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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 computationThu, 22 Dec 2016 19:14:31 +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/Dec/22/t14824304974pyn88b8bnkpalp.htm/, Retrieved Sun, 28 Apr 2024 20:32:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302608, Retrieved Sun, 28 Apr 2024 20:32:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact63

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] [VRM 3] [2016-12-22 18:14:31] [94c1b173d9287822f5e2740a4a602bdd] [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=302608&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=302608&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302608&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)2.78562Range9Trim Var.0.978686
V(Y[t],d=1,D=0)3.66061Range10Trim Var.1.70145
V(Y[t],d=2,D=0)10.8125Range20Trim Var.3.65167
V(Y[t],d=3,D=0)36.0672Range39Trim Var.13.3607
V(Y[t],d=0,D=1)6.66128Range12Trim Var.3.67687
V(Y[t],d=1,D=1)8.74214Range13Trim Var.4.35362
V(Y[t],d=2,D=1)26.1698Range23Trim Var.14.2
V(Y[t],d=3,D=1)89.5064Range41Trim Var.50.4374
V(Y[t],d=0,D=2)20.1107Range21Trim Var.10.5968
V(Y[t],d=1,D=2)26.9663Range21Trim Var.11.8826
V(Y[t],d=2,D=2)80.9256Range40Trim Var.43.4908
V(Y[t],d=3,D=2)284.487Range78Trim Var.174.98

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 2.78562 & Range & 9 & Trim Var. & 0.978686 \tabularnewline
V(Y[t],d=1,D=0) & 3.66061 & Range & 10 & Trim Var. & 1.70145 \tabularnewline
V(Y[t],d=2,D=0) & 10.8125 & Range & 20 & Trim Var. & 3.65167 \tabularnewline
V(Y[t],d=3,D=0) & 36.0672 & Range & 39 & Trim Var. & 13.3607 \tabularnewline
V(Y[t],d=0,D=1) & 6.66128 & Range & 12 & Trim Var. & 3.67687 \tabularnewline
V(Y[t],d=1,D=1) & 8.74214 & Range & 13 & Trim Var. & 4.35362 \tabularnewline
V(Y[t],d=2,D=1) & 26.1698 & Range & 23 & Trim Var. & 14.2 \tabularnewline
V(Y[t],d=3,D=1) & 89.5064 & Range & 41 & Trim Var. & 50.4374 \tabularnewline
V(Y[t],d=0,D=2) & 20.1107 & Range & 21 & Trim Var. & 10.5968 \tabularnewline
V(Y[t],d=1,D=2) & 26.9663 & Range & 21 & Trim Var. & 11.8826 \tabularnewline
V(Y[t],d=2,D=2) & 80.9256 & Range & 40 & Trim Var. & 43.4908 \tabularnewline
V(Y[t],d=3,D=2) & 284.487 & Range & 78 & Trim Var. & 174.98 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302608&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]2.78562[/C][C]Range[/C][C]9[/C][C]Trim Var.[/C][C]0.978686[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]3.66061[/C][C]Range[/C][C]10[/C][C]Trim Var.[/C][C]1.70145[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]10.8125[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]3.65167[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]36.0672[/C][C]Range[/C][C]39[/C][C]Trim Var.[/C][C]13.3607[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]6.66128[/C][C]Range[/C][C]12[/C][C]Trim Var.[/C][C]3.67687[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]8.74214[/C][C]Range[/C][C]13[/C][C]Trim Var.[/C][C]4.35362[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]26.1698[/C][C]Range[/C][C]23[/C][C]Trim Var.[/C][C]14.2[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]89.5064[/C][C]Range[/C][C]41[/C][C]Trim Var.[/C][C]50.4374[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]20.1107[/C][C]Range[/C][C]21[/C][C]Trim Var.[/C][C]10.5968[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]26.9663[/C][C]Range[/C][C]21[/C][C]Trim Var.[/C][C]11.8826[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]80.9256[/C][C]Range[/C][C]40[/C][C]Trim Var.[/C][C]43.4908[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]284.487[/C][C]Range[/C][C]78[/C][C]Trim Var.[/C][C]174.98[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302608&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302608&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)2.78562Range9Trim Var.0.978686
V(Y[t],d=1,D=0)3.66061Range10Trim Var.1.70145
V(Y[t],d=2,D=0)10.8125Range20Trim Var.3.65167
V(Y[t],d=3,D=0)36.0672Range39Trim Var.13.3607
V(Y[t],d=0,D=1)6.66128Range12Trim Var.3.67687
V(Y[t],d=1,D=1)8.74214Range13Trim Var.4.35362
V(Y[t],d=2,D=1)26.1698Range23Trim Var.14.2
V(Y[t],d=3,D=1)89.5064Range41Trim Var.50.4374
V(Y[t],d=0,D=2)20.1107Range21Trim Var.10.5968
V(Y[t],d=1,D=2)26.9663Range21Trim Var.11.8826
V(Y[t],d=2,D=2)80.9256Range40Trim Var.43.4908
V(Y[t],d=3,D=2)284.487Range78Trim Var.174.98


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par2 = grey ; par3 = FALSE ; par4 = Unknown ;
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()