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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_rwalk.wasp
Title produced by softwareLaw of Averages
Date of computationTue, 02 Dec 2008 04:35:28 -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/t1228217778n7k0lvdog0so9j0.htm/, Retrieved Thu, 23 May 2024 07:11:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27612, Retrieved Thu, 23 May 2024 07:11:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact169

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         [Law of Averages] [tinneke_debock.wo...] [2008-12-02 11:35:28] [20137734a2343a7bbbd59daaec7ad301] [Current]
Feedback Forum
2008-12-08 13:39:02 [Dave Bellekens] [reply] 
De student geeft een zeer beknopte uitleg bij de VRM.
Ze merkt inderdaad op dat de variantie het risico meet dat in de tijdreeks zit en dat we op zoek moeten naar de laagste waarde om zoveel mogelijk te verklaren.

Je kan ook kijken naar de getrimde variantie, omdat deze geen rekening houdt met outliers en zo geen vertekend beeld kan geven. (wat bij de gewone variantie wel het geval kan zijn)
2008-12-08 15:40:48 [Jonas Scheltjens] [reply] 
Wat de student zegt is wel juist, maar er wordt echter geen antwoord gegeven op de vraag. Verder is deze conclusie zeer beperkt. 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. Doorgaans beschrijft men de variantie ook wel als het risico of de volaliteit die eigen is aan de tijdreeks.Wanneer men dan deze kleinste waarde heeft gekozen, kan men makkelijk zien welke de beste differentiatie die we moeten nemen om een stationaire reeks te bekomen. Uit de tabel blijkt dat hiervoor d=1en D=0 nodig is.

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Dataset

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27612&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]1 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=27612&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27612&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)391.424913827655Range67Trim Var.287.143700282268
V(Y[t],d=1,D=0)0.990704300166598Range2Trim Var.NA
V(Y[t],d=2,D=0)1.96378269617706Range4Trim Var.0
V(Y[t],d=3,D=0)5.80638670734082Range8Trim Var.2.65963060686016
V(Y[t],d=0,D=1)14.5188507759114Range18Trim Var.6.8935748617638
V(Y[t],d=1,D=1)1.86829585688815Range4Trim Var.0
V(Y[t],d=2,D=1)3.63709643205634Range8Trim Var.2.12017791463519
V(Y[t],d=3,D=1)11.0081963022919Range16Trim Var.6.03331344819923
V(Y[t],d=0,D=2)28.7745953118089Range30Trim Var.15.5662957976047
V(Y[t],d=1,D=2)5.67930712858095Range8Trim Var.2.41125786259776
V(Y[t],d=2,D=2)11.0697496008064Range16Trim Var.5.7540584916608
V(Y[t],d=3,D=2)34.2202673164439Range30Trim Var.20.6564255471406

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 391.424913827655 & Range & 67 & Trim Var. & 287.143700282268 \tabularnewline
V(Y[t],d=1,D=0) & 0.990704300166598 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.96378269617706 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.80638670734082 & Range & 8 & Trim Var. & 2.65963060686016 \tabularnewline
V(Y[t],d=0,D=1) & 14.5188507759114 & Range & 18 & Trim Var. & 6.8935748617638 \tabularnewline
V(Y[t],d=1,D=1) & 1.86829585688815 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.63709643205634 & Range & 8 & Trim Var. & 2.12017791463519 \tabularnewline
V(Y[t],d=3,D=1) & 11.0081963022919 & Range & 16 & Trim Var. & 6.03331344819923 \tabularnewline
V(Y[t],d=0,D=2) & 28.7745953118089 & Range & 30 & Trim Var. & 15.5662957976047 \tabularnewline
V(Y[t],d=1,D=2) & 5.67930712858095 & Range & 8 & Trim Var. & 2.41125786259776 \tabularnewline
V(Y[t],d=2,D=2) & 11.0697496008064 & Range & 16 & Trim Var. & 5.7540584916608 \tabularnewline
V(Y[t],d=3,D=2) & 34.2202673164439 & Range & 30 & Trim Var. & 20.6564255471406 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27612&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]391.424913827655[/C][C]Range[/C][C]67[/C][C]Trim Var.[/C][C]287.143700282268[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.990704300166598[/C][C]Range[/C][C]2[/C][C]Trim Var.[/C][C]NA[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1.96378269617706[/C][C]Range[/C][C]4[/C][C]Trim Var.[/C][C]0[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]5.80638670734082[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.65963060686016[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]14.5188507759114[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]6.8935748617638[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.86829585688815[/C][C]Range[/C][C]4[/C][C]Trim Var.[/C][C]0[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]3.63709643205634[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.12017791463519[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.0081963022919[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.03331344819923[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]28.7745953118089[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]15.5662957976047[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.67930712858095[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.41125786259776[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.0697496008064[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]5.7540584916608[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]34.2202673164439[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]20.6564255471406[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27612&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27612&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)391.424913827655Range67Trim Var.287.143700282268
V(Y[t],d=1,D=0)0.990704300166598Range2Trim Var.NA
V(Y[t],d=2,D=0)1.96378269617706Range4Trim Var.0
V(Y[t],d=3,D=0)5.80638670734082Range8Trim Var.2.65963060686016
V(Y[t],d=0,D=1)14.5188507759114Range18Trim Var.6.8935748617638
V(Y[t],d=1,D=1)1.86829585688815Range4Trim Var.0
V(Y[t],d=2,D=1)3.63709643205634Range8Trim Var.2.12017791463519
V(Y[t],d=3,D=1)11.0081963022919Range16Trim Var.6.03331344819923
V(Y[t],d=0,D=2)28.7745953118089Range30Trim Var.15.5662957976047
V(Y[t],d=1,D=2)5.67930712858095Range8Trim Var.2.41125786259776
V(Y[t],d=2,D=2)11.0697496008064Range16Trim Var.5.7540584916608
V(Y[t],d=3,D=2)34.2202673164439Range30Trim Var.20.6564255471406


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 500 ; par2 = 0.5 ;
Parameters (R input):
par1 = 500 ; par2 = 0.5 ;
R code (references can be found in the software module):
n <- as.numeric(par1)
p <- as.numeric(par2)
heads=rbinom(n-1,1,p)
a=2*(heads)-1
b=diffinv(a,xi=0)
c=1:n
pheads=(diffinv(heads,xi=.5))/c
bitmap(file='test1.png')
op=par(mfrow=c(2,1))
plot(c,b,type='n',main='Law of Averages',xlab='Toss Number',ylab='Excess of Heads',lwd=2,cex.lab=1.5,cex.main=2)
lines(c,b,col='red')
lines(c,rep(0,n),col='black')
plot(c,pheads,type='n',xlab='Toss Number',ylab='Proportion of Heads',lwd=2,cex.lab=1.5)
lines(c,pheads,col='blue')
lines(c,rep(.5,n),col='black')
par(op)
dev.off()
b
par1 <- as.numeric(12)
x <- as.array(b)
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')