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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 computationFri, 23 Dec 2016 10:50:38 +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/23/t1482486878wipcennqc7gj8gc.htm/, Retrieved Wed, 08 May 2024 00:38:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302827, Retrieved Wed, 08 May 2024 00:38:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact73

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] [variance reductio...] [2016-12-23 09:50:38] [bd7223969ac5b08f41438741a34686d6] [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=302827&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=302827&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302827&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)2.22271Range7Trim Var.0.840301
V(Y[t],d=1,D=0)4.95238Range14Trim Var.1.89402
V(Y[t],d=2,D=0)15.4689Range23Trim Var.6.46227
V(Y[t],d=3,D=0)52.9805Range45Trim Var.24.1638
V(Y[t],d=0,D=1)4.36954Range12Trim Var.1.3375
V(Y[t],d=1,D=1)9.05193Range19Trim Var.3.58988
V(Y[t],d=2,D=1)27.8478Range33Trim Var.11.452
V(Y[t],d=3,D=1)95.2187Range64Trim Var.39.0318
V(Y[t],d=0,D=2)13.6109Range19Trim Var.5.77465
V(Y[t],d=1,D=2)28.8517Range31Trim Var.9.94245
V(Y[t],d=2,D=2)90.2611Range55Trim Var.32.1759
V(Y[t],d=3,D=2)310.711Range106Trim Var.128.365

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 2.22271 & Range & 7 & Trim Var. & 0.840301 \tabularnewline
V(Y[t],d=1,D=0) & 4.95238 & Range & 14 & Trim Var. & 1.89402 \tabularnewline
V(Y[t],d=2,D=0) & 15.4689 & Range & 23 & Trim Var. & 6.46227 \tabularnewline
V(Y[t],d=3,D=0) & 52.9805 & Range & 45 & Trim Var. & 24.1638 \tabularnewline
V(Y[t],d=0,D=1) & 4.36954 & Range & 12 & Trim Var. & 1.3375 \tabularnewline
V(Y[t],d=1,D=1) & 9.05193 & Range & 19 & Trim Var. & 3.58988 \tabularnewline
V(Y[t],d=2,D=1) & 27.8478 & Range & 33 & Trim Var. & 11.452 \tabularnewline
V(Y[t],d=3,D=1) & 95.2187 & Range & 64 & Trim Var. & 39.0318 \tabularnewline
V(Y[t],d=0,D=2) & 13.6109 & Range & 19 & Trim Var. & 5.77465 \tabularnewline
V(Y[t],d=1,D=2) & 28.8517 & Range & 31 & Trim Var. & 9.94245 \tabularnewline
V(Y[t],d=2,D=2) & 90.2611 & Range & 55 & Trim Var. & 32.1759 \tabularnewline
V(Y[t],d=3,D=2) & 310.711 & Range & 106 & Trim Var. & 128.365 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302827&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]2.22271[/C][C]Range[/C][C]7[/C][C]Trim Var.[/C][C]0.840301[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]4.95238[/C][C]Range[/C][C]14[/C][C]Trim Var.[/C][C]1.89402[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]15.4689[/C][C]Range[/C][C]23[/C][C]Trim Var.[/C][C]6.46227[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]52.9805[/C][C]Range[/C][C]45[/C][C]Trim Var.[/C][C]24.1638[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]4.36954[/C][C]Range[/C][C]12[/C][C]Trim Var.[/C][C]1.3375[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]9.05193[/C][C]Range[/C][C]19[/C][C]Trim Var.[/C][C]3.58988[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]27.8478[/C][C]Range[/C][C]33[/C][C]Trim Var.[/C][C]11.452[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]95.2187[/C][C]Range[/C][C]64[/C][C]Trim Var.[/C][C]39.0318[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]13.6109[/C][C]Range[/C][C]19[/C][C]Trim Var.[/C][C]5.77465[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]28.8517[/C][C]Range[/C][C]31[/C][C]Trim Var.[/C][C]9.94245[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]90.2611[/C][C]Range[/C][C]55[/C][C]Trim Var.[/C][C]32.1759[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]310.711[/C][C]Range[/C][C]106[/C][C]Trim Var.[/C][C]128.365[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302827&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302827&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)2.22271Range7Trim Var.0.840301
V(Y[t],d=1,D=0)4.95238Range14Trim Var.1.89402
V(Y[t],d=2,D=0)15.4689Range23Trim Var.6.46227
V(Y[t],d=3,D=0)52.9805Range45Trim Var.24.1638
V(Y[t],d=0,D=1)4.36954Range12Trim Var.1.3375
V(Y[t],d=1,D=1)9.05193Range19Trim Var.3.58988
V(Y[t],d=2,D=1)27.8478Range33Trim Var.11.452
V(Y[t],d=3,D=1)95.2187Range64Trim Var.39.0318
V(Y[t],d=0,D=2)13.6109Range19Trim Var.5.77465
V(Y[t],d=1,D=2)28.8517Range31Trim Var.9.94245
V(Y[t],d=2,D=2)90.2611Range55Trim Var.32.1759
V(Y[t],d=3,D=2)310.711Range106Trim Var.128.365


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()