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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, 21 Dec 2016 02:45:09 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/21/t1482284716d5bc0x5ge3p6d2m.htm/, Retrieved Fri, 17 May 2024 12:37:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301841, Retrieved Fri, 17 May 2024 12:37:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact87

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Variance Reduction Matrix] [] [2016-12-21 01:45:09] [361c8dad91b3f1ef2e651cd04783c23b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3082.8
3122.55
3092.15
3081
3146.5
3199.55
3198.7
3232.75
3316
3312.5
3398.5
3442.8
3475.85
3567.8
3605.3
3692.5
3711.25
3682.65
3684.2
3727.6
3766.5
3813.35
3849.45
3953.7
4023.9
4049
4067.85
4082.35
4104.2
4145.55
4146.55
4142.15
4168.2
4320.8
4408.2
4415.75
4520.65
4575.15
4679.45
4702.6
4623.3
4644.2
4737.45
4697.75
4521.1
4684.45
4638.7
4499.15
4646.65
4744.25
4848.45
4861.7
4954.4
5030.55
5068.35
5027.1
4957.3
5156.45
5218
5274.05
5243.5
5198.25
5192.95
5223.25
5287.25
5338.9
5350.9
5427.75
5498.3
5472.65
5514.55
5634.5
5732.6
5812.55
5846.8
5933.4
6002
6064.1
6077.35
6110.35
6047.95
6034.65
6078
6085.8
5938.15
5933.35
5971.6
5962.25
6013.15
6048.85
6092.85
6221.15
6186.8
6202.1
6163.5
6083.3
6147.2
6042.3
5849.45
5863.5
5860.95
5805.75
5832.5
5866.4
5943.6
5956.6
5939.3
5986.95
5881.6
5891
5948.65
6078.75
6058.8
6059.85
6097.95

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301841&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301841&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301841&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Variance Reduction Matrix
V(Y[t],d=0,D=0)997016Range3140.15Trim Var.827173
V(Y[t],d=1,D=0)4349.31Range392Trim Var.2066.43
V(Y[t],d=2,D=0)7923.33Range549.1Trim Var.3628.17
V(Y[t],d=3,D=0)22022.2Range1026.05Trim Var.9560.38
V(Y[t],d=0,D=1)4349.31Range392Trim Var.2066.43
V(Y[t],d=1,D=1)7923.33Range549.1Trim Var.3628.17
V(Y[t],d=2,D=1)22022.2Range1026.05Trim Var.9560.38
V(Y[t],d=3,D=1)67868Range1690.45Trim Var.31998.9
V(Y[t],d=0,D=2)7923.33Range549.1Trim Var.3628.17
V(Y[t],d=1,D=2)22022.2Range1026.05Trim Var.9560.38
V(Y[t],d=2,D=2)67868Range1690.45Trim Var.31998.9
V(Y[t],d=3,D=2)221830Range3197.45Trim Var.107300

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 997016 & Range & 3140.15 & Trim Var. & 827173 \tabularnewline
V(Y[t],d=1,D=0) & 4349.31 & Range & 392 & Trim Var. & 2066.43 \tabularnewline
V(Y[t],d=2,D=0) & 7923.33 & Range & 549.1 & Trim Var. & 3628.17 \tabularnewline
V(Y[t],d=3,D=0) & 22022.2 & Range & 1026.05 & Trim Var. & 9560.38 \tabularnewline
V(Y[t],d=0,D=1) & 4349.31 & Range & 392 & Trim Var. & 2066.43 \tabularnewline
V(Y[t],d=1,D=1) & 7923.33 & Range & 549.1 & Trim Var. & 3628.17 \tabularnewline
V(Y[t],d=2,D=1) & 22022.2 & Range & 1026.05 & Trim Var. & 9560.38 \tabularnewline
V(Y[t],d=3,D=1) & 67868 & Range & 1690.45 & Trim Var. & 31998.9 \tabularnewline
V(Y[t],d=0,D=2) & 7923.33 & Range & 549.1 & Trim Var. & 3628.17 \tabularnewline
V(Y[t],d=1,D=2) & 22022.2 & Range & 1026.05 & Trim Var. & 9560.38 \tabularnewline
V(Y[t],d=2,D=2) & 67868 & Range & 1690.45 & Trim Var. & 31998.9 \tabularnewline
V(Y[t],d=3,D=2) & 221830 & Range & 3197.45 & Trim Var. & 107300 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301841&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]997016[/C][C]Range[/C][C]3140.15[/C][C]Trim Var.[/C][C]827173[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]4349.31[/C][C]Range[/C][C]392[/C][C]Trim Var.[/C][C]2066.43[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]7923.33[/C][C]Range[/C][C]549.1[/C][C]Trim Var.[/C][C]3628.17[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]22022.2[/C][C]Range[/C][C]1026.05[/C][C]Trim Var.[/C][C]9560.38[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]4349.31[/C][C]Range[/C][C]392[/C][C]Trim Var.[/C][C]2066.43[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]7923.33[/C][C]Range[/C][C]549.1[/C][C]Trim Var.[/C][C]3628.17[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]22022.2[/C][C]Range[/C][C]1026.05[/C][C]Trim Var.[/C][C]9560.38[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]67868[/C][C]Range[/C][C]1690.45[/C][C]Trim Var.[/C][C]31998.9[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]7923.33[/C][C]Range[/C][C]549.1[/C][C]Trim Var.[/C][C]3628.17[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]22022.2[/C][C]Range[/C][C]1026.05[/C][C]Trim Var.[/C][C]9560.38[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]67868[/C][C]Range[/C][C]1690.45[/C][C]Trim Var.[/C][C]31998.9[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]221830[/C][C]Range[/C][C]3197.45[/C][C]Trim Var.[/C][C]107300[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301841&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301841&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)997016Range3140.15Trim Var.827173
V(Y[t],d=1,D=0)4349.31Range392Trim Var.2066.43
V(Y[t],d=2,D=0)7923.33Range549.1Trim Var.3628.17
V(Y[t],d=3,D=0)22022.2Range1026.05Trim Var.9560.38
V(Y[t],d=0,D=1)4349.31Range392Trim Var.2066.43
V(Y[t],d=1,D=1)7923.33Range549.1Trim Var.3628.17
V(Y[t],d=2,D=1)22022.2Range1026.05Trim Var.9560.38
V(Y[t],d=3,D=1)67868Range1690.45Trim Var.31998.9
V(Y[t],d=0,D=2)7923.33Range549.1Trim Var.3628.17
V(Y[t],d=1,D=2)22022.2Range1026.05Trim Var.9560.38
V(Y[t],d=2,D=2)67868Range1690.45Trim Var.31998.9
V(Y[t],d=3,D=2)221830Range3197.45Trim Var.107300


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 1 ;
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()