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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 computationWed, 07 Dec 2011 09:12:57 -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/07/t1323267270k3ar5q10pmvb0c7.htm/, Retrieved Thu, 02 May 2024 22:59:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=152418, Retrieved Thu, 02 May 2024 22:59:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact142

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 09:09:37] [b98453cac15ba1066b407e146608df68]
- R PD    [(Partial) Autocorrelation Function] [autocorrelatie d=...] [2011-12-07 13:53:53] [141ef847e2c5f8e947fe4eabcb0cf143]
- RM        [Spectral Analysis] [CP D=1] [2011-12-07 14:00:06] [141ef847e2c5f8e947fe4eabcb0cf143]
- RM D          [Variance Reduction Matrix] [VRM] [2011-12-07 14:12:57] [1a4698f17d8e7f554418314cf0e4bd67] [Current]
- RMPD            [(Partial) Autocorrelation Function] [ACF] [2011-12-19 18:47:21] [141ef847e2c5f8e947fe4eabcb0cf143]
- R P               [(Partial) Autocorrelation Function] [AFC d=1 D=1] [2011-12-19 19:04:58] [141ef847e2c5f8e947fe4eabcb0cf143]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
114,7
108
101,3
108,4
105,6
120,4
107,6
111,4
122,1
104,8
103,2
112,3
123,1
115,5
106,3
119,9
119,5
120,9
127,5
116,6
126,7
110,6
100,4
125,2
125
105,2
102,7
94,2
97
111,1
102
97,3
109,8
98,9
93,2
115,2
115
107
104,1
106
110,8
127,8
116,9
113,8
131,6
106,1
107,2
127,4
123
121,8
117,6
118,4
121,8
141,9
122,1
132,2
131,6
108,8
120,4
134,7

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152418&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152418&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152418&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 time2 seconds
R Server'George Udny Yule' @ yule.wessa.net






Variance Reduction Matrix
V(Y[t],d=0,D=0)117.610463276836Range48.7Trim Var.80.9308176100629
V(Y[t],d=1,D=0)137.948281706604Range50.3Trim Var.88.5168740573152
V(Y[t],d=2,D=0)361.43257108288Range78.3Trim Var.255.59165535445
V(Y[t],d=3,D=0)1087.14146616541Range134.1Trim Var.739.800549019608
V(Y[t],d=0,D=1)150.999782801418Range47.5Trim Var.94.1987979094077
V(Y[t],d=1,D=1)83.6740055504163Range41.5Trim Var.49.4338048780488
V(Y[t],d=2,D=1)256.626144927536Range66.9Trim Var.160.262301282051
V(Y[t],d=3,D=1)872.61891919192Range121Trim Var.531.726518218624
V(Y[t],d=0,D=2)512.055142857143Range85.8Trim Var.365.734425403226
V(Y[t],d=1,D=2)226.639613445378Range67.6Trim Var.130.564731182796
V(Y[t],d=2,D=2)672.647736185384Range117.2Trim Var.420.855126436782
V(Y[t],d=3,D=2)2305.5068939394Range203.7Trim Var.1470.33933497537

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 117.610463276836 & Range & 48.7 & Trim Var. & 80.9308176100629 \tabularnewline
V(Y[t],d=1,D=0) & 137.948281706604 & Range & 50.3 & Trim Var. & 88.5168740573152 \tabularnewline
V(Y[t],d=2,D=0) & 361.43257108288 & Range & 78.3 & Trim Var. & 255.59165535445 \tabularnewline
V(Y[t],d=3,D=0) & 1087.14146616541 & Range & 134.1 & Trim Var. & 739.800549019608 \tabularnewline
V(Y[t],d=0,D=1) & 150.999782801418 & Range & 47.5 & Trim Var. & 94.1987979094077 \tabularnewline
V(Y[t],d=1,D=1) & 83.6740055504163 & Range & 41.5 & Trim Var. & 49.4338048780488 \tabularnewline
V(Y[t],d=2,D=1) & 256.626144927536 & Range & 66.9 & Trim Var. & 160.262301282051 \tabularnewline
V(Y[t],d=3,D=1) & 872.61891919192 & Range & 121 & Trim Var. & 531.726518218624 \tabularnewline
V(Y[t],d=0,D=2) & 512.055142857143 & Range & 85.8 & Trim Var. & 365.734425403226 \tabularnewline
V(Y[t],d=1,D=2) & 226.639613445378 & Range & 67.6 & Trim Var. & 130.564731182796 \tabularnewline
V(Y[t],d=2,D=2) & 672.647736185384 & Range & 117.2 & Trim Var. & 420.855126436782 \tabularnewline
V(Y[t],d=3,D=2) & 2305.5068939394 & Range & 203.7 & Trim Var. & 1470.33933497537 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152418&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]117.610463276836[/C][C]Range[/C][C]48.7[/C][C]Trim Var.[/C][C]80.9308176100629[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]137.948281706604[/C][C]Range[/C][C]50.3[/C][C]Trim Var.[/C][C]88.5168740573152[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]361.43257108288[/C][C]Range[/C][C]78.3[/C][C]Trim Var.[/C][C]255.59165535445[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]1087.14146616541[/C][C]Range[/C][C]134.1[/C][C]Trim Var.[/C][C]739.800549019608[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]150.999782801418[/C][C]Range[/C][C]47.5[/C][C]Trim Var.[/C][C]94.1987979094077[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]83.6740055504163[/C][C]Range[/C][C]41.5[/C][C]Trim Var.[/C][C]49.4338048780488[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]256.626144927536[/C][C]Range[/C][C]66.9[/C][C]Trim Var.[/C][C]160.262301282051[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]872.61891919192[/C][C]Range[/C][C]121[/C][C]Trim Var.[/C][C]531.726518218624[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]512.055142857143[/C][C]Range[/C][C]85.8[/C][C]Trim Var.[/C][C]365.734425403226[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]226.639613445378[/C][C]Range[/C][C]67.6[/C][C]Trim Var.[/C][C]130.564731182796[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]672.647736185384[/C][C]Range[/C][C]117.2[/C][C]Trim Var.[/C][C]420.855126436782[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]2305.5068939394[/C][C]Range[/C][C]203.7[/C][C]Trim Var.[/C][C]1470.33933497537[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152418&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152418&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)117.610463276836Range48.7Trim Var.80.9308176100629
V(Y[t],d=1,D=0)137.948281706604Range50.3Trim Var.88.5168740573152
V(Y[t],d=2,D=0)361.43257108288Range78.3Trim Var.255.59165535445
V(Y[t],d=3,D=0)1087.14146616541Range134.1Trim Var.739.800549019608
V(Y[t],d=0,D=1)150.999782801418Range47.5Trim Var.94.1987979094077
V(Y[t],d=1,D=1)83.6740055504163Range41.5Trim Var.49.4338048780488
V(Y[t],d=2,D=1)256.626144927536Range66.9Trim Var.160.262301282051
V(Y[t],d=3,D=1)872.61891919192Range121Trim Var.531.726518218624
V(Y[t],d=0,D=2)512.055142857143Range85.8Trim Var.365.734425403226
V(Y[t],d=1,D=2)226.639613445378Range67.6Trim Var.130.564731182796
V(Y[t],d=2,D=2)672.647736185384Range117.2Trim Var.420.855126436782
V(Y[t],d=3,D=2)2305.5068939394Range203.7Trim Var.1470.33933497537


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; 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()