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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 computationSun, 18 Dec 2016 13:42:26 +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/18/t1482064967njbr2xxaioab2oy.htm/, Retrieved Fri, 21 Feb 2025 18:13:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301037, Retrieved Fri, 21 Feb 2025 18:13:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact159

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2016-12-18 12:31:12] [683f400e1b95307fc738e729f07c4fce]
- RM D    [Variance Reduction Matrix] [] [2016-12-18 12:42:26] [404ac5ee4f7301873f6a96ef36861981] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
305
408
2730
954
272
486
801
21
933
821
310
452
313
968
882
470
504
561
98
793
781
321
84
705
252
737
832
330
469
758
903
55
731
390
976
323
921
878
835
318
503
390
717
68
286
500
632
678
765
3
703
2
981
2671
15
19
246
997
296
111
551
522
165
641
758
558
662
577
540
298
537
690
920
622
355
405
603
106
44
678
754
259
2605
858
514
223
832
550
250
23
520
581
680
581
929
686
335
153
494
534
666
52
184
357
742
559
563
373
758
101
367
216
682
90
124
998
180
764
877
637
971
637
169
404
949
477
2228
781
330
248
647
170
29
721

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=301037&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=301037&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301037&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)202754Range2728Trim Var.67502.5
V(Y[t],d=1,D=0)406644Range5002Trim Var.143683
V(Y[t],d=2,D=0)1160230Range7187Trim Var.419392
V(Y[t],d=3,D=0)3711520Range13940Trim Var.1396350
V(Y[t],d=0,D=1)340525Range4394Trim Var.106594
V(Y[t],d=1,D=1)725812Range5743Trim Var.272183
V(Y[t],d=2,D=1)2147060Range9436Trim Var.966948
V(Y[t],d=3,D=1)6950940Range15921Trim Var.3344930
V(Y[t],d=0,D=2)894910Range7043Trim Var.349966
V(Y[t],d=1,D=2)1997640Range9848Trim Var.886274
V(Y[t],d=2,D=2)6006880Range15921Trim Var.2852970
V(Y[t],d=3,D=2)19743600Range28184Trim Var.9851100

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 202754 & Range & 2728 & Trim Var. & 67502.5 \tabularnewline
V(Y[t],d=1,D=0) & 406644 & Range & 5002 & Trim Var. & 143683 \tabularnewline
V(Y[t],d=2,D=0) & 1160230 & Range & 7187 & Trim Var. & 419392 \tabularnewline
V(Y[t],d=3,D=0) & 3711520 & Range & 13940 & Trim Var. & 1396350 \tabularnewline
V(Y[t],d=0,D=1) & 340525 & Range & 4394 & Trim Var. & 106594 \tabularnewline
V(Y[t],d=1,D=1) & 725812 & Range & 5743 & Trim Var. & 272183 \tabularnewline
V(Y[t],d=2,D=1) & 2147060 & Range & 9436 & Trim Var. & 966948 \tabularnewline
V(Y[t],d=3,D=1) & 6950940 & Range & 15921 & Trim Var. & 3344930 \tabularnewline
V(Y[t],d=0,D=2) & 894910 & Range & 7043 & Trim Var. & 349966 \tabularnewline
V(Y[t],d=1,D=2) & 1997640 & Range & 9848 & Trim Var. & 886274 \tabularnewline
V(Y[t],d=2,D=2) & 6006880 & Range & 15921 & Trim Var. & 2852970 \tabularnewline
V(Y[t],d=3,D=2) & 19743600 & Range & 28184 & Trim Var. & 9851100 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301037&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]202754[/C][C]Range[/C][C]2728[/C][C]Trim Var.[/C][C]67502.5[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]406644[/C][C]Range[/C][C]5002[/C][C]Trim Var.[/C][C]143683[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1160230[/C][C]Range[/C][C]7187[/C][C]Trim Var.[/C][C]419392[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]3711520[/C][C]Range[/C][C]13940[/C][C]Trim Var.[/C][C]1396350[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]340525[/C][C]Range[/C][C]4394[/C][C]Trim Var.[/C][C]106594[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]725812[/C][C]Range[/C][C]5743[/C][C]Trim Var.[/C][C]272183[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]2147060[/C][C]Range[/C][C]9436[/C][C]Trim Var.[/C][C]966948[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]6950940[/C][C]Range[/C][C]15921[/C][C]Trim Var.[/C][C]3344930[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]894910[/C][C]Range[/C][C]7043[/C][C]Trim Var.[/C][C]349966[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]1997640[/C][C]Range[/C][C]9848[/C][C]Trim Var.[/C][C]886274[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]6006880[/C][C]Range[/C][C]15921[/C][C]Trim Var.[/C][C]2852970[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]19743600[/C][C]Range[/C][C]28184[/C][C]Trim Var.[/C][C]9851100[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301037&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301037&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)202754Range2728Trim Var.67502.5
V(Y[t],d=1,D=0)406644Range5002Trim Var.143683
V(Y[t],d=2,D=0)1160230Range7187Trim Var.419392
V(Y[t],d=3,D=0)3711520Range13940Trim Var.1396350
V(Y[t],d=0,D=1)340525Range4394Trim Var.106594
V(Y[t],d=1,D=1)725812Range5743Trim Var.272183
V(Y[t],d=2,D=1)2147060Range9436Trim Var.966948
V(Y[t],d=3,D=1)6950940Range15921Trim Var.3344930
V(Y[t],d=0,D=2)894910Range7043Trim Var.349966
V(Y[t],d=1,D=2)1997640Range9848Trim Var.886274
V(Y[t],d=2,D=2)6006880Range15921Trim Var.2852970
V(Y[t],d=3,D=2)19743600Range28184Trim Var.9851100


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 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()