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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

Sun, 19 Dec 2010 12:56:08 +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/19/t1292763323ge262rbf9ts08r1.htm/, Retrieved Sun, 05 May 2024 05:33:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112342, Retrieved Sun, 05 May 2024 05:33:00 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

147

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

F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
-  MPD  [Univariate Data Series] [WS8 1] [2010-11-30 15:47:30] [07a238a5afc23eb944f8545182f29d5a]
- RMP     [Classical Decomposition] [WS8 2] [2010-11-30 15:54:02] [07a238a5afc23eb944f8545182f29d5a]
- RMPD      [Univariate Data Series] [Statistiek: Werkl...] [2010-12-12 15:20:09] [07a238a5afc23eb944f8545182f29d5a]
-    D        [Univariate Data Series] [Statistiek: Werkl...] [2010-12-14 09:08:05] [07a238a5afc23eb944f8545182f29d5a]
-               [Univariate Data Series] [Statistiek: Werkl...] [2010-12-14 09:12:36] [07a238a5afc23eb944f8545182f29d5a]
- RMPD            [Classical Decomposition] [statistiek classi...] [2010-12-19 09:09:14] [07a238a5afc23eb944f8545182f29d5a]
- RMP               [(Partial) Autocorrelation Function] [Statistiek: ACF D...] [2010-12-19 10:44:26] [07a238a5afc23eb944f8545182f29d5a]
-   P                 [(Partial) Autocorrelation Function] [Statistiek: ACF D...] [2010-12-19 12:30:15] [07a238a5afc23eb944f8545182f29d5a]
-   P                   [(Partial) Autocorrelation Function] [Statistiek: ACF D...] [2010-12-19 12:34:49] [07a238a5afc23eb944f8545182f29d5a]
-   P                     [(Partial) Autocorrelation Function] [Statistiek: ACF D...] [2010-12-19 12:39:46] [07a238a5afc23eb944f8545182f29d5a]
- RM                        [Spectral Analysis] [statistiek: spectrum] [2010-12-19 12:54:11] [07a238a5afc23eb944f8545182f29d5a]
- RM                            [Variance Reduction Matrix] [statistiek: VRM] [2010-12-19 12:56:08] [67e3c2d70de1dbb070b545ca6c893d5e] [Current]

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Dataseries X:

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Histogram

Boxplots

6.5
6.3
5.9
5.5
5.2
4.9
5.4
5.8
5.7
5.6
5.5
5.4
5.4
5.4
5.5
5.8
5.7
5.4
5.6
5.8
6.2
6.8
6.7
6.7
6.4
6.3
6.3
6.4
6.3
6
6.3
6.3
6.6
7.5
7.8
7.9
7.8
7.6
7.5
7.6
7.5
7.3
7.6
7.5
7.6
7.9
7.9
8.1
8.2
8
7.5
6.8
6.5
6.6
7.6
8
8.1
7.7
7.5
7.6
7.8
7.8
7.8
7.5
7.5
7.1
7.5
7.5
7.6
7.7
7.7
7.9
8.1
8.2
8.2
8.2
7.9
7.3
6.9
6.6
6.7
6.9
7
7.1
7.2
7.1
6.9
7
6.8
6.4
6.7
6.6
6.4
6.3
6.2
6.5
6.8
6.8
6.4
6.1
5.8
6.1
7.2
7.3
6.9
6.1
5.8
6.2
7.1
7.7
8
7.8
7.4
7.4
7.7
7.8
7.8
8
8.1
8.4

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112342&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112342&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112342&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	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Variance Reduction Matrix
V(Y[t],d=0,D=0)	0.746806022408963	Range	3.5	Trim Var.	0.54331217326363
V(Y[t],d=1,D=0)	0.102031049708019	Range	1.9	Trim Var.	0.051505907247399
V(Y[t],d=2,D=0)	0.118187020136173	Range	1.9	Trim Var.	0.0670416355489171
V(Y[t],d=3,D=0)	0.253091659298556	Range	3	Trim Var.	0.133851648351648
V(Y[t],d=0,D=1)	0.673730529595016	Range	3.6	Trim Var.	0.452183650615901
V(Y[t],d=1,D=1)	0.129700229236466	Range	1.8	Trim Var.	0.061456043956044
V(Y[t],d=2,D=1)	0.126182389937107	Range	1.6	Trim Var.	0.07804884004884
V(Y[t],d=3,D=1)	0.221095238095238	Range	2.5	Trim Var.	0.117379616643291
V(Y[t],d=0,D=2)	1.14756140350877	Range	4.9	Trim Var.	0.609998565691337
V(Y[t],d=1,D=2)	0.286365061590146	Range	3.3	Trim Var.	0.133549019607843
V(Y[t],d=2,D=2)	0.290213909860444	Range	2.7	Trim Var.	0.178531267928858
V(Y[t],d=3,D=2)	0.537470780738662	Range	4.20000000000001	Trim Var.	0.285133705553922

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.746806022408963 & Range & 3.5 & Trim Var. & 0.54331217326363 \tabularnewline
V(Y[t],d=1,D=0) & 0.102031049708019 & Range & 1.9 & Trim Var. & 0.051505907247399 \tabularnewline
V(Y[t],d=2,D=0) & 0.118187020136173 & Range & 1.9 & Trim Var. & 0.0670416355489171 \tabularnewline
V(Y[t],d=3,D=0) & 0.253091659298556 & Range & 3 & Trim Var. & 0.133851648351648 \tabularnewline
V(Y[t],d=0,D=1) & 0.673730529595016 & Range & 3.6 & Trim Var. & 0.452183650615901 \tabularnewline
V(Y[t],d=1,D=1) & 0.129700229236466 & Range & 1.8 & Trim Var. & 0.061456043956044 \tabularnewline
V(Y[t],d=2,D=1) & 0.126182389937107 & Range & 1.6 & Trim Var. & 0.07804884004884 \tabularnewline
V(Y[t],d=3,D=1) & 0.221095238095238 & Range & 2.5 & Trim Var. & 0.117379616643291 \tabularnewline
V(Y[t],d=0,D=2) & 1.14756140350877 & Range & 4.9 & Trim Var. & 0.609998565691337 \tabularnewline
V(Y[t],d=1,D=2) & 0.286365061590146 & Range & 3.3 & Trim Var. & 0.133549019607843 \tabularnewline
V(Y[t],d=2,D=2) & 0.290213909860444 & Range & 2.7 & Trim Var. & 0.178531267928858 \tabularnewline
V(Y[t],d=3,D=2) & 0.537470780738662 & Range & 4.20000000000001 & Trim Var. & 0.285133705553922 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112342&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.746806022408963[/C][C]Range[/C][C]3.5[/C][C]Trim Var.[/C][C]0.54331217326363[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.102031049708019[/C][C]Range[/C][C]1.9[/C][C]Trim Var.[/C][C]0.051505907247399[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.118187020136173[/C][C]Range[/C][C]1.9[/C][C]Trim Var.[/C][C]0.0670416355489171[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.253091659298556[/C][C]Range[/C][C]3[/C][C]Trim Var.[/C][C]0.133851648351648[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.673730529595016[/C][C]Range[/C][C]3.6[/C][C]Trim Var.[/C][C]0.452183650615901[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.129700229236466[/C][C]Range[/C][C]1.8[/C][C]Trim Var.[/C][C]0.061456043956044[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.126182389937107[/C][C]Range[/C][C]1.6[/C][C]Trim Var.[/C][C]0.07804884004884[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]0.221095238095238[/C][C]Range[/C][C]2.5[/C][C]Trim Var.[/C][C]0.117379616643291[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]1.14756140350877[/C][C]Range[/C][C]4.9[/C][C]Trim Var.[/C][C]0.609998565691337[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.286365061590146[/C][C]Range[/C][C]3.3[/C][C]Trim Var.[/C][C]0.133549019607843[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.290213909860444[/C][C]Range[/C][C]2.7[/C][C]Trim Var.[/C][C]0.178531267928858[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]0.537470780738662[/C][C]Range[/C][C]4.20000000000001[/C][C]Trim Var.[/C][C]0.285133705553922[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112342&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112342&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)	0.746806022408963	Range	3.5	Trim Var.	0.54331217326363
V(Y[t],d=1,D=0)	0.102031049708019	Range	1.9	Trim Var.	0.051505907247399
V(Y[t],d=2,D=0)	0.118187020136173	Range	1.9	Trim Var.	0.0670416355489171
V(Y[t],d=3,D=0)	0.253091659298556	Range	3	Trim Var.	0.133851648351648
V(Y[t],d=0,D=1)	0.673730529595016	Range	3.6	Trim Var.	0.452183650615901
V(Y[t],d=1,D=1)	0.129700229236466	Range	1.8	Trim Var.	0.061456043956044
V(Y[t],d=2,D=1)	0.126182389937107	Range	1.6	Trim Var.	0.07804884004884
V(Y[t],d=3,D=1)	0.221095238095238	Range	2.5	Trim Var.	0.117379616643291
V(Y[t],d=0,D=2)	1.14756140350877	Range	4.9	Trim Var.	0.609998565691337
V(Y[t],d=1,D=2)	0.286365061590146	Range	3.3	Trim Var.	0.133549019607843
V(Y[t],d=2,D=2)	0.290213909860444	Range	2.7	Trim Var.	0.178531267928858
V(Y[t],d=3,D=2)	0.537470780738662	Range	4.20000000000001	Trim Var.	0.285133705553922

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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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Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code