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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, 16 Dec 2016 12:46:27 +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/16/t1481888895peci111xnpht0yc.htm/, Retrieved Thu, 02 May 2024 19:41:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300185, Retrieved Thu, 02 May 2024 19:41:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact62

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] [Variance Reductio...] [2016-12-16 11:46:27] [d5bfc1731fe289380efec318f4354749] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3280
3444
3855
3811
3785
4075
3547
3863
4064
4176
4191
4307
4179
4622
4798
4673
4635
4875
4097
4262
4135
4238
3891
3573
3963
4192
4306
4316
4249
4408
3731
4096
4102
3962
3845
3734
3933
4176
4150
4137
4016
4113
3611
3474
3654
3712
3394
3348
3476
3908
4009
4102
4253
4532
4080
4402
4597
4844
4877
4735
4768
5251
5553
5548
5519
5798
4918
5271
5492
5547
5244
5149
5453
5584
5773
5811
5687
5647
4892
5235
5311
5378
4994
4559
4895
5104
5477
5302
5360
5540
4877
5241
5233
5561
5049
4482
4846
4636
4431
4702
4775
4834
4344
4800
4981
5069
4655
4254
4753
4888
5048
4991
4962
5150
4444
4815

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time0 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 time0 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300185&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]0 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300185&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300185&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 time0 seconds
R ServerBig Analytics Cloud Computing Center






Variance Reduction Matrix
V(Y[t],d=0,D=0)420488Range2531Trim Var.312785
V(Y[t],d=1,D=0)91621Range1379Trim Var.56602
V(Y[t],d=2,D=0)223621Range2392Trim Var.129213
V(Y[t],d=3,D=0)682850Range3897Trim Var.405944
V(Y[t],d=0,D=1)349823Range2590Trim Var.235534
V(Y[t],d=1,D=1)46871.1Range1096Trim Var.27402.9
V(Y[t],d=2,D=1)98081.1Range1756Trim Var.49283.9
V(Y[t],d=3,D=1)288040Range3037Trim Var.162908
V(Y[t],d=0,D=2)750701Range3542Trim Var.524146
V(Y[t],d=1,D=2)135799Range1735Trim Var.79267
V(Y[t],d=2,D=2)282662Range3138Trim Var.153804
V(Y[t],d=3,D=2)807646Range4621Trim Var.450306

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 420488 & Range & 2531 & Trim Var. & 312785 \tabularnewline
V(Y[t],d=1,D=0) & 91621 & Range & 1379 & Trim Var. & 56602 \tabularnewline
V(Y[t],d=2,D=0) & 223621 & Range & 2392 & Trim Var. & 129213 \tabularnewline
V(Y[t],d=3,D=0) & 682850 & Range & 3897 & Trim Var. & 405944 \tabularnewline
V(Y[t],d=0,D=1) & 349823 & Range & 2590 & Trim Var. & 235534 \tabularnewline
V(Y[t],d=1,D=1) & 46871.1 & Range & 1096 & Trim Var. & 27402.9 \tabularnewline
V(Y[t],d=2,D=1) & 98081.1 & Range & 1756 & Trim Var. & 49283.9 \tabularnewline
V(Y[t],d=3,D=1) & 288040 & Range & 3037 & Trim Var. & 162908 \tabularnewline
V(Y[t],d=0,D=2) & 750701 & Range & 3542 & Trim Var. & 524146 \tabularnewline
V(Y[t],d=1,D=2) & 135799 & Range & 1735 & Trim Var. & 79267 \tabularnewline
V(Y[t],d=2,D=2) & 282662 & Range & 3138 & Trim Var. & 153804 \tabularnewline
V(Y[t],d=3,D=2) & 807646 & Range & 4621 & Trim Var. & 450306 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300185&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]420488[/C][C]Range[/C][C]2531[/C][C]Trim Var.[/C][C]312785[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]91621[/C][C]Range[/C][C]1379[/C][C]Trim Var.[/C][C]56602[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]223621[/C][C]Range[/C][C]2392[/C][C]Trim Var.[/C][C]129213[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]682850[/C][C]Range[/C][C]3897[/C][C]Trim Var.[/C][C]405944[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]349823[/C][C]Range[/C][C]2590[/C][C]Trim Var.[/C][C]235534[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]46871.1[/C][C]Range[/C][C]1096[/C][C]Trim Var.[/C][C]27402.9[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]98081.1[/C][C]Range[/C][C]1756[/C][C]Trim Var.[/C][C]49283.9[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]288040[/C][C]Range[/C][C]3037[/C][C]Trim Var.[/C][C]162908[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]750701[/C][C]Range[/C][C]3542[/C][C]Trim Var.[/C][C]524146[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]135799[/C][C]Range[/C][C]1735[/C][C]Trim Var.[/C][C]79267[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]282662[/C][C]Range[/C][C]3138[/C][C]Trim Var.[/C][C]153804[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]807646[/C][C]Range[/C][C]4621[/C][C]Trim Var.[/C][C]450306[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300185&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300185&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)420488Range2531Trim Var.312785
V(Y[t],d=1,D=0)91621Range1379Trim Var.56602
V(Y[t],d=2,D=0)223621Range2392Trim Var.129213
V(Y[t],d=3,D=0)682850Range3897Trim Var.405944
V(Y[t],d=0,D=1)349823Range2590Trim Var.235534
V(Y[t],d=1,D=1)46871.1Range1096Trim Var.27402.9
V(Y[t],d=2,D=1)98081.1Range1756Trim Var.49283.9
V(Y[t],d=3,D=1)288040Range3037Trim Var.162908
V(Y[t],d=0,D=2)750701Range3542Trim Var.524146
V(Y[t],d=1,D=2)135799Range1735Trim Var.79267
V(Y[t],d=2,D=2)282662Range3138Trim Var.153804
V(Y[t],d=3,D=2)807646Range4621Trim Var.450306


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
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()