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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_variancereduction.wasp
Title produced by softwareVariance Reduction Matrix
Date of computationThu, 29 Nov 2007 07:19:54 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/29/t1196345376tqvvvo3y41j4xbi.htm/, Retrieved Wed, 11 Feb 2026 09:29:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7485, Retrieved Wed, 11 Feb 2026 09:29:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsstationary time series
Estimated Impact408

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] [variantie reducti...] [2007-11-29 14:19:54] [7eb5b05bf0841f2a6d4b99da83be8d69] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7485&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7485&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7485&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)0.000306866197183099Range0.06Trim Var.0.000141666666666667
V(Y[t],d=1,D=0)2.53923541247485e-05Range0.02Trim Var.0
V(Y[t],d=2,D=0)6.37681159420291e-05Range0.04Trim Var.0
V(Y[t],d=3,D=0)0.000200000000000000Range0.07Trim Var.8.12429378531075e-05
V(Y[t],d=0,D=1)0.000112853107344633Range0.04Trim Var.6.16470588235295e-05
V(Y[t],d=1,D=1)4.65225014611339e-05Range0.03Trim Var.0
V(Y[t],d=2,D=1)9.47368421052633e-05Range0.05Trim Var.2.02702702702703e-05
V(Y[t],d=3,D=1)0.00028389724310777Range0.09Trim Var.0.000133333333333334
V(Y[t],d=0,D=2)0.000377127659574469Range0.08Trim Var.0.000162887989203779
V(Y[t],d=1,D=2)0.000122756706753007Range0.05Trim Var.4.32432432432433e-05
V(Y[t],d=2,D=2)0.000217777777777778Range0.07Trim Var.4.63054187192119e-05
V(Y[t],d=3,D=2)0.000645252525252526Range0.11Trim Var.0.000239304812834225

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.000306866197183099 & Range & 0.06 & Trim Var. & 0.000141666666666667 \tabularnewline
V(Y[t],d=1,D=0) & 2.53923541247485e-05 & Range & 0.02 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=0) & 6.37681159420291e-05 & Range & 0.04 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 0.000200000000000000 & Range & 0.07 & Trim Var. & 8.12429378531075e-05 \tabularnewline
V(Y[t],d=0,D=1) & 0.000112853107344633 & Range & 0.04 & Trim Var. & 6.16470588235295e-05 \tabularnewline
V(Y[t],d=1,D=1) & 4.65225014611339e-05 & Range & 0.03 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 9.47368421052633e-05 & Range & 0.05 & Trim Var. & 2.02702702702703e-05 \tabularnewline
V(Y[t],d=3,D=1) & 0.00028389724310777 & Range & 0.09 & Trim Var. & 0.000133333333333334 \tabularnewline
V(Y[t],d=0,D=2) & 0.000377127659574469 & Range & 0.08 & Trim Var. & 0.000162887989203779 \tabularnewline
V(Y[t],d=1,D=2) & 0.000122756706753007 & Range & 0.05 & Trim Var. & 4.32432432432433e-05 \tabularnewline
V(Y[t],d=2,D=2) & 0.000217777777777778 & Range & 0.07 & Trim Var. & 4.63054187192119e-05 \tabularnewline
V(Y[t],d=3,D=2) & 0.000645252525252526 & Range & 0.11 & Trim Var. & 0.000239304812834225 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7485&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.000306866197183099[/C][C]Range[/C][C]0.06[/C][C]Trim Var.[/C][C]0.000141666666666667[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]2.53923541247485e-05[/C][C]Range[/C][C]0.02[/C][C]Trim Var.[/C][C]0[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]6.37681159420291e-05[/C][C]Range[/C][C]0.04[/C][C]Trim Var.[/C][C]0[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.000200000000000000[/C][C]Range[/C][C]0.07[/C][C]Trim Var.[/C][C]8.12429378531075e-05[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.000112853107344633[/C][C]Range[/C][C]0.04[/C][C]Trim Var.[/C][C]6.16470588235295e-05[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]4.65225014611339e-05[/C][C]Range[/C][C]0.03[/C][C]Trim Var.[/C][C]0[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]9.47368421052633e-05[/C][C]Range[/C][C]0.05[/C][C]Trim Var.[/C][C]2.02702702702703e-05[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]0.00028389724310777[/C][C]Range[/C][C]0.09[/C][C]Trim Var.[/C][C]0.000133333333333334[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]0.000377127659574469[/C][C]Range[/C][C]0.08[/C][C]Trim Var.[/C][C]0.000162887989203779[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.000122756706753007[/C][C]Range[/C][C]0.05[/C][C]Trim Var.[/C][C]4.32432432432433e-05[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.000217777777777778[/C][C]Range[/C][C]0.07[/C][C]Trim Var.[/C][C]4.63054187192119e-05[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]0.000645252525252526[/C][C]Range[/C][C]0.11[/C][C]Trim Var.[/C][C]0.000239304812834225[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7485&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7485&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)0.000306866197183099Range0.06Trim Var.0.000141666666666667
V(Y[t],d=1,D=0)2.53923541247485e-05Range0.02Trim Var.0
V(Y[t],d=2,D=0)6.37681159420291e-05Range0.04Trim Var.0
V(Y[t],d=3,D=0)0.000200000000000000Range0.07Trim Var.8.12429378531075e-05
V(Y[t],d=0,D=1)0.000112853107344633Range0.04Trim Var.6.16470588235295e-05
V(Y[t],d=1,D=1)4.65225014611339e-05Range0.03Trim Var.0
V(Y[t],d=2,D=1)9.47368421052633e-05Range0.05Trim Var.2.02702702702703e-05
V(Y[t],d=3,D=1)0.00028389724310777Range0.09Trim Var.0.000133333333333334
V(Y[t],d=0,D=2)0.000377127659574469Range0.08Trim Var.0.000162887989203779
V(Y[t],d=1,D=2)0.000122756706753007Range0.05Trim Var.4.32432432432433e-05
V(Y[t],d=2,D=2)0.000217777777777778Range0.07Trim Var.4.63054187192119e-05
V(Y[t],d=3,D=2)0.000645252525252526Range0.11Trim Var.0.000239304812834225


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
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)
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(x,lag=1,differences=smalld)
if (bigd > 0) myx <- diff(myx,lag=par1,differences=bigd)
a<-table.element(a,var(myx))
a<-table.element(a,'Range',header=TRUE)
a<-table.element(a,max(myx)-min(myx))
a<-table.element(a,'Trim Var.',header=TRUE)
smyx <- sort(myx)
sn <- length(smyx)
a<-table.element(a,var(smyx[smyx>quantile(smyx,0.05) & smyxa<-table.row.end(a)
}
}
a<-table.end(a)
table.save(a,file='mytable.tab')