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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_variancereduction.wasp

Title produced by software

Variance Reduction Matrix

Date of computation

Mon, 20 Dec 2010 11:55:41 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/20/t1292846026xqnickeoqlyhkp0.htm/, Retrieved Sat, 04 May 2024 05:17:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112857, Retrieved Sat, 04 May 2024 05:17:41 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

162

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [Unemployment] [2010-11-30 13:37:23] [b98453cac15ba1066b407e146608df68]
- RMPD      [Variance Reduction Matrix] [Consumentenvertro...] [2010-12-20 11:55:41] [4c7d8c32b2e34fcaa7f14928b91d45ae] [Current]

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Dataseries X:

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Histogram

Boxplots

9
11
13
12
13
15
13
16
10
14
14
45
13
8
7
3
3
4
4
0
-4
-14
-18
-8
-1
1
2
0
1
0
-1
-3
-3
-3
-4
-8
-9
-13
-18
-11
-9
-10
-13
-11
-5
-15
-6
-6
-3
-1
-3
-4
-6
0
-4
-2
-2
-6
-7
-6
-6
-3
-2
-5
-11
-11
-11
-10
-14
-8
-9
-5
-1
-2
-5
-4
-6
-2
-2
-2
-2
2
1
-8
-1
1
-1
2
2
1
-1
-2
-2
-1
-8
-4
-6
-3
-3
-7
-9
-11
-13
-11
-9
-17
-22
-25
-20
-24
-24
-22
-19
-18
-17
-11
-11
-12
-10
-15
-15
-15
-13
-8
-13
-9
-7
-4
-4
-2
0

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112857&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112857&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112857&T=0

As an alternative you can also use a 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 Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Variance Reduction Matrix
V(Y[t],d=0,D=0)	92.7934233705226	Range	70	Trim Var.	40.6315789473684
V(Y[t],d=1,D=0)	28.1114490161002	Range	63	Trim Var.	6.32175032175032
V(Y[t],d=2,D=0)	72.375	Range	94	Trim Var.	15.2892408011178
V(Y[t],d=3,D=0)	234.314960629921	Range	184	Trim Var.	43.7527939949958
V(Y[t],d=0,D=1)	111.553197550207	Range	68	Trim Var.	61.630929289367
V(Y[t],d=1,D=1)	43.1426915833695	Range	60	Trim Var.	16.9039532794250
V(Y[t],d=2,D=1)	99.3153551429414	Range	92	Trim Var.	33.6354464115743
V(Y[t],d=3,D=1)	315.326761619190	Range	169	Trim Var.	122.296396564600
V(Y[t],d=0,D=2)	245.864926820667	Range	78	Trim Var.	150.858902575588
V(Y[t],d=1,D=2)	97.3865229110512	Range	73	Trim Var.	42.0750400366049
V(Y[t],d=2,D=2)	200.7	Range	90	Trim Var.	83.3340345956054
V(Y[t],d=3,D=2)	622.90926064227	Range	158	Trim Var.	268.22491638796

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 92.7934233705226 & Range & 70 & Trim Var. & 40.6315789473684 \tabularnewline
V(Y[t],d=1,D=0) & 28.1114490161002 & Range & 63 & Trim Var. & 6.32175032175032 \tabularnewline
V(Y[t],d=2,D=0) & 72.375 & Range & 94 & Trim Var. & 15.2892408011178 \tabularnewline
V(Y[t],d=3,D=0) & 234.314960629921 & Range & 184 & Trim Var. & 43.7527939949958 \tabularnewline
V(Y[t],d=0,D=1) & 111.553197550207 & Range & 68 & Trim Var. & 61.630929289367 \tabularnewline
V(Y[t],d=1,D=1) & 43.1426915833695 & Range & 60 & Trim Var. & 16.9039532794250 \tabularnewline
V(Y[t],d=2,D=1) & 99.3153551429414 & Range & 92 & Trim Var. & 33.6354464115743 \tabularnewline
V(Y[t],d=3,D=1) & 315.326761619190 & Range & 169 & Trim Var. & 122.296396564600 \tabularnewline
V(Y[t],d=0,D=2) & 245.864926820667 & Range & 78 & Trim Var. & 150.858902575588 \tabularnewline
V(Y[t],d=1,D=2) & 97.3865229110512 & Range & 73 & Trim Var. & 42.0750400366049 \tabularnewline
V(Y[t],d=2,D=2) & 200.7 & Range & 90 & Trim Var. & 83.3340345956054 \tabularnewline
V(Y[t],d=3,D=2) & 622.90926064227 & Range & 158 & Trim Var. & 268.22491638796 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112857&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]92.7934233705226[/C][C]Range[/C][C]70[/C][C]Trim Var.[/C][C]40.6315789473684[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]28.1114490161002[/C][C]Range[/C][C]63[/C][C]Trim Var.[/C][C]6.32175032175032[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]72.375[/C][C]Range[/C][C]94[/C][C]Trim Var.[/C][C]15.2892408011178[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]234.314960629921[/C][C]Range[/C][C]184[/C][C]Trim Var.[/C][C]43.7527939949958[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]111.553197550207[/C][C]Range[/C][C]68[/C][C]Trim Var.[/C][C]61.630929289367[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]43.1426915833695[/C][C]Range[/C][C]60[/C][C]Trim Var.[/C][C]16.9039532794250[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]99.3153551429414[/C][C]Range[/C][C]92[/C][C]Trim Var.[/C][C]33.6354464115743[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]315.326761619190[/C][C]Range[/C][C]169[/C][C]Trim Var.[/C][C]122.296396564600[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]245.864926820667[/C][C]Range[/C][C]78[/C][C]Trim Var.[/C][C]150.858902575588[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]97.3865229110512[/C][C]Range[/C][C]73[/C][C]Trim Var.[/C][C]42.0750400366049[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]200.7[/C][C]Range[/C][C]90[/C][C]Trim Var.[/C][C]83.3340345956054[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]622.90926064227[/C][C]Range[/C][C]158[/C][C]Trim Var.[/C][C]268.22491638796[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112857&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112857&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Variance Reduction Matrix
V(Y[t],d=0,D=0)	92.7934233705226	Range	70	Trim Var.	40.6315789473684
V(Y[t],d=1,D=0)	28.1114490161002	Range	63	Trim Var.	6.32175032175032
V(Y[t],d=2,D=0)	72.375	Range	94	Trim Var.	15.2892408011178
V(Y[t],d=3,D=0)	234.314960629921	Range	184	Trim Var.	43.7527939949958
V(Y[t],d=0,D=1)	111.553197550207	Range	68	Trim Var.	61.630929289367
V(Y[t],d=1,D=1)	43.1426915833695	Range	60	Trim Var.	16.9039532794250
V(Y[t],d=2,D=1)	99.3153551429414	Range	92	Trim Var.	33.6354464115743
V(Y[t],d=3,D=1)	315.326761619190	Range	169	Trim Var.	122.296396564600
V(Y[t],d=0,D=2)	245.864926820667	Range	78	Trim Var.	150.858902575588
V(Y[t],d=1,D=2)	97.3865229110512	Range	73	Trim Var.	42.0750400366049
V(Y[t],d=2,D=2)	200.7	Range	90	Trim Var.	83.3340345956054
V(Y[t],d=3,D=2)	622.90926064227	Range	158	Trim Var.	268.22491638796

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 12 ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
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)
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,var(myx))
a<-table.element(a,'Range',header=TRUE)
a<-table.element(a,max(myx)-min(myx))
a<-table.element(a,'Trim Var.',header=TRUE)
smyx <- sort(myx)
sn <- length(smyx)
a<-table.element(a,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()

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Input Parameters & R Code