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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 computationThu, 17 Nov 2016 10:58:07 +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/Nov/17/t1479376699uissbd18xfkh1ff.htm/, Retrieved Sun, 05 May 2024 08:45:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296802, Retrieved Sun, 05 May 2024 08:45:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75

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] [] [2016-11-17 09:58:07] [219800a2f11ddd28e3280d87dbde8c8d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
945
18
46
47
665
872
743
194
8
246
862
437
615
470
635
413
91
169
36
675
130
110
63
3384
168
169
79
107
936
331
837
861
641
177
645
594
34
153
81
994
42
354
813
995
35
219
571
642
417
63
646
525
4529
799
287
212
942
750
201
284
124
39
540
310
958
124
275
835
38
485
704
720
837
553
999
754
344
314
909
947
944
36
43
860
469
494
788
239
692
626
344
423
159
807
418
86
200
999
534
299
732
24
5265
871
354
15
337
427
127
496
864
88
1
429
386
610
486
936
566
5
491
117
2495
698
202
886
486
528
301

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=296802&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=296802&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296802&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)494551Range5264Trim Var.86476.6
V(Y[t],d=1,D=0)1016410Range9635Trim Var.152168
V(Y[t],d=2,D=0)3007630Range15584Trim Var.454682
V(Y[t],d=3,D=0)10066300Range29096Trim Var.1636290
V(Y[t],d=0,D=1)1076290Range9800Trim Var.201387
V(Y[t],d=1,D=1)2211530Range10807Trim Var.485840
V(Y[t],d=2,D=1)6715860Range19898Trim Var.1889850
V(Y[t],d=3,D=1)22879000Range32483Trim Var.6974150
V(Y[t],d=0,D=2)3518660Range15286Trim Var.635435
V(Y[t],d=1,D=2)7142680Range19898Trim Var.1682790
V(Y[t],d=2,D=2)21780900Range32483Trim Var.6621520
V(Y[t],d=3,D=2)74238600Range60826Trim Var.23902200

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 494551 & Range & 5264 & Trim Var. & 86476.6 \tabularnewline
V(Y[t],d=1,D=0) & 1016410 & Range & 9635 & Trim Var. & 152168 \tabularnewline
V(Y[t],d=2,D=0) & 3007630 & Range & 15584 & Trim Var. & 454682 \tabularnewline
V(Y[t],d=3,D=0) & 10066300 & Range & 29096 & Trim Var. & 1636290 \tabularnewline
V(Y[t],d=0,D=1) & 1076290 & Range & 9800 & Trim Var. & 201387 \tabularnewline
V(Y[t],d=1,D=1) & 2211530 & Range & 10807 & Trim Var. & 485840 \tabularnewline
V(Y[t],d=2,D=1) & 6715860 & Range & 19898 & Trim Var. & 1889850 \tabularnewline
V(Y[t],d=3,D=1) & 22879000 & Range & 32483 & Trim Var. & 6974150 \tabularnewline
V(Y[t],d=0,D=2) & 3518660 & Range & 15286 & Trim Var. & 635435 \tabularnewline
V(Y[t],d=1,D=2) & 7142680 & Range & 19898 & Trim Var. & 1682790 \tabularnewline
V(Y[t],d=2,D=2) & 21780900 & Range & 32483 & Trim Var. & 6621520 \tabularnewline
V(Y[t],d=3,D=2) & 74238600 & Range & 60826 & Trim Var. & 23902200 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296802&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]494551[/C][C]Range[/C][C]5264[/C][C]Trim Var.[/C][C]86476.6[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1016410[/C][C]Range[/C][C]9635[/C][C]Trim Var.[/C][C]152168[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]3007630[/C][C]Range[/C][C]15584[/C][C]Trim Var.[/C][C]454682[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]10066300[/C][C]Range[/C][C]29096[/C][C]Trim Var.[/C][C]1636290[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]1076290[/C][C]Range[/C][C]9800[/C][C]Trim Var.[/C][C]201387[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2211530[/C][C]Range[/C][C]10807[/C][C]Trim Var.[/C][C]485840[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]6715860[/C][C]Range[/C][C]19898[/C][C]Trim Var.[/C][C]1889850[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]22879000[/C][C]Range[/C][C]32483[/C][C]Trim Var.[/C][C]6974150[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]3518660[/C][C]Range[/C][C]15286[/C][C]Trim Var.[/C][C]635435[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]7142680[/C][C]Range[/C][C]19898[/C][C]Trim Var.[/C][C]1682790[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]21780900[/C][C]Range[/C][C]32483[/C][C]Trim Var.[/C][C]6621520[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]74238600[/C][C]Range[/C][C]60826[/C][C]Trim Var.[/C][C]23902200[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296802&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296802&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)494551Range5264Trim Var.86476.6
V(Y[t],d=1,D=0)1016410Range9635Trim Var.152168
V(Y[t],d=2,D=0)3007630Range15584Trim Var.454682
V(Y[t],d=3,D=0)10066300Range29096Trim Var.1636290
V(Y[t],d=0,D=1)1076290Range9800Trim Var.201387
V(Y[t],d=1,D=1)2211530Range10807Trim Var.485840
V(Y[t],d=2,D=1)6715860Range19898Trim Var.1889850
V(Y[t],d=3,D=1)22879000Range32483Trim Var.6974150
V(Y[t],d=0,D=2)3518660Range15286Trim Var.635435
V(Y[t],d=1,D=2)7142680Range19898Trim Var.1682790
V(Y[t],d=2,D=2)21780900Range32483Trim Var.6621520
V(Y[t],d=3,D=2)74238600Range60826Trim Var.23902200


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()