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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 computationTue, 20 Dec 2016 00:07:50 +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/20/t148218897852n2afdh813pqg3.htm/, Retrieved Sat, 27 Apr 2024 16:07:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301542, Retrieved Sat, 27 Apr 2024 16:07:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103

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] [] [2016-12-19 23:07:50] [b2e25925e4919b0d6985405fcb461c0d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4020
3540
3430
4200
3360
4440
4390
4940
3940
4560
4850
5070
6210
5200
4860
5160
5530
8830
4410
4850
8960
4620
5120
4520
8870
9470
6590
3970
3770
5500
6580
5280
8640
5510
5690
7620
4010
3570
4040
3600
4000
3070
3230
4060
3480
3750
3990
3100
3950
3010
3160
2960
2750
3590
3060
2970
3590
3450
2930
2660
3540
3160
2680
2900
2920
2900
3150
3150
3120
3720
3360
2740
3250
2700
2610
2410
2590
2630
2650
2600
3060
2650
2700
2620
2630
2850
2680
2430
2550
2570
2520
2500
2550
2790
2770
2460
2800
2770
2450
2370
2540
3470
2690
4110
3840
2860
3540
3370

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=301542&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=301542&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301542&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)2391430Range7100Trim Var.997712
V(Y[t],d=1,D=0)1586490Range8770Trim Var.288019
V(Y[t],d=2,D=0)4322740Range13400Trim Var.1131880
V(Y[t],d=3,D=0)13550300Range25410Trim Var.2907110
V(Y[t],d=0,D=1)2864640Range10920Trim Var.905833
V(Y[t],d=1,D=1)3392560Range13460Trim Var.1056650
V(Y[t],d=2,D=1)8977440Range17830Trim Var.3110160
V(Y[t],d=3,D=1)27722800Range32700Trim Var.8950250
V(Y[t],d=0,D=2)7147840Range15510Trim Var.2430490
V(Y[t],d=1,D=2)10132800Range23590Trim Var.3208780
V(Y[t],d=2,D=2)26192600Range32290Trim Var.9412260
V(Y[t],d=3,D=2)80119500Range53150Trim Var.29499800

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 2391430 & Range & 7100 & Trim Var. & 997712 \tabularnewline
V(Y[t],d=1,D=0) & 1586490 & Range & 8770 & Trim Var. & 288019 \tabularnewline
V(Y[t],d=2,D=0) & 4322740 & Range & 13400 & Trim Var. & 1131880 \tabularnewline
V(Y[t],d=3,D=0) & 13550300 & Range & 25410 & Trim Var. & 2907110 \tabularnewline
V(Y[t],d=0,D=1) & 2864640 & Range & 10920 & Trim Var. & 905833 \tabularnewline
V(Y[t],d=1,D=1) & 3392560 & Range & 13460 & Trim Var. & 1056650 \tabularnewline
V(Y[t],d=2,D=1) & 8977440 & Range & 17830 & Trim Var. & 3110160 \tabularnewline
V(Y[t],d=3,D=1) & 27722800 & Range & 32700 & Trim Var. & 8950250 \tabularnewline
V(Y[t],d=0,D=2) & 7147840 & Range & 15510 & Trim Var. & 2430490 \tabularnewline
V(Y[t],d=1,D=2) & 10132800 & Range & 23590 & Trim Var. & 3208780 \tabularnewline
V(Y[t],d=2,D=2) & 26192600 & Range & 32290 & Trim Var. & 9412260 \tabularnewline
V(Y[t],d=3,D=2) & 80119500 & Range & 53150 & Trim Var. & 29499800 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301542&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]2391430[/C][C]Range[/C][C]7100[/C][C]Trim Var.[/C][C]997712[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1586490[/C][C]Range[/C][C]8770[/C][C]Trim Var.[/C][C]288019[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]4322740[/C][C]Range[/C][C]13400[/C][C]Trim Var.[/C][C]1131880[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]13550300[/C][C]Range[/C][C]25410[/C][C]Trim Var.[/C][C]2907110[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]2864640[/C][C]Range[/C][C]10920[/C][C]Trim Var.[/C][C]905833[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]3392560[/C][C]Range[/C][C]13460[/C][C]Trim Var.[/C][C]1056650[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]8977440[/C][C]Range[/C][C]17830[/C][C]Trim Var.[/C][C]3110160[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]27722800[/C][C]Range[/C][C]32700[/C][C]Trim Var.[/C][C]8950250[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]7147840[/C][C]Range[/C][C]15510[/C][C]Trim Var.[/C][C]2430490[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]10132800[/C][C]Range[/C][C]23590[/C][C]Trim Var.[/C][C]3208780[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]26192600[/C][C]Range[/C][C]32290[/C][C]Trim Var.[/C][C]9412260[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]80119500[/C][C]Range[/C][C]53150[/C][C]Trim Var.[/C][C]29499800[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301542&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301542&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)2391430Range7100Trim Var.997712
V(Y[t],d=1,D=0)1586490Range8770Trim Var.288019
V(Y[t],d=2,D=0)4322740Range13400Trim Var.1131880
V(Y[t],d=3,D=0)13550300Range25410Trim Var.2907110
V(Y[t],d=0,D=1)2864640Range10920Trim Var.905833
V(Y[t],d=1,D=1)3392560Range13460Trim Var.1056650
V(Y[t],d=2,D=1)8977440Range17830Trim Var.3110160
V(Y[t],d=3,D=1)27722800Range32700Trim Var.8950250
V(Y[t],d=0,D=2)7147840Range15510Trim Var.2430490
V(Y[t],d=1,D=2)10132800Range23590Trim Var.3208780
V(Y[t],d=2,D=2)26192600Range32290Trim Var.9412260
V(Y[t],d=3,D=2)80119500Range53150Trim Var.29499800


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; 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()