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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 13:43:41 +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/t1481892240t8siq56g837wfa3.htm/, Retrieved Thu, 02 May 2024 14:51:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300225, Retrieved Thu, 02 May 2024 14:51:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact81

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] [forecast variance...] [2016-12-16 12:43:41] [111362aa4cdbe055231fbc5cb9e916c4] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4030
4320
4840
4410
4180
4240
3680
4270
4140
4470
4180
4510
4490
3960
3750
3670
3590
2840
3530
4320
3740
3710
3830
3490
4200
4280
4650
2100
2410
1230
2420
2360
1870
2250
1960
2550
3180
3330
3760
3930
3710
3250
3450
3480
3090
3690
3250
3300
4040
3630
3820
3400
2500
2380
2520
2340
2420
2430
2080
2420
2430
2400
2790
2370
2700
2640
2910
2420
2800
2830
2310
2540
2780
2820
3610
3270
3030
3250
3040
3630
3320
3440
3110
3180
3330
3100
3440
3320
3380
3610
3320
3860
3430
3510
3290
3010
3860
3530
3610
3370
3700
3500
4110
4590
3680
4220
3740
3550
4150
4110
4160
3780
3150
3260
4750
4110
3610
3890
2800
2610
3600
3400
3400
3120
3150
3240

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=300225&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=300225&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300225&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)485904Range3610Trim Var.318137
V(Y[t],d=1,D=0)254411Range4040Trim Var.115661
V(Y[t],d=2,D=0)672412Range5780Trim Var.344800
V(Y[t],d=3,D=0)2207490Range10130Trim Var.1136930
V(Y[t],d=0,D=1)701467Range3980Trim Var.461222
V(Y[t],d=1,D=1)341582Range5190Trim Var.142733
V(Y[t],d=2,D=1)888781Range6110Trim Var.410586
V(Y[t],d=3,D=1)2938630Range11820Trim Var.1474030
V(Y[t],d=0,D=2)2084670Range6520Trim Var.1221160
V(Y[t],d=1,D=2)972436Range8500Trim Var.334828
V(Y[t],d=2,D=2)2465910Range11820Trim Var.1170950
V(Y[t],d=3,D=2)8125320Range20000Trim Var.4100590

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 485904 & Range & 3610 & Trim Var. & 318137 \tabularnewline
V(Y[t],d=1,D=0) & 254411 & Range & 4040 & Trim Var. & 115661 \tabularnewline
V(Y[t],d=2,D=0) & 672412 & Range & 5780 & Trim Var. & 344800 \tabularnewline
V(Y[t],d=3,D=0) & 2207490 & Range & 10130 & Trim Var. & 1136930 \tabularnewline
V(Y[t],d=0,D=1) & 701467 & Range & 3980 & Trim Var. & 461222 \tabularnewline
V(Y[t],d=1,D=1) & 341582 & Range & 5190 & Trim Var. & 142733 \tabularnewline
V(Y[t],d=2,D=1) & 888781 & Range & 6110 & Trim Var. & 410586 \tabularnewline
V(Y[t],d=3,D=1) & 2938630 & Range & 11820 & Trim Var. & 1474030 \tabularnewline
V(Y[t],d=0,D=2) & 2084670 & Range & 6520 & Trim Var. & 1221160 \tabularnewline
V(Y[t],d=1,D=2) & 972436 & Range & 8500 & Trim Var. & 334828 \tabularnewline
V(Y[t],d=2,D=2) & 2465910 & Range & 11820 & Trim Var. & 1170950 \tabularnewline
V(Y[t],d=3,D=2) & 8125320 & Range & 20000 & Trim Var. & 4100590 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300225&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]485904[/C][C]Range[/C][C]3610[/C][C]Trim Var.[/C][C]318137[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]254411[/C][C]Range[/C][C]4040[/C][C]Trim Var.[/C][C]115661[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]672412[/C][C]Range[/C][C]5780[/C][C]Trim Var.[/C][C]344800[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]2207490[/C][C]Range[/C][C]10130[/C][C]Trim Var.[/C][C]1136930[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]701467[/C][C]Range[/C][C]3980[/C][C]Trim Var.[/C][C]461222[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]341582[/C][C]Range[/C][C]5190[/C][C]Trim Var.[/C][C]142733[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]888781[/C][C]Range[/C][C]6110[/C][C]Trim Var.[/C][C]410586[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]2938630[/C][C]Range[/C][C]11820[/C][C]Trim Var.[/C][C]1474030[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]2084670[/C][C]Range[/C][C]6520[/C][C]Trim Var.[/C][C]1221160[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]972436[/C][C]Range[/C][C]8500[/C][C]Trim Var.[/C][C]334828[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]2465910[/C][C]Range[/C][C]11820[/C][C]Trim Var.[/C][C]1170950[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]8125320[/C][C]Range[/C][C]20000[/C][C]Trim Var.[/C][C]4100590[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300225&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300225&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)485904Range3610Trim Var.318137
V(Y[t],d=1,D=0)254411Range4040Trim Var.115661
V(Y[t],d=2,D=0)672412Range5780Trim Var.344800
V(Y[t],d=3,D=0)2207490Range10130Trim Var.1136930
V(Y[t],d=0,D=1)701467Range3980Trim Var.461222
V(Y[t],d=1,D=1)341582Range5190Trim Var.142733
V(Y[t],d=2,D=1)888781Range6110Trim Var.410586
V(Y[t],d=3,D=1)2938630Range11820Trim Var.1474030
V(Y[t],d=0,D=2)2084670Range6520Trim Var.1221160
V(Y[t],d=1,D=2)972436Range8500Trim Var.334828
V(Y[t],d=2,D=2)2465910Range11820Trim Var.1170950
V(Y[t],d=3,D=2)8125320Range20000Trim Var.4100590


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = 12 ; par3 = BFGS ;
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()