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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, 09 Dec 2016 16:38:37 +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/09/t1481297950og2qqeoqavx5dyq.htm/, Retrieved Sun, 09 Mar 2025 22:49:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298577, Retrieved Sun, 09 Mar 2025 22:49:29 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact105

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [Autocorr eerste] [2016-12-07 13:39:31] [5f979cb1c6fa86b57093c7542788c28c]
- RM D    [Variance Reduction Matrix] [ksdn] [2016-12-09 15:38:37] [4c05fa0998bf98e29c2e453b139976f4] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5345
5245
5100
5070
5035
5050
5065
5255
5335
5440
5490
5445
5675
5615
5545
5510
5570
5610
5555
5630
5685
5545
5625
5570
5555
5635
5535
5430
5400
5410
5255
5350
5405
5420
5430
5580
5595
5485
5295
5055
4975
4895
4795
4855
4785
4875
5010
4970
4995
5020
4950
4880
4850
4885
4785
5025
5030
5160
5240
5175
5130
5140
5140
5055
5015
5015
4920
5095
5010
5100
5115
5060
5035
5005
4960
5035
4980
4940
4810
5025
5035
5060
5140
4955
5135
5135
5070
5070
5005
5045
4975
5080
5125
5225
5240
5090
5105
5200
5115
4990
4905
4980
4840
4960
4970
5035
5030
4965
4925
4920
4895
4890
4895
4850
4830
4870

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=298577&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=298577&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298577&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)60211.5Range900Trim Var.45979
V(Y[t],d=1,D=0)8190.9Range480Trim Var.4710.03
V(Y[t],d=2,D=0)17250.2Range655Trim Var.9895.91
V(Y[t],d=3,D=0)55028.8Range1205Trim Var.29508.7
V(Y[t],d=0,D=1)60352.5Range1180Trim Var.32348.2
V(Y[t],d=1,D=1)8508.7Range450Trim Var.4841.83
V(Y[t],d=2,D=1)17964.9Range700Trim Var.10441.8
V(Y[t],d=3,D=1)55629.8Range1175Trim Var.30326.7
V(Y[t],d=0,D=2)130732Range1655Trim Var.76228.4
V(Y[t],d=1,D=2)23456.3Range795Trim Var.13738.5
V(Y[t],d=2,D=2)49790.5Range1040Trim Var.28982.9
V(Y[t],d=3,D=2)154905Range1845Trim Var.88631.2

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 60211.5 & Range & 900 & Trim Var. & 45979 \tabularnewline
V(Y[t],d=1,D=0) & 8190.9 & Range & 480 & Trim Var. & 4710.03 \tabularnewline
V(Y[t],d=2,D=0) & 17250.2 & Range & 655 & Trim Var. & 9895.91 \tabularnewline
V(Y[t],d=3,D=0) & 55028.8 & Range & 1205 & Trim Var. & 29508.7 \tabularnewline
V(Y[t],d=0,D=1) & 60352.5 & Range & 1180 & Trim Var. & 32348.2 \tabularnewline
V(Y[t],d=1,D=1) & 8508.7 & Range & 450 & Trim Var. & 4841.83 \tabularnewline
V(Y[t],d=2,D=1) & 17964.9 & Range & 700 & Trim Var. & 10441.8 \tabularnewline
V(Y[t],d=3,D=1) & 55629.8 & Range & 1175 & Trim Var. & 30326.7 \tabularnewline
V(Y[t],d=0,D=2) & 130732 & Range & 1655 & Trim Var. & 76228.4 \tabularnewline
V(Y[t],d=1,D=2) & 23456.3 & Range & 795 & Trim Var. & 13738.5 \tabularnewline
V(Y[t],d=2,D=2) & 49790.5 & Range & 1040 & Trim Var. & 28982.9 \tabularnewline
V(Y[t],d=3,D=2) & 154905 & Range & 1845 & Trim Var. & 88631.2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298577&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]60211.5[/C][C]Range[/C][C]900[/C][C]Trim Var.[/C][C]45979[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]8190.9[/C][C]Range[/C][C]480[/C][C]Trim Var.[/C][C]4710.03[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]17250.2[/C][C]Range[/C][C]655[/C][C]Trim Var.[/C][C]9895.91[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]55028.8[/C][C]Range[/C][C]1205[/C][C]Trim Var.[/C][C]29508.7[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]60352.5[/C][C]Range[/C][C]1180[/C][C]Trim Var.[/C][C]32348.2[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]8508.7[/C][C]Range[/C][C]450[/C][C]Trim Var.[/C][C]4841.83[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]17964.9[/C][C]Range[/C][C]700[/C][C]Trim Var.[/C][C]10441.8[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]55629.8[/C][C]Range[/C][C]1175[/C][C]Trim Var.[/C][C]30326.7[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]130732[/C][C]Range[/C][C]1655[/C][C]Trim Var.[/C][C]76228.4[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]23456.3[/C][C]Range[/C][C]795[/C][C]Trim Var.[/C][C]13738.5[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]49790.5[/C][C]Range[/C][C]1040[/C][C]Trim Var.[/C][C]28982.9[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]154905[/C][C]Range[/C][C]1845[/C][C]Trim Var.[/C][C]88631.2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298577&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298577&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)60211.5Range900Trim Var.45979
V(Y[t],d=1,D=0)8190.9Range480Trim Var.4710.03
V(Y[t],d=2,D=0)17250.2Range655Trim Var.9895.91
V(Y[t],d=3,D=0)55028.8Range1205Trim Var.29508.7
V(Y[t],d=0,D=1)60352.5Range1180Trim Var.32348.2
V(Y[t],d=1,D=1)8508.7Range450Trim Var.4841.83
V(Y[t],d=2,D=1)17964.9Range700Trim Var.10441.8
V(Y[t],d=3,D=1)55629.8Range1175Trim Var.30326.7
V(Y[t],d=0,D=2)130732Range1655Trim Var.76228.4
V(Y[t],d=1,D=2)23456.3Range795Trim Var.13738.5
V(Y[t],d=2,D=2)49790.5Range1040Trim Var.28982.9
V(Y[t],d=3,D=2)154905Range1845Trim Var.88631.2


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 4 ; 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.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()