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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, 23 Dec 2016 09:50:27 +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/23/t1482483068ctv0vf8nb9tj8ro.htm/, Retrieved Sat, 03 May 2025 15:41:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302785, Retrieved Sat, 03 May 2025 15:41:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact135

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Forecasting] [ ARIMA FORECAST] [2016-12-15 19:00:32] [d1d385d9b7e195437bdc484ddbefdda4]
- RMPD  [ARIMA Backward Selection] [Arima Backward Se...] [2016-12-19 20:48:05] [d1d385d9b7e195437bdc484ddbefdda4]
- RMP     [ARIMA Forecasting] [Arima Forecast new ] [2016-12-21 12:59:28] [d1d385d9b7e195437bdc484ddbefdda4]
- RM          [Variance Reduction Matrix] [Variance Reductio...] [2016-12-23 08:50:27] [b95f76f605693b3a3343a287ab24f42a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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4100
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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=302785&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=302785&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302785&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)2099820Range5600Trim Var.1606670
V(Y[t],d=1,D=0)441728Range4200Trim Var.183675
V(Y[t],d=2,D=0)1290440Range7500Trim Var.576481
V(Y[t],d=3,D=0)4158220Range13300Trim Var.1765240
V(Y[t],d=0,D=1)116804Range1800Trim Var.62086.3
V(Y[t],d=1,D=1)208825Range3050Trim Var.83782.3
V(Y[t],d=2,D=1)656130Range5400Trim Var.268728
V(Y[t],d=3,D=1)2169000Range10450Trim Var.836389
V(Y[t],d=0,D=2)263654Range3050Trim Var.123378
V(Y[t],d=1,D=2)555651Range5400Trim Var.187896
V(Y[t],d=2,D=2)1736170Range10450Trim Var.525260
V(Y[t],d=3,D=2)5675500Range18150Trim Var.1551490

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 2099820 & Range & 5600 & Trim Var. & 1606670 \tabularnewline
V(Y[t],d=1,D=0) & 441728 & Range & 4200 & Trim Var. & 183675 \tabularnewline
V(Y[t],d=2,D=0) & 1290440 & Range & 7500 & Trim Var. & 576481 \tabularnewline
V(Y[t],d=3,D=0) & 4158220 & Range & 13300 & Trim Var. & 1765240 \tabularnewline
V(Y[t],d=0,D=1) & 116804 & Range & 1800 & Trim Var. & 62086.3 \tabularnewline
V(Y[t],d=1,D=1) & 208825 & Range & 3050 & Trim Var. & 83782.3 \tabularnewline
V(Y[t],d=2,D=1) & 656130 & Range & 5400 & Trim Var. & 268728 \tabularnewline
V(Y[t],d=3,D=1) & 2169000 & Range & 10450 & Trim Var. & 836389 \tabularnewline
V(Y[t],d=0,D=2) & 263654 & Range & 3050 & Trim Var. & 123378 \tabularnewline
V(Y[t],d=1,D=2) & 555651 & Range & 5400 & Trim Var. & 187896 \tabularnewline
V(Y[t],d=2,D=2) & 1736170 & Range & 10450 & Trim Var. & 525260 \tabularnewline
V(Y[t],d=3,D=2) & 5675500 & Range & 18150 & Trim Var. & 1551490 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302785&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]2099820[/C][C]Range[/C][C]5600[/C][C]Trim Var.[/C][C]1606670[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]441728[/C][C]Range[/C][C]4200[/C][C]Trim Var.[/C][C]183675[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1290440[/C][C]Range[/C][C]7500[/C][C]Trim Var.[/C][C]576481[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]4158220[/C][C]Range[/C][C]13300[/C][C]Trim Var.[/C][C]1765240[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]116804[/C][C]Range[/C][C]1800[/C][C]Trim Var.[/C][C]62086.3[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]208825[/C][C]Range[/C][C]3050[/C][C]Trim Var.[/C][C]83782.3[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]656130[/C][C]Range[/C][C]5400[/C][C]Trim Var.[/C][C]268728[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]2169000[/C][C]Range[/C][C]10450[/C][C]Trim Var.[/C][C]836389[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]263654[/C][C]Range[/C][C]3050[/C][C]Trim Var.[/C][C]123378[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]555651[/C][C]Range[/C][C]5400[/C][C]Trim Var.[/C][C]187896[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]1736170[/C][C]Range[/C][C]10450[/C][C]Trim Var.[/C][C]525260[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]5675500[/C][C]Range[/C][C]18150[/C][C]Trim Var.[/C][C]1551490[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302785&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302785&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)2099820Range5600Trim Var.1606670
V(Y[t],d=1,D=0)441728Range4200Trim Var.183675
V(Y[t],d=2,D=0)1290440Range7500Trim Var.576481
V(Y[t],d=3,D=0)4158220Range13300Trim Var.1765240
V(Y[t],d=0,D=1)116804Range1800Trim Var.62086.3
V(Y[t],d=1,D=1)208825Range3050Trim Var.83782.3
V(Y[t],d=2,D=1)656130Range5400Trim Var.268728
V(Y[t],d=3,D=1)2169000Range10450Trim Var.836389
V(Y[t],d=0,D=2)263654Range3050Trim Var.123378
V(Y[t],d=1,D=2)555651Range5400Trim Var.187896
V(Y[t],d=2,D=2)1736170Range10450Trim Var.525260
V(Y[t],d=3,D=2)5675500Range18150Trim Var.1551490


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = 3 ; par4 = TRUE ;
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()