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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 computationTue, 02 Dec 2008 06:18:18 -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/2008/Dec/02/t1228223982slatsyusmp3etek.htm/, Retrieved Wed, 13 May 2026 18:50:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27732, Retrieved Wed, 13 May 2026 18:50:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact484

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Variance Reduction Matrix] [] [2008-12-02 13:18:18] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum
2008-12-04 09:50:06 [72e979bcc364082694890d2eccc1a66f] [reply] 
Uit deze tabel kan je inderdaad afleiden dat de éénmaal trendmatig differentiëren tot de beste resultaten zou leiden aangezien hier de kleinste variantie wordt weergegeven.
2008-12-05 19:53:48 [Bert Moons] [reply] 
De laagste variatie treed inderdaad op bij d=1 D=0, en ook de laagste getrimde variatie treed op bij deze differentiaties.
2008-12-06 16:24:35 [Bénédicte Soens] [reply] 
Het juiste aantal keer dat er gedifferentieerd moet worden, werd op de juiste manier gevonden bij d is 1. (laagste variantie). Dus er moet 1 maal niet-seizoenaal gedifferentieerd worden dichter bij een stationaire tijdreeks te komen.
2008-12-07 12:27:49 [Lana Van Wesemael] [reply] 
De student is hier vergeten om de ACF en spectral analysis toe te passen. Hij heeft enkel gebruik gemaakt van de VRM en de standard deviation mean plot. Dit is niet voldoende, het zou immers kunnen de andere methodes een andere d of D waarde bekomen.
2008-12-09 14:01:23 [Jules De Bruycker] [reply] 
Hier werd er enkel gewerkt met de variance reduction matrix om de waarden voor d, D en lambda te vinden. Men had beter ook nog gewerkt met de autocorrelatie functie en met de spectrum analyse.
2008-12-14 14:53:24 [Steven Vanhooreweghe] [reply] 
het vrm is goed geintrepreteerd. Als reactie op voorgaande collega-studenten: De ACF en de spectrum analyse zijn toch wel degelijk gemaakt? Er is wel geen link gemaakt naar de berekening van de spectrum analyse.
2008-12-15 13:46:26 [Katja van Hek] [reply] 
De VRM heeft de kleinste waarde bij d=1 en D=0, er moet dus 1 keer trendmatig gedifferentieerd worden om het model meer stationair te maken. De getrimde variantie is bij d=1 ook het kleinst. Een goede interpretatie dus.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5,1
4,9
5,2
5,1
4,6
3,7
3,9
3,1
2,8
2,6
2,2
1,8
1,3
1,2
1,4
1,3
1,3
1,9
1,9
2,1
2,0
1,9
1,9
1,9
1,8
1,7
1,6
1,7
1,9
1,7
1,3
2,0
2,0
2,3
2,0
1,7
2,3
2,4
2,4
2,3
2,1
2,1
2,5
2,0
1,8
1,7
1,9
2,1
1,4
1,6
1,7
1,6
1,9
1,6
1,1
1,3
1,6
1,6
1,7
1,6
1,7
1,6
1,5
1,6
1,1
1,5
1,4
1,3
0,9
1,2
0,9
1,1
1,3
1,3
1,4
1,2
1,7
2,0
3,0
3,1
3,2
2,7
2,8
3,0
2,8
3,1
3,1
3,2
3,1
2,7
2,2
2,2
2,1
2,3
2,5
2,3
2,6

Tables (Output of Computation)





Summary of computational 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 computational 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=27732&T=0

[TABLE]
[ROW][C]Summary of computational 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=27732&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27732&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 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)0.835798969072165Range4.3Trim Var.0.378535151029137
V(Y[t],d=1,D=0)0.100051535087719Range1.9Trim Var.0.04275
V(Y[t],d=2,D=0)0.200716685330347Range2.1Trim Var.0.120238095238095
V(Y[t],d=3,D=0)0.618064516129032Range3.9Trim Var.0.381495983935743
V(Y[t],d=0,D=1)1.531Range6.1Trim Var.0.537624953720844
V(Y[t],d=1,D=1)0.28512908777969Range3Trim Var.0.129434663536776
V(Y[t],d=2,D=1)0.620220393770203Range3.6Trim Var.0.380464231354642
V(Y[t],d=3,D=1)1.91821288768443Range5.9Trim Var.1.21360719874804
V(Y[t],d=0,D=2)2.8635197869102Range7.7Trim Var.1.67066346153846
V(Y[t],d=1,D=2)0.890422535211267Range4.7Trim Var.0.455437788018433
V(Y[t],d=2,D=2)2.07179879275654Range6.5Trim Var.1.35197132616487
V(Y[t],d=3,D=2)6.39321739130435Range10.2Trim Var.4.37290322580645

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.835798969072165 & Range & 4.3 & Trim Var. & 0.378535151029137 \tabularnewline
V(Y[t],d=1,D=0) & 0.100051535087719 & Range & 1.9 & Trim Var. & 0.04275 \tabularnewline
V(Y[t],d=2,D=0) & 0.200716685330347 & Range & 2.1 & Trim Var. & 0.120238095238095 \tabularnewline
V(Y[t],d=3,D=0) & 0.618064516129032 & Range & 3.9 & Trim Var. & 0.381495983935743 \tabularnewline
V(Y[t],d=0,D=1) & 1.531 & Range & 6.1 & Trim Var. & 0.537624953720844 \tabularnewline
V(Y[t],d=1,D=1) & 0.28512908777969 & Range & 3 & Trim Var. & 0.129434663536776 \tabularnewline
V(Y[t],d=2,D=1) & 0.620220393770203 & Range & 3.6 & Trim Var. & 0.380464231354642 \tabularnewline
V(Y[t],d=3,D=1) & 1.91821288768443 & Range & 5.9 & Trim Var. & 1.21360719874804 \tabularnewline
V(Y[t],d=0,D=2) & 2.8635197869102 & Range & 7.7 & Trim Var. & 1.67066346153846 \tabularnewline
V(Y[t],d=1,D=2) & 0.890422535211267 & Range & 4.7 & Trim Var. & 0.455437788018433 \tabularnewline
V(Y[t],d=2,D=2) & 2.07179879275654 & Range & 6.5 & Trim Var. & 1.35197132616487 \tabularnewline
V(Y[t],d=3,D=2) & 6.39321739130435 & Range & 10.2 & Trim Var. & 4.37290322580645 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27732&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.835798969072165[/C][C]Range[/C][C]4.3[/C][C]Trim Var.[/C][C]0.378535151029137[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.100051535087719[/C][C]Range[/C][C]1.9[/C][C]Trim Var.[/C][C]0.04275[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.200716685330347[/C][C]Range[/C][C]2.1[/C][C]Trim Var.[/C][C]0.120238095238095[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.618064516129032[/C][C]Range[/C][C]3.9[/C][C]Trim Var.[/C][C]0.381495983935743[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]1.531[/C][C]Range[/C][C]6.1[/C][C]Trim Var.[/C][C]0.537624953720844[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.28512908777969[/C][C]Range[/C][C]3[/C][C]Trim Var.[/C][C]0.129434663536776[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.620220393770203[/C][C]Range[/C][C]3.6[/C][C]Trim Var.[/C][C]0.380464231354642[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]1.91821288768443[/C][C]Range[/C][C]5.9[/C][C]Trim Var.[/C][C]1.21360719874804[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]2.8635197869102[/C][C]Range[/C][C]7.7[/C][C]Trim Var.[/C][C]1.67066346153846[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.890422535211267[/C][C]Range[/C][C]4.7[/C][C]Trim Var.[/C][C]0.455437788018433[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]2.07179879275654[/C][C]Range[/C][C]6.5[/C][C]Trim Var.[/C][C]1.35197132616487[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]6.39321739130435[/C][C]Range[/C][C]10.2[/C][C]Trim Var.[/C][C]4.37290322580645[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27732&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27732&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)0.835798969072165Range4.3Trim Var.0.378535151029137
V(Y[t],d=1,D=0)0.100051535087719Range1.9Trim Var.0.04275
V(Y[t],d=2,D=0)0.200716685330347Range2.1Trim Var.0.120238095238095
V(Y[t],d=3,D=0)0.618064516129032Range3.9Trim Var.0.381495983935743
V(Y[t],d=0,D=1)1.531Range6.1Trim Var.0.537624953720844
V(Y[t],d=1,D=1)0.28512908777969Range3Trim Var.0.129434663536776
V(Y[t],d=2,D=1)0.620220393770203Range3.6Trim Var.0.380464231354642
V(Y[t],d=3,D=1)1.91821288768443Range5.9Trim Var.1.21360719874804
V(Y[t],d=0,D=2)2.8635197869102Range7.7Trim Var.1.67066346153846
V(Y[t],d=1,D=2)0.890422535211267Range4.7Trim Var.0.455437788018433
V(Y[t],d=2,D=2)2.07179879275654Range6.5Trim Var.1.35197132616487
V(Y[t],d=3,D=2)6.39321739130435Range10.2Trim Var.4.37290322580645


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')