=1)1799476.46214884Range6896.64000000001Trim Var.910485.004014808
V(Y[t],d=0,D=2)20416201.3273029Range15058.17Trim Var.16437568.7622104
V(Y[t],d=1,D=2)1600426.21108659Range6620.66Trim Var.848288.675753932
V(Y[t],d=2,D=2)2181387.14391261Range6861.76Trim Var.1236843.00712581
V(Y[t],d=3,D=2)6008929.05898146Range11294.37Trim Var.3431943.83733896


Figures (Output of Computation)

Input Parameters & R Code

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()