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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, 22 Dec 2016 18:19:44 +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/22/t14824273600k5q9vfm64vcc3o.htm/, Retrieved Sun, 28 Apr 2024 20:51:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302584, Retrieved Sun, 28 Apr 2024 20:51:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact63

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 (F1)] [2016-12-22 17:19:44] [bde5266f17215258f6d7c4cd7e531432] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1549.5
1746.5
1869.5
1784
1795
1942.5
2100
2072.5
2075
2278
2451
2290.5
2388
2574.5
2939.5
2924
3087.5
3259.5
3474.5
3376
3496
3771.5
3743
3474.5
3405
3684.5
3804
3470.5
3453.5
3842
4156.5
4055
4133.5
4552
4588
4423.5
4462.5
4846
4869.5
4637
4841
5114.5
5374.5
5166.5
5236.5
5740.5
5992
5842
5844.5
6384.5
6487
6372
6583.5
6990
6874
6710
6924
7428.5
7415.5
7228.5
6734
7158.5
7192

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=302584&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=302584&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302584&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)3126860Range5879Trim Var.2423750
V(Y[t],d=1,D=0)47966.4Range1034.5Trim Var.28576.3
V(Y[t],d=2,D=0)98128.8Range1441.5Trim Var.65489.9
V(Y[t],d=3,D=0)233865Range2536.5Trim Var.147682
V(Y[t],d=0,D=1)58973.5Range1009Trim Var.38207.9
V(Y[t],d=1,D=1)23447Range945Trim Var.10558.5
V(Y[t],d=2,D=1)41674.6Range1314Trim Var.19560.8
V(Y[t],d=3,D=1)117813Range1917.5Trim Var.63132
V(Y[t],d=0,D=2)96388.7Range1396.5Trim Var.56619.5
V(Y[t],d=1,D=2)46135.9Range1102.5Trim Var.26288.4
V(Y[t],d=2,D=2)81671.2Range1376.5Trim Var.48441.4
V(Y[t],d=3,D=2)234587Range2495Trim Var.130693

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 3126860 & Range & 5879 & Trim Var. & 2423750 \tabularnewline
V(Y[t],d=1,D=0) & 47966.4 & Range & 1034.5 & Trim Var. & 28576.3 \tabularnewline
V(Y[t],d=2,D=0) & 98128.8 & Range & 1441.5 & Trim Var. & 65489.9 \tabularnewline
V(Y[t],d=3,D=0) & 233865 & Range & 2536.5 & Trim Var. & 147682 \tabularnewline
V(Y[t],d=0,D=1) & 58973.5 & Range & 1009 & Trim Var. & 38207.9 \tabularnewline
V(Y[t],d=1,D=1) & 23447 & Range & 945 & Trim Var. & 10558.5 \tabularnewline
V(Y[t],d=2,D=1) & 41674.6 & Range & 1314 & Trim Var. & 19560.8 \tabularnewline
V(Y[t],d=3,D=1) & 117813 & Range & 1917.5 & Trim Var. & 63132 \tabularnewline
V(Y[t],d=0,D=2) & 96388.7 & Range & 1396.5 & Trim Var. & 56619.5 \tabularnewline
V(Y[t],d=1,D=2) & 46135.9 & Range & 1102.5 & Trim Var. & 26288.4 \tabularnewline
V(Y[t],d=2,D=2) & 81671.2 & Range & 1376.5 & Trim Var. & 48441.4 \tabularnewline
V(Y[t],d=3,D=2) & 234587 & Range & 2495 & Trim Var. & 130693 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302584&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]3126860[/C][C]Range[/C][C]5879[/C][C]Trim Var.[/C][C]2423750[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]47966.4[/C][C]Range[/C][C]1034.5[/C][C]Trim Var.[/C][C]28576.3[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]98128.8[/C][C]Range[/C][C]1441.5[/C][C]Trim Var.[/C][C]65489.9[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]233865[/C][C]Range[/C][C]2536.5[/C][C]Trim Var.[/C][C]147682[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]58973.5[/C][C]Range[/C][C]1009[/C][C]Trim Var.[/C][C]38207.9[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]23447[/C][C]Range[/C][C]945[/C][C]Trim Var.[/C][C]10558.5[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]41674.6[/C][C]Range[/C][C]1314[/C][C]Trim Var.[/C][C]19560.8[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]117813[/C][C]Range[/C][C]1917.5[/C][C]Trim Var.[/C][C]63132[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]96388.7[/C][C]Range[/C][C]1396.5[/C][C]Trim Var.[/C][C]56619.5[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]46135.9[/C][C]Range[/C][C]1102.5[/C][C]Trim Var.[/C][C]26288.4[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]81671.2[/C][C]Range[/C][C]1376.5[/C][C]Trim Var.[/C][C]48441.4[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]234587[/C][C]Range[/C][C]2495[/C][C]Trim Var.[/C][C]130693[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302584&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302584&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)3126860Range5879Trim Var.2423750
V(Y[t],d=1,D=0)47966.4Range1034.5Trim Var.28576.3
V(Y[t],d=2,D=0)98128.8Range1441.5Trim Var.65489.9
V(Y[t],d=3,D=0)233865Range2536.5Trim Var.147682
V(Y[t],d=0,D=1)58973.5Range1009Trim Var.38207.9
V(Y[t],d=1,D=1)23447Range945Trim Var.10558.5
V(Y[t],d=2,D=1)41674.6Range1314Trim Var.19560.8
V(Y[t],d=3,D=1)117813Range1917.5Trim Var.63132
V(Y[t],d=0,D=2)96388.7Range1396.5Trim Var.56619.5
V(Y[t],d=1,D=2)46135.9Range1102.5Trim Var.26288.4
V(Y[t],d=2,D=2)81671.2Range1376.5Trim Var.48441.4
V(Y[t],d=3,D=2)234587Range2495Trim Var.130693


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ; par4 = 12 ;
Parameters (R input):
par1 = 4 ;
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()