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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_variancereduction.wasp
Title produced by softwareVariance Reduction Matrix
Date of computationFri, 23 Dec 2011 06:50:48 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/23/t1324641125txgwgpssdy82cv2.htm/, Retrieved Mon, 29 Apr 2024 23:09:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160313, Retrieved Mon, 29 Apr 2024 23:09:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108

Tree of Dependent Computations

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   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
- R P     [(Partial) Autocorrelation Function] [ws9] [2011-12-04 18:35:07] [8501ca4b76170905b8a207a77f626994]
-    D      [(Partial) Autocorrelation Function] [Workshop 9_Graph1] [2011-12-06 09:05:34] [f722e8e78b9e5c5ebaa2263f273aa636]
- RMP         [Spectral Analysis] [Workshop 9_Graph2] [2011-12-06 09:28:52] [f722e8e78b9e5c5ebaa2263f273aa636]
- R P           [Spectral Analysis] [Workshop 9_Graph2] [2011-12-06 09:35:47] [f722e8e78b9e5c5ebaa2263f273aa636]
-   PD            [Spectral Analysis] [Paper: CP ] [2011-12-23 11:41:11] [f722e8e78b9e5c5ebaa2263f273aa636]
- RM                  [Variance Reduction Matrix] [Paper: Variance R...] [2011-12-23 11:50:48] [3e64eea457df40fcb7af8f28e1ee6256] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
24.90
25.06
25.10
24.92
25.46
25.89
25.39
25.38
25.25
24.88
25.00
25.00
24.07
23.60
23.18
23.25
23.04
22.77
22.25
22.41
22.50
22.91
22.88
21.69
21.19
21.56
22.00
22.13
22.27
22.30
21.94
22.40
22.77
22.90
23.03
23.05
22.41
22.26
21.90
22.01
22.62
22.76
23.40
23.63
24.05
23.82
23.71
23.95
23.61
23.98
23.56
23.99
24.33
24.48
24.31
24.38
24.63
25.54
25.75
25.73
25.85
25.78
25.86
26.86
27.36
27.38
26.58
27.65
27.73
27.18
27.32
27.30
26.90
26.70
26.75
26.41
26.29
27.51
27.91
27.70
27.28
28.25
27.62
27.30
25.94
24.99
25.50
24.42
26.58
25.84
26.76
26.74
26.68
25.55
26.40
25.19
23.94
24.20
24.20
23.07
24.07
25.02
24.65
24.68
24.63
24.49
25.05
24.31
23.90
23.68
24.50
25.22
25.48
26.00
26.07
26.06
26.22
26.70
27.20
26.77
26.11
25.43
24.99
25.51
24.00
23.86
22.96
23.41
23.17
24.12
23.87
24.27
24.40
24.16
25.15
25.09
24.60
24.33
24.14
24.36
25.40
26.15
26.77
26.94
26.33
26.24
26.23
25.88
27.00
26.91
27.15
27.78
28.73
28.83
28.68
27.56
27.15
27.41
27.47
28.76
28.47
27.94
27.23
27.01
26.15
26.11
27.20
27.36
27.33
27.43
28.92
29.45
29.01
29.25
29.14
29.64
30.40
30.62
31.25
31.75
31.30
30.70
31.03
31.46
31.28
31.03
30.95
31.17
31.29
31.91
32.10
31.71
31.90
32.02
32.65
33.77
33.51
34.26
34.21
34.13
34.73
34.73
34.57
34.80
33.98
34.40
34.21
34.61
35.25
35.23
35.00
34.52
33.82
34.35
34.81
34.96
36.69
36.42
36.44
37.41
36.40
36.15
35.78
36.95
36.14
36.36
37.31
37.58
38.00
37.23
37.00
37.87
37.70
36.17
36.56
37.70
38.77
39.02
39.88
39.56
38.52
37.20
38.58
39.41
39.08
38.81
38.73
38.70
39.23
39.82
39.97
40.37
39.54
39.21
39.07
39.78
39.40
38.92

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160313&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160313&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160313&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Variance Reduction Matrix
V(Y[t],d=0,D=0)28.3414489488131Range19.18Trim Var.22.2264976489028
V(Y[t],d=1,D=0)0.354913959143969Range3.69Trim Var.0.206892539055148
V(Y[t],d=2,D=0)0.70859294117647Range6.13999999999999Trim Var.0.383111503702297
V(Y[t],d=3,D=0)2.10535983634399Range10.97Trim Var.1.06972851451774
V(Y[t],d=0,D=1)2.96377016260163Range7.84Trim Var.1.99009624533001
V(Y[t],d=1,D=1)0.632463907661425Range4.65Trim Var.0.362071965501205
V(Y[t],d=2,D=1)1.40241183970856Range7.81999999999999Trim Var.0.785991614171564
V(Y[t],d=3,D=1)4.42232004897459Range13.98Trim Var.2.47547414661205
V(Y[t],d=0,D=2)5.83296930596823Range13.14Trim Var.3.58733649806334
V(Y[t],d=1,D=2)1.89671384120172Range7.50999999999999Trim Var.1.10177554747884
V(Y[t],d=2,D=2)4.2015105762054Range13.15Trim Var.2.40107450761799
V(Y[t],d=3,D=2)13.2613567287785Range23.77Trim Var.7.45024386285822

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 28.3414489488131 & Range & 19.18 & Trim Var. & 22.2264976489028 \tabularnewline
V(Y[t],d=1,D=0) & 0.354913959143969 & Range & 3.69 & Trim Var. & 0.206892539055148 \tabularnewline
V(Y[t],d=2,D=0) & 0.70859294117647 & Range & 6.13999999999999 & Trim Var. & 0.383111503702297 \tabularnewline
V(Y[t],d=3,D=0) & 2.10535983634399 & Range & 10.97 & Trim Var. & 1.06972851451774 \tabularnewline
V(Y[t],d=0,D=1) & 2.96377016260163 & Range & 7.84 & Trim Var. & 1.99009624533001 \tabularnewline
V(Y[t],d=1,D=1) & 0.632463907661425 & Range & 4.65 & Trim Var. & 0.362071965501205 \tabularnewline
V(Y[t],d=2,D=1) & 1.40241183970856 & Range & 7.81999999999999 & Trim Var. & 0.785991614171564 \tabularnewline
V(Y[t],d=3,D=1) & 4.42232004897459 & Range & 13.98 & Trim Var. & 2.47547414661205 \tabularnewline
V(Y[t],d=0,D=2) & 5.83296930596823 & Range & 13.14 & Trim Var. & 3.58733649806334 \tabularnewline
V(Y[t],d=1,D=2) & 1.89671384120172 & Range & 7.50999999999999 & Trim Var. & 1.10177554747884 \tabularnewline
V(Y[t],d=2,D=2) & 4.2015105762054 & Range & 13.15 & Trim Var. & 2.40107450761799 \tabularnewline
V(Y[t],d=3,D=2) & 13.2613567287785 & Range & 23.77 & Trim Var. & 7.45024386285822 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160313&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]28.3414489488131[/C][C]Range[/C][C]19.18[/C][C]Trim Var.[/C][C]22.2264976489028[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.354913959143969[/C][C]Range[/C][C]3.69[/C][C]Trim Var.[/C][C]0.206892539055148[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.70859294117647[/C][C]Range[/C][C]6.13999999999999[/C][C]Trim Var.[/C][C]0.383111503702297[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]2.10535983634399[/C][C]Range[/C][C]10.97[/C][C]Trim Var.[/C][C]1.06972851451774[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]2.96377016260163[/C][C]Range[/C][C]7.84[/C][C]Trim Var.[/C][C]1.99009624533001[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.632463907661425[/C][C]Range[/C][C]4.65[/C][C]Trim Var.[/C][C]0.362071965501205[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]1.40241183970856[/C][C]Range[/C][C]7.81999999999999[/C][C]Trim Var.[/C][C]0.785991614171564[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]4.42232004897459[/C][C]Range[/C][C]13.98[/C][C]Trim Var.[/C][C]2.47547414661205[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]5.83296930596823[/C][C]Range[/C][C]13.14[/C][C]Trim Var.[/C][C]3.58733649806334[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]1.89671384120172[/C][C]Range[/C][C]7.50999999999999[/C][C]Trim Var.[/C][C]1.10177554747884[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]4.2015105762054[/C][C]Range[/C][C]13.15[/C][C]Trim Var.[/C][C]2.40107450761799[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]13.2613567287785[/C][C]Range[/C][C]23.77[/C][C]Trim Var.[/C][C]7.45024386285822[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160313&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160313&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Variance Reduction Matrix
V(Y[t],d=0,D=0)28.3414489488131Range19.18Trim Var.22.2264976489028
V(Y[t],d=1,D=0)0.354913959143969Range3.69Trim Var.0.206892539055148
V(Y[t],d=2,D=0)0.70859294117647Range6.13999999999999Trim Var.0.383111503702297
V(Y[t],d=3,D=0)2.10535983634399Range10.97Trim Var.1.06972851451774
V(Y[t],d=0,D=1)2.96377016260163Range7.84Trim Var.1.99009624533001
V(Y[t],d=1,D=1)0.632463907661425Range4.65Trim Var.0.362071965501205
V(Y[t],d=2,D=1)1.40241183970856Range7.81999999999999Trim Var.0.785991614171564
V(Y[t],d=3,D=1)4.42232004897459Range13.98Trim Var.2.47547414661205
V(Y[t],d=0,D=2)5.83296930596823Range13.14Trim Var.3.58733649806334
V(Y[t],d=1,D=2)1.89671384120172Range7.50999999999999Trim Var.1.10177554747884
V(Y[t],d=2,D=2)4.2015105762054Range13.15Trim Var.2.40107450761799
V(Y[t],d=3,D=2)13.2613567287785Range23.77Trim Var.7.45024386285822


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Valutakoersen Eur-Dollar ; 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()