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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

Tue, 20 Dec 2011 17:00:14 -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/20/t1324418454f1r9yfpr19m53ty.htm/, Retrieved Mon, 06 May 2024 09:48:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=158303, Retrieved Mon, 06 May 2024 09:48:26 +0000

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No (this computation is public)

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Estimated Impact

143

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [(Partial) Autocorrelation Function] [Births] [2010-11-29 09:36:27] [b98453cac15ba1066b407e146608df68]
- R PD          [(Partial) Autocorrelation Function] [WS9 3.1 ACF d=0, D=0] [2010-12-07 10:00:49] [afe9379cca749d06b3d6872e02cc47ed]
- R PD            [(Partial) Autocorrelation Function] [] [2011-12-04 10:34:49] [ec2187f7727da5d5d939740b21b8b68a]
- RMPD                [Variance Reduction Matrix] [] [2011-12-20 22:00:14] [542c32830549043c4555f1bd78aefedb] [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	'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158303&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158303&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158303&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	'AstonUniversity' @ aston.wessa.net

Variance Reduction Matrix
V(Y[t],d=0,D=0)	257677536.964841	Range	65187	Trim Var.	191041660.92815
V(Y[t],d=1,D=0)	96124443.0109327	Range	50353	Trim Var.	54531433.0103737
V(Y[t],d=2,D=0)	212198869.174308	Range	91344	Trim Var.	115543096.362413
V(Y[t],d=3,D=0)	587733518.721277	Range	160440	Trim Var.	296507841.082839
V(Y[t],d=0,D=1)	160679301.315001	Range	72133	Trim Var.	57887462.5974214
V(Y[t],d=1,D=1)	29323920.0971227	Range	34606	Trim Var.	13110512.2410846
V(Y[t],d=2,D=1)	69989567.6045915	Range	62796	Trim Var.	35904491.7901049
V(Y[t],d=3,D=1)	230167071.49031	Range	118576	Trim Var.	113477517.091228
V(Y[t],d=0,D=2)	438422118.056022	Range	121783	Trim Var.	179869655.323988
V(Y[t],d=1,D=2)	67438248.6943455	Range	56134	Trim Var.	34401794.5177217
V(Y[t],d=2,D=2)	129918277.103288	Range	67326	Trim Var.	70982905.0824798
V(Y[t],d=3,D=2)	413220556.571765	Range	120182	Trim Var.	221177012.994139

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 257677536.964841 & Range & 65187 & Trim Var. & 191041660.92815 \tabularnewline
V(Y[t],d=1,D=0) & 96124443.0109327 & Range & 50353 & Trim Var. & 54531433.0103737 \tabularnewline
V(Y[t],d=2,D=0) & 212198869.174308 & Range & 91344 & Trim Var. & 115543096.362413 \tabularnewline
V(Y[t],d=3,D=0) & 587733518.721277 & Range & 160440 & Trim Var. & 296507841.082839 \tabularnewline
V(Y[t],d=0,D=1) & 160679301.315001 & Range & 72133 & Trim Var. & 57887462.5974214 \tabularnewline
V(Y[t],d=1,D=1) & 29323920.0971227 & Range & 34606 & Trim Var. & 13110512.2410846 \tabularnewline
V(Y[t],d=2,D=1) & 69989567.6045915 & Range & 62796 & Trim Var. & 35904491.7901049 \tabularnewline
V(Y[t],d=3,D=1) & 230167071.49031 & Range & 118576 & Trim Var. & 113477517.091228 \tabularnewline
V(Y[t],d=0,D=2) & 438422118.056022 & Range & 121783 & Trim Var. & 179869655.323988 \tabularnewline
V(Y[t],d=1,D=2) & 67438248.6943455 & Range & 56134 & Trim Var. & 34401794.5177217 \tabularnewline
V(Y[t],d=2,D=2) & 129918277.103288 & Range & 67326 & Trim Var. & 70982905.0824798 \tabularnewline
V(Y[t],d=3,D=2) & 413220556.571765 & Range & 120182 & Trim Var. & 221177012.994139 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158303&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]257677536.964841[/C][C]Range[/C][C]65187[/C][C]Trim Var.[/C][C]191041660.92815[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]96124443.0109327[/C][C]Range[/C][C]50353[/C][C]Trim Var.[/C][C]54531433.0103737[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]212198869.174308[/C][C]Range[/C][C]91344[/C][C]Trim Var.[/C][C]115543096.362413[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]587733518.721277[/C][C]Range[/C][C]160440[/C][C]Trim Var.[/C][C]296507841.082839[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]160679301.315001[/C][C]Range[/C][C]72133[/C][C]Trim Var.[/C][C]57887462.5974214[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]29323920.0971227[/C][C]Range[/C][C]34606[/C][C]Trim Var.[/C][C]13110512.2410846[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]69989567.6045915[/C][C]Range[/C][C]62796[/C][C]Trim Var.[/C][C]35904491.7901049[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]230167071.49031[/C][C]Range[/C][C]118576[/C][C]Trim Var.[/C][C]113477517.091228[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]438422118.056022[/C][C]Range[/C][C]121783[/C][C]Trim Var.[/C][C]179869655.323988[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]67438248.6943455[/C][C]Range[/C][C]56134[/C][C]Trim Var.[/C][C]34401794.5177217[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]129918277.103288[/C][C]Range[/C][C]67326[/C][C]Trim Var.[/C][C]70982905.0824798[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]413220556.571765[/C][C]Range[/C][C]120182[/C][C]Trim Var.[/C][C]221177012.994139[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158303&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158303&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)	257677536.964841	Range	65187	Trim Var.	191041660.92815
V(Y[t],d=1,D=0)	96124443.0109327	Range	50353	Trim Var.	54531433.0103737
V(Y[t],d=2,D=0)	212198869.174308	Range	91344	Trim Var.	115543096.362413
V(Y[t],d=3,D=0)	587733518.721277	Range	160440	Trim Var.	296507841.082839
V(Y[t],d=0,D=1)	160679301.315001	Range	72133	Trim Var.	57887462.5974214
V(Y[t],d=1,D=1)	29323920.0971227	Range	34606	Trim Var.	13110512.2410846
V(Y[t],d=2,D=1)	69989567.6045915	Range	62796	Trim Var.	35904491.7901049
V(Y[t],d=3,D=1)	230167071.49031	Range	118576	Trim Var.	113477517.091228
V(Y[t],d=0,D=2)	438422118.056022	Range	121783	Trim Var.	179869655.323988
V(Y[t],d=1,D=2)	67438248.6943455	Range	56134	Trim Var.	34401794.5177217
V(Y[t],d=2,D=2)	129918277.103288	Range	67326	Trim Var.	70982905.0824798
V(Y[t],d=3,D=2)	413220556.571765	Range	120182	Trim Var.	221177012.994139

Figure 1

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Parameters (Session):

par1 = 4 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

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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