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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 12:49:31 +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/23/t148249378182v3atuej0907a6.htm/, Retrieved Tue, 07 May 2024 10:00:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302879, Retrieved Tue, 07 May 2024 10:00:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66

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] [N2797] [2016-12-23 11:49:31] [8e56909c70ba580a071e942d9a393c42] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3560
5360
5720
7360
7400
9120
9400
9680
9600
6920
4560
3840
4160
3760
3840
6120
7080
8840
9320
9600
8400
7040
4320
2520
1160
1680
5040
6360
7280
8880
9920
8800
8400
6760
6040
2400
2560
4680
4440
6400
8120
9080
10320
9960
9240
6000
4960
3320
3640
2880
5040
6000
7560
8960
8760
9040
7640
6720
4520
4640
2880
5640
5160
6920
7760
9680
9280
9320
8960
7280
4400
4600
3720
4680
5480
5920
7480
8720

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=302879&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=302879&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302879&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
V(Y[t],d=0,D=0)5588080Range9160Trim Var.4227890
V(Y[t],d=1,D=0)2196310Range7000Trim Var.1446000
V(Y[t],d=2,D=0)2764060Range7760Trim Var.1822400
V(Y[t],d=3,D=0)8324620Range14480Trim Var.5413040
V(Y[t],d=0,D=1)1175850Range6000Trim Var.609951
V(Y[t],d=1,D=1)1979440Range7120Trim Var.1059140
V(Y[t],d=2,D=1)5957730Range11760Trim Var.3206680
V(Y[t],d=3,D=1)20325900Range21360Trim Var.11428600
V(Y[t],d=0,D=2)3870590Range9880Trim Var.1909740
V(Y[t],d=1,D=2)7012390Range13280Trim Var.3465710
V(Y[t],d=2,D=2)21505300Range21920Trim Var.12641200
V(Y[t],d=3,D=2)74609600Range38360Trim Var.42436600

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 5588080 & Range & 9160 & Trim Var. & 4227890 \tabularnewline
V(Y[t],d=1,D=0) & 2196310 & Range & 7000 & Trim Var. & 1446000 \tabularnewline
V(Y[t],d=2,D=0) & 2764060 & Range & 7760 & Trim Var. & 1822400 \tabularnewline
V(Y[t],d=3,D=0) & 8324620 & Range & 14480 & Trim Var. & 5413040 \tabularnewline
V(Y[t],d=0,D=1) & 1175850 & Range & 6000 & Trim Var. & 609951 \tabularnewline
V(Y[t],d=1,D=1) & 1979440 & Range & 7120 & Trim Var. & 1059140 \tabularnewline
V(Y[t],d=2,D=1) & 5957730 & Range & 11760 & Trim Var. & 3206680 \tabularnewline
V(Y[t],d=3,D=1) & 20325900 & Range & 21360 & Trim Var. & 11428600 \tabularnewline
V(Y[t],d=0,D=2) & 3870590 & Range & 9880 & Trim Var. & 1909740 \tabularnewline
V(Y[t],d=1,D=2) & 7012390 & Range & 13280 & Trim Var. & 3465710 \tabularnewline
V(Y[t],d=2,D=2) & 21505300 & Range & 21920 & Trim Var. & 12641200 \tabularnewline
V(Y[t],d=3,D=2) & 74609600 & Range & 38360 & Trim Var. & 42436600 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302879&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]5588080[/C][C]Range[/C][C]9160[/C][C]Trim Var.[/C][C]4227890[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]2196310[/C][C]Range[/C][C]7000[/C][C]Trim Var.[/C][C]1446000[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]2764060[/C][C]Range[/C][C]7760[/C][C]Trim Var.[/C][C]1822400[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]8324620[/C][C]Range[/C][C]14480[/C][C]Trim Var.[/C][C]5413040[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]1175850[/C][C]Range[/C][C]6000[/C][C]Trim Var.[/C][C]609951[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1979440[/C][C]Range[/C][C]7120[/C][C]Trim Var.[/C][C]1059140[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]5957730[/C][C]Range[/C][C]11760[/C][C]Trim Var.[/C][C]3206680[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]20325900[/C][C]Range[/C][C]21360[/C][C]Trim Var.[/C][C]11428600[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]3870590[/C][C]Range[/C][C]9880[/C][C]Trim Var.[/C][C]1909740[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]7012390[/C][C]Range[/C][C]13280[/C][C]Trim Var.[/C][C]3465710[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]21505300[/C][C]Range[/C][C]21920[/C][C]Trim Var.[/C][C]12641200[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]74609600[/C][C]Range[/C][C]38360[/C][C]Trim Var.[/C][C]42436600[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302879&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302879&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)5588080Range9160Trim Var.4227890
V(Y[t],d=1,D=0)2196310Range7000Trim Var.1446000
V(Y[t],d=2,D=0)2764060Range7760Trim Var.1822400
V(Y[t],d=3,D=0)8324620Range14480Trim Var.5413040
V(Y[t],d=0,D=1)1175850Range6000Trim Var.609951
V(Y[t],d=1,D=1)1979440Range7120Trim Var.1059140
V(Y[t],d=2,D=1)5957730Range11760Trim Var.3206680
V(Y[t],d=3,D=1)20325900Range21360Trim Var.11428600
V(Y[t],d=0,D=2)3870590Range9880Trim Var.1909740
V(Y[t],d=1,D=2)7012390Range13280Trim Var.3465710
V(Y[t],d=2,D=2)21505300Range21920Trim Var.12641200
V(Y[t],d=3,D=2)74609600Range38360Trim Var.42436600


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = additive ; par2 = 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()