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R Software Module

rwasp_variancereduction.wasp

Title produced by software

Variance Reduction Matrix

Date of computation

Fri, 16 Dec 2016 17:30:45 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/16/t1481905990r267flsksvpwhqh.htm/, Retrieved Thu, 02 May 2024 21:53:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300432, Retrieved Thu, 02 May 2024 21:53:24 +0000

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-       [Variance Reduction Matrix] [] [2016-12-16 16:30:45] [349958aef20b862f8399a5ba04d6f6e3] [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	0 seconds
R Server	Big 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=300432&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=300432&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300432&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	0 seconds
R Server	Big Analytics Cloud Computing Center

Variance Reduction Matrix
V(Y[t],d=0,D=0)	383903	Range	1983	Trim Var.	308105
V(Y[t],d=1,D=0)	1735.58	Range	243	Trim Var.	921.813
V(Y[t],d=2,D=0)	4626.85	Range	377	Trim Var.	2525.98
V(Y[t],d=3,D=0)	15466.4	Range	680	Trim Var.	9026.16
V(Y[t],d=0,D=1)	5030.45	Range	318	Trim Var.	2477.85
V(Y[t],d=1,D=1)	3002.12	Range	280	Trim Var.	1737.29
V(Y[t],d=2,D=1)	7924.99	Range	445	Trim Var.	4075.15
V(Y[t],d=3,D=1)	26597.6	Range	769	Trim Var.	14717.1
V(Y[t],d=0,D=2)	9617.15	Range	422	Trim Var.	6390
V(Y[t],d=1,D=2)	7050.48	Range	416	Trim Var.	3964.12
V(Y[t],d=2,D=2)	16651.7	Range	577	Trim Var.	10041.5
V(Y[t],d=3,D=2)	53359.2	Range	965	Trim Var.	34828.7

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 383903 & Range & 1983 & Trim Var. & 308105 \tabularnewline
V(Y[t],d=1,D=0) & 1735.58 & Range & 243 & Trim Var. & 921.813 \tabularnewline
V(Y[t],d=2,D=0) & 4626.85 & Range & 377 & Trim Var. & 2525.98 \tabularnewline
V(Y[t],d=3,D=0) & 15466.4 & Range & 680 & Trim Var. & 9026.16 \tabularnewline
V(Y[t],d=0,D=1) & 5030.45 & Range & 318 & Trim Var. & 2477.85 \tabularnewline
V(Y[t],d=1,D=1) & 3002.12 & Range & 280 & Trim Var. & 1737.29 \tabularnewline
V(Y[t],d=2,D=1) & 7924.99 & Range & 445 & Trim Var. & 4075.15 \tabularnewline
V(Y[t],d=3,D=1) & 26597.6 & Range & 769 & Trim Var. & 14717.1 \tabularnewline
V(Y[t],d=0,D=2) & 9617.15 & Range & 422 & Trim Var. & 6390 \tabularnewline
V(Y[t],d=1,D=2) & 7050.48 & Range & 416 & Trim Var. & 3964.12 \tabularnewline
V(Y[t],d=2,D=2) & 16651.7 & Range & 577 & Trim Var. & 10041.5 \tabularnewline
V(Y[t],d=3,D=2) & 53359.2 & Range & 965 & Trim Var. & 34828.7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300432&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]383903[/C][C]Range[/C][C]1983[/C][C]Trim Var.[/C][C]308105[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1735.58[/C][C]Range[/C][C]243[/C][C]Trim Var.[/C][C]921.813[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]4626.85[/C][C]Range[/C][C]377[/C][C]Trim Var.[/C][C]2525.98[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]15466.4[/C][C]Range[/C][C]680[/C][C]Trim Var.[/C][C]9026.16[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]5030.45[/C][C]Range[/C][C]318[/C][C]Trim Var.[/C][C]2477.85[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]3002.12[/C][C]Range[/C][C]280[/C][C]Trim Var.[/C][C]1737.29[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]7924.99[/C][C]Range[/C][C]445[/C][C]Trim Var.[/C][C]4075.15[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]26597.6[/C][C]Range[/C][C]769[/C][C]Trim Var.[/C][C]14717.1[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]9617.15[/C][C]Range[/C][C]422[/C][C]Trim Var.[/C][C]6390[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]7050.48[/C][C]Range[/C][C]416[/C][C]Trim Var.[/C][C]3964.12[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]16651.7[/C][C]Range[/C][C]577[/C][C]Trim Var.[/C][C]10041.5[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]53359.2[/C][C]Range[/C][C]965[/C][C]Trim Var.[/C][C]34828.7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300432&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300432&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)	383903	Range	1983	Trim Var.	308105
V(Y[t],d=1,D=0)	1735.58	Range	243	Trim Var.	921.813
V(Y[t],d=2,D=0)	4626.85	Range	377	Trim Var.	2525.98
V(Y[t],d=3,D=0)	15466.4	Range	680	Trim Var.	9026.16
V(Y[t],d=0,D=1)	5030.45	Range	318	Trim Var.	2477.85
V(Y[t],d=1,D=1)	3002.12	Range	280	Trim Var.	1737.29
V(Y[t],d=2,D=1)	7924.99	Range	445	Trim Var.	4075.15
V(Y[t],d=3,D=1)	26597.6	Range	769	Trim Var.	14717.1
V(Y[t],d=0,D=2)	9617.15	Range	422	Trim Var.	6390
V(Y[t],d=1,D=2)	7050.48	Range	416	Trim Var.	3964.12
V(Y[t],d=2,D=2)	16651.7	Range	577	Trim Var.	10041.5
V(Y[t],d=3,D=2)	53359.2	Range	965	Trim Var.	34828.7

Figure 1

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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()

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