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*The author of this computation has been verified*

R Software Module

rwasp_variancereduction.wasp

Title produced by software

Variance Reduction Matrix

Date of computation

Thu, 15 Dec 2011 10:59:00 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/15/t1323964756ilie6jx7gw7z5qt.htm/, Retrieved Thu, 09 May 2024 00:40:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=155527, Retrieved Thu, 09 May 2024 00:40:28 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

109

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

-     [Kendall tau Correlation Matrix] [] [2010-12-05 17:44:33] [b98453cac15ba1066b407e146608df68]
- RMPD  [Kendall tau Correlation Matrix] [WS 10 - Pearson c...] [2010-12-10 16:13:49] [033eb2749a430605d9b2be7c4aac4a0c]
-         [Kendall tau Correlation Matrix] [] [2010-12-13 18:15:16] [d7b28a0391ab3b2ddc9f9fba95a43f33]
- RMPD      [Variance Reduction Matrix] [] [2010-12-24 12:02:39] [b07cd1964830aab808142229b1166ece]
-   PD          [Variance Reduction Matrix] [VRM paper Ba 2] [2011-12-15 15:59:00] [0e2c18186cab982e7ba7b89fbe242e59] [Current]

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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	'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=155527&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=155527&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155527&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Variance Reduction Matrix
V(Y[t],d=0,D=0)	135821.959483265	Range	1809	Trim Var.	83575.830386089
V(Y[t],d=1,D=0)	235238.278831246	Range	2151	Trim Var.	157835.636581709
V(Y[t],d=2,D=0)	758265.020469961	Range	3709	Trim Var.	544397.347368421
V(Y[t],d=3,D=0)	2636743.79964321	Range	6770	Trim Var.	1918374.44123583
V(Y[t],d=0,D=1)	100189.406637231	Range	1744	Trim Var.	52551.0848174925
V(Y[t],d=1,D=1)	158172.334130088	Range	2351	Trim Var.	93583.6736747529
V(Y[t],d=2,D=1)	525094.98467433	Range	4195	Trim Var.	293371.950549451
V(Y[t],d=3,D=1)	1792450.20029985	Range	8073	Trim Var.	987247.611277072
V(Y[t],d=0,D=2)	205026.090107565	Range	2585	Trim Var.	113237.427099664
V(Y[t],d=1,D=2)	367725.052021563	Range	3064	Trim Var.	210326.572463768
V(Y[t],d=2,D=2)	1222109.75952381	Range	5541	Trim Var.	747540.077372604
V(Y[t],d=3,D=2)	4219423.53360717	Range	9405	Trim Var.	2547181.74617774

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 135821.959483265 & Range & 1809 & Trim Var. & 83575.830386089 \tabularnewline
V(Y[t],d=1,D=0) & 235238.278831246 & Range & 2151 & Trim Var. & 157835.636581709 \tabularnewline
V(Y[t],d=2,D=0) & 758265.020469961 & Range & 3709 & Trim Var. & 544397.347368421 \tabularnewline
V(Y[t],d=3,D=0) & 2636743.79964321 & Range & 6770 & Trim Var. & 1918374.44123583 \tabularnewline
V(Y[t],d=0,D=1) & 100189.406637231 & Range & 1744 & Trim Var. & 52551.0848174925 \tabularnewline
V(Y[t],d=1,D=1) & 158172.334130088 & Range & 2351 & Trim Var. & 93583.6736747529 \tabularnewline
V(Y[t],d=2,D=1) & 525094.98467433 & Range & 4195 & Trim Var. & 293371.950549451 \tabularnewline
V(Y[t],d=3,D=1) & 1792450.20029985 & Range & 8073 & Trim Var. & 987247.611277072 \tabularnewline
V(Y[t],d=0,D=2) & 205026.090107565 & Range & 2585 & Trim Var. & 113237.427099664 \tabularnewline
V(Y[t],d=1,D=2) & 367725.052021563 & Range & 3064 & Trim Var. & 210326.572463768 \tabularnewline
V(Y[t],d=2,D=2) & 1222109.75952381 & Range & 5541 & Trim Var. & 747540.077372604 \tabularnewline
V(Y[t],d=3,D=2) & 4219423.53360717 & Range & 9405 & Trim Var. & 2547181.74617774 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=155527&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]135821.959483265[/C][C]Range[/C][C]1809[/C][C]Trim Var.[/C][C]83575.830386089[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]235238.278831246[/C][C]Range[/C][C]2151[/C][C]Trim Var.[/C][C]157835.636581709[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]758265.020469961[/C][C]Range[/C][C]3709[/C][C]Trim Var.[/C][C]544397.347368421[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]2636743.79964321[/C][C]Range[/C][C]6770[/C][C]Trim Var.[/C][C]1918374.44123583[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]100189.406637231[/C][C]Range[/C][C]1744[/C][C]Trim Var.[/C][C]52551.0848174925[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]158172.334130088[/C][C]Range[/C][C]2351[/C][C]Trim Var.[/C][C]93583.6736747529[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]525094.98467433[/C][C]Range[/C][C]4195[/C][C]Trim Var.[/C][C]293371.950549451[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]1792450.20029985[/C][C]Range[/C][C]8073[/C][C]Trim Var.[/C][C]987247.611277072[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]205026.090107565[/C][C]Range[/C][C]2585[/C][C]Trim Var.[/C][C]113237.427099664[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]367725.052021563[/C][C]Range[/C][C]3064[/C][C]Trim Var.[/C][C]210326.572463768[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]1222109.75952381[/C][C]Range[/C][C]5541[/C][C]Trim Var.[/C][C]747540.077372604[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]4219423.53360717[/C][C]Range[/C][C]9405[/C][C]Trim Var.[/C][C]2547181.74617774[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=155527&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155527&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)	135821.959483265	Range	1809	Trim Var.	83575.830386089
V(Y[t],d=1,D=0)	235238.278831246	Range	2151	Trim Var.	157835.636581709
V(Y[t],d=2,D=0)	758265.020469961	Range	3709	Trim Var.	544397.347368421
V(Y[t],d=3,D=0)	2636743.79964321	Range	6770	Trim Var.	1918374.44123583
V(Y[t],d=0,D=1)	100189.406637231	Range	1744	Trim Var.	52551.0848174925
V(Y[t],d=1,D=1)	158172.334130088	Range	2351	Trim Var.	93583.6736747529
V(Y[t],d=2,D=1)	525094.98467433	Range	4195	Trim Var.	293371.950549451
V(Y[t],d=3,D=1)	1792450.20029985	Range	8073	Trim Var.	987247.611277072
V(Y[t],d=0,D=2)	205026.090107565	Range	2585	Trim Var.	113237.427099664
V(Y[t],d=1,D=2)	367725.052021563	Range	3064	Trim Var.	210326.572463768
V(Y[t],d=2,D=2)	1222109.75952381	Range	5541	Trim Var.	747540.077372604
V(Y[t],d=3,D=2)	4219423.53360717	Range	9405	Trim Var.	2547181.74617774

Figure 1

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Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 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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