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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 19:15:52 +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/t1481912212wpzlznu0hpxw2zl.htm/, Retrieved Thu, 02 May 2024 19:49:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300468, Retrieved Thu, 02 May 2024 19:49:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65

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 18:15:52] [9fb47d69755d1f4b66b6f2591280f9e0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4307.5
4234
5156.5
4844
4606
4850
4294
3190
3811.5
4160.5
4538.5
3792.5
4660
3504.5
3521
4560
4549
3543
2996
3762
4156.5
4525
4058
4871.5
4870
4953
5028.5
5252.5
4907
4641
5447.5
4544.5
4493
5522
3896.5
3108.5
4415
2912.5
3536
3183
3643.5
3412
3202.5
3374.5
3226.5
3927.5
3498.5
3614.5
3740
2857.5
4100
3684
3601.5
3663.5
2586.5
2825
2866.5
2722
2164
2113.5
2379
2811
3539
3474
3909.5
4049.5
3156.5
3435
3058.5
4103
3726.5
4703.5
4020.5
3636
4289
5570.5
5283
4618
4765
3937.5
4717.5
4206.5
4506.5
4306
5281.5
5495.5
5304
5935
5974
9239
6054.5
6072
6279
5260
5966
6764.5
8028.5
6063.5
7531.5
7347
6571
7337.5
7519.5
7358
4746
5173.5
6433.5
4508
4912.5
6246
7557.5
7111
6304.5
6166
5735
4583
4657.5
4712.5
5647
5277
4812.5
4702
6047
5470
4540.5
5112.5

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=300468&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=300468&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300468&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)1749620Range7125.5Trim Var.1022420
V(Y[t],d=1,D=0)734484Range6449.5Trim Var.352128
V(Y[t],d=2,D=0)1972250Range9882.5Trim Var.909127
V(Y[t],d=3,D=0)6238400Range19327Trim Var.2871550
V(Y[t],d=0,D=1)1769770Range7737Trim Var.1105910
V(Y[t],d=1,D=1)1441320Range7261.5Trim Var.699878
V(Y[t],d=2,D=1)3904150Range13126.5Trim Var.2134670
V(Y[t],d=3,D=1)12176000Range22303Trim Var.6414930
V(Y[t],d=0,D=2)4330570Range10613.5Trim Var.2393980
V(Y[t],d=1,D=2)4652720Range13126.5Trim Var.2120670
V(Y[t],d=2,D=2)12474800Range22233Trim Var.7078120
V(Y[t],d=3,D=2)38247300Range39262Trim Var.20499800

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 1749620 & Range & 7125.5 & Trim Var. & 1022420 \tabularnewline
V(Y[t],d=1,D=0) & 734484 & Range & 6449.5 & Trim Var. & 352128 \tabularnewline
V(Y[t],d=2,D=0) & 1972250 & Range & 9882.5 & Trim Var. & 909127 \tabularnewline
V(Y[t],d=3,D=0) & 6238400 & Range & 19327 & Trim Var. & 2871550 \tabularnewline
V(Y[t],d=0,D=1) & 1769770 & Range & 7737 & Trim Var. & 1105910 \tabularnewline
V(Y[t],d=1,D=1) & 1441320 & Range & 7261.5 & Trim Var. & 699878 \tabularnewline
V(Y[t],d=2,D=1) & 3904150 & Range & 13126.5 & Trim Var. & 2134670 \tabularnewline
V(Y[t],d=3,D=1) & 12176000 & Range & 22303 & Trim Var. & 6414930 \tabularnewline
V(Y[t],d=0,D=2) & 4330570 & Range & 10613.5 & Trim Var. & 2393980 \tabularnewline
V(Y[t],d=1,D=2) & 4652720 & Range & 13126.5 & Trim Var. & 2120670 \tabularnewline
V(Y[t],d=2,D=2) & 12474800 & Range & 22233 & Trim Var. & 7078120 \tabularnewline
V(Y[t],d=3,D=2) & 38247300 & Range & 39262 & Trim Var. & 20499800 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300468&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]1749620[/C][C]Range[/C][C]7125.5[/C][C]Trim Var.[/C][C]1022420[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]734484[/C][C]Range[/C][C]6449.5[/C][C]Trim Var.[/C][C]352128[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1972250[/C][C]Range[/C][C]9882.5[/C][C]Trim Var.[/C][C]909127[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]6238400[/C][C]Range[/C][C]19327[/C][C]Trim Var.[/C][C]2871550[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]1769770[/C][C]Range[/C][C]7737[/C][C]Trim Var.[/C][C]1105910[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1441320[/C][C]Range[/C][C]7261.5[/C][C]Trim Var.[/C][C]699878[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]3904150[/C][C]Range[/C][C]13126.5[/C][C]Trim Var.[/C][C]2134670[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12176000[/C][C]Range[/C][C]22303[/C][C]Trim Var.[/C][C]6414930[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]4330570[/C][C]Range[/C][C]10613.5[/C][C]Trim Var.[/C][C]2393980[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]4652720[/C][C]Range[/C][C]13126.5[/C][C]Trim Var.[/C][C]2120670[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12474800[/C][C]Range[/C][C]22233[/C][C]Trim Var.[/C][C]7078120[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]38247300[/C][C]Range[/C][C]39262[/C][C]Trim Var.[/C][C]20499800[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300468&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300468&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)1749620Range7125.5Trim Var.1022420
V(Y[t],d=1,D=0)734484Range6449.5Trim Var.352128
V(Y[t],d=2,D=0)1972250Range9882.5Trim Var.909127
V(Y[t],d=3,D=0)6238400Range19327Trim Var.2871550
V(Y[t],d=0,D=1)1769770Range7737Trim Var.1105910
V(Y[t],d=1,D=1)1441320Range7261.5Trim Var.699878
V(Y[t],d=2,D=1)3904150Range13126.5Trim Var.2134670
V(Y[t],d=3,D=1)12176000Range22303Trim Var.6414930
V(Y[t],d=0,D=2)4330570Range10613.5Trim Var.2393980
V(Y[t],d=1,D=2)4652720Range13126.5Trim Var.2120670
V(Y[t],d=2,D=2)12474800Range22233Trim Var.7078120
V(Y[t],d=3,D=2)38247300Range39262Trim Var.20499800


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 4 ; 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()