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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 computationSat, 19 Nov 2016 15:50:51 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Nov/19/t1479567089bsezqb1wsgesk0c.htm/, Retrieved Sat, 04 May 2024 09:25:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296848, Retrieved Sat, 04 May 2024 09:25:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact92

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] [] [2016-11-19 14:50:51] [219800a2f11ddd28e3280d87dbde8c8d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time0 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296848&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]0 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=296848&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296848&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R ServerBig Analytics Cloud Computing Center






Variance Reduction Matrix
V(Y[t],d=0,D=0)1.81621Range7Trim Var.0.863255
V(Y[t],d=1,D=0)3.67356Range9Trim Var.1.37857
V(Y[t],d=2,D=0)10.7638Range16Trim Var.6.24731
V(Y[t],d=3,D=0)35.769Range28Trim Var.21.6779
V(Y[t],d=0,D=1)3.90393Range11Trim Var.2.01709
V(Y[t],d=1,D=1)8.05277Range14Trim Var.3.75055
V(Y[t],d=2,D=1)23.5274Range24Trim Var.14.2144
V(Y[t],d=3,D=1)78.1415Range40Trim Var.51.883
V(Y[t],d=0,D=2)12.0338Range19Trim Var.5.7899
V(Y[t],d=1,D=2)24.3327Range26Trim Var.14.638
V(Y[t],d=2,D=2)70.1425Range37Trim Var.45.5421
V(Y[t],d=3,D=2)231.711Range68Trim Var.147.124

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 1.81621 & Range & 7 & Trim Var. & 0.863255 \tabularnewline
V(Y[t],d=1,D=0) & 3.67356 & Range & 9 & Trim Var. & 1.37857 \tabularnewline
V(Y[t],d=2,D=0) & 10.7638 & Range & 16 & Trim Var. & 6.24731 \tabularnewline
V(Y[t],d=3,D=0) & 35.769 & Range & 28 & Trim Var. & 21.6779 \tabularnewline
V(Y[t],d=0,D=1) & 3.90393 & Range & 11 & Trim Var. & 2.01709 \tabularnewline
V(Y[t],d=1,D=1) & 8.05277 & Range & 14 & Trim Var. & 3.75055 \tabularnewline
V(Y[t],d=2,D=1) & 23.5274 & Range & 24 & Trim Var. & 14.2144 \tabularnewline
V(Y[t],d=3,D=1) & 78.1415 & Range & 40 & Trim Var. & 51.883 \tabularnewline
V(Y[t],d=0,D=2) & 12.0338 & Range & 19 & Trim Var. & 5.7899 \tabularnewline
V(Y[t],d=1,D=2) & 24.3327 & Range & 26 & Trim Var. & 14.638 \tabularnewline
V(Y[t],d=2,D=2) & 70.1425 & Range & 37 & Trim Var. & 45.5421 \tabularnewline
V(Y[t],d=3,D=2) & 231.711 & Range & 68 & Trim Var. & 147.124 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296848&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]1.81621[/C][C]Range[/C][C]7[/C][C]Trim Var.[/C][C]0.863255[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]3.67356[/C][C]Range[/C][C]9[/C][C]Trim Var.[/C][C]1.37857[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]10.7638[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.24731[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]35.769[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]21.6779[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]3.90393[/C][C]Range[/C][C]11[/C][C]Trim Var.[/C][C]2.01709[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]8.05277[/C][C]Range[/C][C]14[/C][C]Trim Var.[/C][C]3.75055[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]23.5274[/C][C]Range[/C][C]24[/C][C]Trim Var.[/C][C]14.2144[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]78.1415[/C][C]Range[/C][C]40[/C][C]Trim Var.[/C][C]51.883[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]12.0338[/C][C]Range[/C][C]19[/C][C]Trim Var.[/C][C]5.7899[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]24.3327[/C][C]Range[/C][C]26[/C][C]Trim Var.[/C][C]14.638[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]70.1425[/C][C]Range[/C][C]37[/C][C]Trim Var.[/C][C]45.5421[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]231.711[/C][C]Range[/C][C]68[/C][C]Trim Var.[/C][C]147.124[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296848&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296848&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)1.81621Range7Trim Var.0.863255
V(Y[t],d=1,D=0)3.67356Range9Trim Var.1.37857
V(Y[t],d=2,D=0)10.7638Range16Trim Var.6.24731
V(Y[t],d=3,D=0)35.769Range28Trim Var.21.6779
V(Y[t],d=0,D=1)3.90393Range11Trim Var.2.01709
V(Y[t],d=1,D=1)8.05277Range14Trim Var.3.75055
V(Y[t],d=2,D=1)23.5274Range24Trim Var.14.2144
V(Y[t],d=3,D=1)78.1415Range40Trim Var.51.883
V(Y[t],d=0,D=2)12.0338Range19Trim Var.5.7899
V(Y[t],d=1,D=2)24.3327Range26Trim Var.14.638
V(Y[t],d=2,D=2)70.1425Range37Trim Var.45.5421
V(Y[t],d=3,D=2)231.711Range68Trim Var.147.124


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.orig <- length(x)
x <- na.omit(x)
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)
if(n.orig!=n) {
a<-table.row.start(a)
a<-table.element(a,'Warning: NAs were removed from the time series! The results shown below will only be correct if the NAs are all located at the start and/or end of the time series.',6,F)
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,signif(var(myx), digits=6))
a<-table.element(a,'Range',header=TRUE)
a<-table.element(a,signif(max(myx)-min(myx), digits=6))
a<-table.element(a,'Trim Var.',header=TRUE)
smyx <- sort(myx)
sn <- length(smyx)
a<-table.element(a,signif(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()