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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, 25 Jan 2017 09:45:49 +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/2017/Jan/25/t1485334017n75vltdveknoy26.htm/, Retrieved Tue, 14 May 2024 04:56:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=305773, Retrieved Tue, 14 May 2024 04:56:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact53

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] [] [2017-01-25 08:45:49] [c75f012def48c39be2b07a10feb7caf4] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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16
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NA
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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 time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=305773&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=305773&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=305773&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 time1 seconds
R ServerBig Analytics Cloud Computing Center






Variance Reduction Matrix
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.
V(Y[t],d=0,D=0)3.50676Range10Trim Var.1.60728
V(Y[t],d=1,D=0)8.18725Range14Trim Var.4.27678
V(Y[t],d=2,D=0)26.8291Range28Trim Var.12.8685
V(Y[t],d=3,D=0)95.0605Range54Trim Var.50.8379
V(Y[t],d=0,D=1)7.2884Range15Trim Var.3.32878
V(Y[t],d=1,D=1)15.0742Range18Trim Var.8.66217
V(Y[t],d=2,D=1)46.954Range34Trim Var.26.7641
V(Y[t],d=3,D=1)159.113Range64Trim Var.91.8537
V(Y[t],d=0,D=2)21.5222Range27Trim Var.9.87996
V(Y[t],d=1,D=2)43.5413Range30Trim Var.27.0416
V(Y[t],d=2,D=2)135.861Range53Trim Var.90.8227
V(Y[t],d=3,D=2)458.677Range92Trim Var.312.952

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
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. \tabularnewline
V(Y[t],d=0,D=0) & 3.50676 & Range & 10 & Trim Var. & 1.60728 \tabularnewline
V(Y[t],d=1,D=0) & 8.18725 & Range & 14 & Trim Var. & 4.27678 \tabularnewline
V(Y[t],d=2,D=0) & 26.8291 & Range & 28 & Trim Var. & 12.8685 \tabularnewline
V(Y[t],d=3,D=0) & 95.0605 & Range & 54 & Trim Var. & 50.8379 \tabularnewline
V(Y[t],d=0,D=1) & 7.2884 & Range & 15 & Trim Var. & 3.32878 \tabularnewline
V(Y[t],d=1,D=1) & 15.0742 & Range & 18 & Trim Var. & 8.66217 \tabularnewline
V(Y[t],d=2,D=1) & 46.954 & Range & 34 & Trim Var. & 26.7641 \tabularnewline
V(Y[t],d=3,D=1) & 159.113 & Range & 64 & Trim Var. & 91.8537 \tabularnewline
V(Y[t],d=0,D=2) & 21.5222 & Range & 27 & Trim Var. & 9.87996 \tabularnewline
V(Y[t],d=1,D=2) & 43.5413 & Range & 30 & Trim Var. & 27.0416 \tabularnewline
V(Y[t],d=2,D=2) & 135.861 & Range & 53 & Trim Var. & 90.8227 \tabularnewline
V(Y[t],d=3,D=2) & 458.677 & Range & 92 & Trim Var. & 312.952 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=305773&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]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.[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]3.50676[/C][C]Range[/C][C]10[/C][C]Trim Var.[/C][C]1.60728[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]8.18725[/C][C]Range[/C][C]14[/C][C]Trim Var.[/C][C]4.27678[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]26.8291[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]12.8685[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]95.0605[/C][C]Range[/C][C]54[/C][C]Trim Var.[/C][C]50.8379[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]7.2884[/C][C]Range[/C][C]15[/C][C]Trim Var.[/C][C]3.32878[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]15.0742[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]8.66217[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]46.954[/C][C]Range[/C][C]34[/C][C]Trim Var.[/C][C]26.7641[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]159.113[/C][C]Range[/C][C]64[/C][C]Trim Var.[/C][C]91.8537[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]21.5222[/C][C]Range[/C][C]27[/C][C]Trim Var.[/C][C]9.87996[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]43.5413[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]27.0416[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]135.861[/C][C]Range[/C][C]53[/C][C]Trim Var.[/C][C]90.8227[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]458.677[/C][C]Range[/C][C]92[/C][C]Trim Var.[/C][C]312.952[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=305773&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=305773&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
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.
V(Y[t],d=0,D=0)3.50676Range10Trim Var.1.60728
V(Y[t],d=1,D=0)8.18725Range14Trim Var.4.27678
V(Y[t],d=2,D=0)26.8291Range28Trim Var.12.8685
V(Y[t],d=3,D=0)95.0605Range54Trim Var.50.8379
V(Y[t],d=0,D=1)7.2884Range15Trim Var.3.32878
V(Y[t],d=1,D=1)15.0742Range18Trim Var.8.66217
V(Y[t],d=2,D=1)46.954Range34Trim Var.26.7641
V(Y[t],d=3,D=1)159.113Range64Trim Var.91.8537
V(Y[t],d=0,D=2)21.5222Range27Trim Var.9.87996
V(Y[t],d=1,D=2)43.5413Range30Trim Var.27.0416
V(Y[t],d=2,D=2)135.861Range53Trim Var.90.8227
V(Y[t],d=3,D=2)458.677Range92Trim Var.312.952


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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()