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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 08:57:49 -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/t1228233495ely9lqwlff8pg29.htm/, Retrieved Fri, 17 May 2024 05:02:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27986, Retrieved Fri, 17 May 2024 05:02:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact177

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Law of Averages] [Random Walk Simul...] [2008-11-25 18:31:28] [b98453cac15ba1066b407e146608df68]
F RMPD    [Variance Reduction Matrix] [W7Q8] [2008-12-02 15:57:49] [823d674fbf3a4e0ec71bbbd5140f82c6] [Current]
Feedback Forum
2008-12-08 16:02:49 [Kevin Vermeiren] [reply] 
De student geeft een beperkt antwoord. Het klopt dat via de variance reduction matrix de waarden voor de parameters het gemakkelijkst kunnen worden afgelezen. Hier had nog wel vermeld mogen worden dat deze methode minder betrouwbaar is daar deze gevoelig is voor outliers. Indien deze aanwezig zijn is het beter te werken met de getrimde varianties. Hier uit zijn de 5% hoogste en laagste waarden uit de reeks weggelaten. Dit geeft dan een betrouwbaarder beeld. Het klopt dat de parameter d de waarde 1 krijgt en D de waarde 0. Dit is duidelijk te zien in de tabel.
2008-12-08 21:45:34 [] [reply] 
De Variance Reduction Matrix wordt gebruikt om op een snelle manier de varianties weer te geven en dusdanig dient men de kleinste variantie te kiezen, want des te kleiner de variantie, des te meer er kan verklaard worden van de tijdreeks. Men beschrijft de variantie ook wel als het risico of de volaliteit die eigen is aan de tijdreeks. Men moet kiezen voor de kleinste variantie omdat hierbij vermeldt staat welke de beste differentiatie is die we moeten nemen om een stationaire reeks te bekomen. Hier is dat bij d=1 en D=0.
2008-12-09 11:41:41 [Yannick Van Schil] [reply] 
correct geantwoord,op de variance reduction matrix kunnen de waarden van de parameters kunnen worden afgelezen. Als al op vorige vragen vermeld kan je beter de getrimde variance gebruiken bij aanwezigheid van outliers

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
115,6
120,3
121,9
121,7
118,9
113,4
114
117,5
120,9
125,1
124,7
128,2
149,7
163,6
173,9
164,5
154,2
147,9
159,3
170,3
170
174,2
190,8
179,9
240,8
241,9
241,1
239,6
220,8
209,3
209,9
228,3
242,1
226,4
231,5
229,7
257,6
260
264,4
268,8
271,4
273,8
277,4
268,2
264,6
266,6
266
267,4
289,8
294
310,3
311,7
302,1
298,2
299,2
296,2
299
300
299,4
300,2
470,2
472,1
484,8
513,4
547,2
548,1
544,7
521,1
459
413,2

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27986&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27986&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27986&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'George Udny Yule' @ 72.249.76.132






Variance Reduction Matrix
V(Y[t],d=0,D=0)13844.5742857143Range434.7Trim Var.8983.11958751983
V(Y[t],d=1,D=0)660.457621483376Range232.1Trim Var.72.8199617486339
V(Y[t],d=2,D=0)1147.15651229148Range337.3Trim Var.124.763330508475
V(Y[t],d=3,D=0)3483.66913161465Range516.2Trim Var.357.186329631795
V(Y[t],d=0,D=1)3920.25817301875Range233.1Trim Var.2354.31505279035
V(Y[t],d=1,D=1)693.70073934837Range212.5Trim Var.124.864517647059
V(Y[t],d=2,D=1)1217.55272727273Range298.1Trim Var.280.219432653061
V(Y[t],d=3,D=1)3605.61055218855Range446.9Trim Var.812.088537414965
V(Y[t],d=0,D=2)6124.34388405797Range299.8Trim Var.3583.91101923077
V(Y[t],d=1,D=2)1246.83427272727Range225.5Trim Var.380.915762483131
V(Y[t],d=2,D=2)2286.90386892177Range314.1Trim Var.679.83348506401
V(Y[t],d=3,D=2)6700.6072535991Range496.5Trim Var.1896.69355855855

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 13844.5742857143 & Range & 434.7 & Trim Var. & 8983.11958751983 \tabularnewline
V(Y[t],d=1,D=0) & 660.457621483376 & Range & 232.1 & Trim Var. & 72.8199617486339 \tabularnewline
V(Y[t],d=2,D=0) & 1147.15651229148 & Range & 337.3 & Trim Var. & 124.763330508475 \tabularnewline
V(Y[t],d=3,D=0) & 3483.66913161465 & Range & 516.2 & Trim Var. & 357.186329631795 \tabularnewline
V(Y[t],d=0,D=1) & 3920.25817301875 & Range & 233.1 & Trim Var. & 2354.31505279035 \tabularnewline
V(Y[t],d=1,D=1) & 693.70073934837 & Range & 212.5 & Trim Var. & 124.864517647059 \tabularnewline
V(Y[t],d=2,D=1) & 1217.55272727273 & Range & 298.1 & Trim Var. & 280.219432653061 \tabularnewline
V(Y[t],d=3,D=1) & 3605.61055218855 & Range & 446.9 & Trim Var. & 812.088537414965 \tabularnewline
V(Y[t],d=0,D=2) & 6124.34388405797 & Range & 299.8 & Trim Var. & 3583.91101923077 \tabularnewline
V(Y[t],d=1,D=2) & 1246.83427272727 & Range & 225.5 & Trim Var. & 380.915762483131 \tabularnewline
V(Y[t],d=2,D=2) & 2286.90386892177 & Range & 314.1 & Trim Var. & 679.83348506401 \tabularnewline
V(Y[t],d=3,D=2) & 6700.6072535991 & Range & 496.5 & Trim Var. & 1896.69355855855 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27986&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]13844.5742857143[/C][C]Range[/C][C]434.7[/C][C]Trim Var.[/C][C]8983.11958751983[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]660.457621483376[/C][C]Range[/C][C]232.1[/C][C]Trim Var.[/C][C]72.8199617486339[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1147.15651229148[/C][C]Range[/C][C]337.3[/C][C]Trim Var.[/C][C]124.763330508475[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]3483.66913161465[/C][C]Range[/C][C]516.2[/C][C]Trim Var.[/C][C]357.186329631795[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]3920.25817301875[/C][C]Range[/C][C]233.1[/C][C]Trim Var.[/C][C]2354.31505279035[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]693.70073934837[/C][C]Range[/C][C]212.5[/C][C]Trim Var.[/C][C]124.864517647059[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]1217.55272727273[/C][C]Range[/C][C]298.1[/C][C]Trim Var.[/C][C]280.219432653061[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]3605.61055218855[/C][C]Range[/C][C]446.9[/C][C]Trim Var.[/C][C]812.088537414965[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]6124.34388405797[/C][C]Range[/C][C]299.8[/C][C]Trim Var.[/C][C]3583.91101923077[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]1246.83427272727[/C][C]Range[/C][C]225.5[/C][C]Trim Var.[/C][C]380.915762483131[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]2286.90386892177[/C][C]Range[/C][C]314.1[/C][C]Trim Var.[/C][C]679.83348506401[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]6700.6072535991[/C][C]Range[/C][C]496.5[/C][C]Trim Var.[/C][C]1896.69355855855[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27986&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27986&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)13844.5742857143Range434.7Trim Var.8983.11958751983
V(Y[t],d=1,D=0)660.457621483376Range232.1Trim Var.72.8199617486339
V(Y[t],d=2,D=0)1147.15651229148Range337.3Trim Var.124.763330508475
V(Y[t],d=3,D=0)3483.66913161465Range516.2Trim Var.357.186329631795
V(Y[t],d=0,D=1)3920.25817301875Range233.1Trim Var.2354.31505279035
V(Y[t],d=1,D=1)693.70073934837Range212.5Trim Var.124.864517647059
V(Y[t],d=2,D=1)1217.55272727273Range298.1Trim Var.280.219432653061
V(Y[t],d=3,D=1)3605.61055218855Range446.9Trim Var.812.088537414965
V(Y[t],d=0,D=2)6124.34388405797Range299.8Trim Var.3583.91101923077
V(Y[t],d=1,D=2)1246.83427272727Range225.5Trim Var.380.915762483131
V(Y[t],d=2,D=2)2286.90386892177Range314.1Trim Var.679.83348506401
V(Y[t],d=3,D=2)6700.6072535991Range496.5Trim Var.1896.69355855855


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 12 ; par5 = 1 ; par6 = 0 ; par7 = 0 ;
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')