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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 04:34:39 -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/t1228217740f3drwqyrurrkal1.htm/, Retrieved Fri, 17 May 2024 06:16:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27611, Retrieved Fri, 17 May 2024 06:16:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact176

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] [marlies.polfliet_...] [2008-12-02 11:34:39] [e221948dd14811c7d88a6530ac2a8702] [Current]
Feedback Forum
2008-12-06 12:36:40 [Glenn Maras] [reply] 
correcte berekening en bespreking. De kleinste variantie ligt inderdaad bij d=1 en D=0, de variantie moet zo klein mogelijk zijn omdat dan het risico, de volatiliteit ook het kleinst is. Het is ook goed dat de student vermeld heeft wat d en D juist betekent.
2008-12-08 11:56:40 [Li Tang Hu] [reply] 
het is inderdaad zo dat men moet kijken naar de kleinste variantie om te weten hoe vaak men trendmatig en/of seizonaal moet differentieeren (in dit geval 1 keer trendmatig) kleinste variantie betekent het minste risico en dus het beste model.
2008-12-09 13:40:10 [Julian De Ruyter] [reply] 
Goede berekening, uitleg en legende opgemaakt.
Je merkt correct op dat bij d=1 en D=0 de variantie het laagste is (0.99987927662554). d=1 vormt dus het beste model...

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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=27611&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=27611&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27611&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)136.180104208417Range45Trim Var.99.1388357731733
V(Y[t],d=1,D=0)0.99987927662554Range2Trim Var.NA
V(Y[t],d=2,D=0)2.07645875251509Range4Trim Var.0
V(Y[t],d=3,D=0)6.31449990264166Range8Trim Var.2.72243276562714
V(Y[t],d=0,D=1)10.4147675632006Range16Trim Var.4.37909586756524
V(Y[t],d=1,D=1)2.02469135802469Range4Trim Var.0
V(Y[t],d=2,D=1)4.37936447329345Range8Trim Var.2.41091288229842
V(Y[t],d=3,D=1)13.5041322314050Range16Trim Var.6.65139949109415
V(Y[t],d=0,D=2)20.8862450243255Range26Trim Var.9.75139680568881
V(Y[t],d=1,D=2)6.10110592938041Range8Trim Var.2.69409900609785
V(Y[t],d=2,D=2)13.4545276134914Range16Trim Var.6.61969696969697
V(Y[t],d=3,D=2)42.0677249435625Range32Trim Var.25.5343837362997

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 136.180104208417 & Range & 45 & Trim Var. & 99.1388357731733 \tabularnewline
V(Y[t],d=1,D=0) & 0.99987927662554 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.07645875251509 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.31449990264166 & Range & 8 & Trim Var. & 2.72243276562714 \tabularnewline
V(Y[t],d=0,D=1) & 10.4147675632006 & Range & 16 & Trim Var. & 4.37909586756524 \tabularnewline
V(Y[t],d=1,D=1) & 2.02469135802469 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.37936447329345 & Range & 8 & Trim Var. & 2.41091288229842 \tabularnewline
V(Y[t],d=3,D=1) & 13.5041322314050 & Range & 16 & Trim Var. & 6.65139949109415 \tabularnewline
V(Y[t],d=0,D=2) & 20.8862450243255 & Range & 26 & Trim Var. & 9.75139680568881 \tabularnewline
V(Y[t],d=1,D=2) & 6.10110592938041 & Range & 8 & Trim Var. & 2.69409900609785 \tabularnewline
V(Y[t],d=2,D=2) & 13.4545276134914 & Range & 16 & Trim Var. & 6.61969696969697 \tabularnewline
V(Y[t],d=3,D=2) & 42.0677249435625 & Range & 32 & Trim Var. & 25.5343837362997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27611&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]136.180104208417[/C][C]Range[/C][C]45[/C][C]Trim Var.[/C][C]99.1388357731733[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.99987927662554[/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]2.07645875251509[/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]6.31449990264166[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.72243276562714[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]10.4147675632006[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]4.37909586756524[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.02469135802469[/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]4.37936447329345[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.41091288229842[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]13.5041322314050[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.65139949109415[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]20.8862450243255[/C][C]Range[/C][C]26[/C][C]Trim Var.[/C][C]9.75139680568881[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.10110592938041[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.69409900609785[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]13.4545276134914[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.61969696969697[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]42.0677249435625[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]25.5343837362997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27611&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27611&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)136.180104208417Range45Trim Var.99.1388357731733
V(Y[t],d=1,D=0)0.99987927662554Range2Trim Var.NA
V(Y[t],d=2,D=0)2.07645875251509Range4Trim Var.0
V(Y[t],d=3,D=0)6.31449990264166Range8Trim Var.2.72243276562714
V(Y[t],d=0,D=1)10.4147675632006Range16Trim Var.4.37909586756524
V(Y[t],d=1,D=1)2.02469135802469Range4Trim Var.0
V(Y[t],d=2,D=1)4.37936447329345Range8Trim Var.2.41091288229842
V(Y[t],d=3,D=1)13.5041322314050Range16Trim Var.6.65139949109415
V(Y[t],d=0,D=2)20.8862450243255Range26Trim Var.9.75139680568881
V(Y[t],d=1,D=2)6.10110592938041Range8Trim Var.2.69409900609785
V(Y[t],d=2,D=2)13.4545276134914Range16Trim Var.6.61969696969697
V(Y[t],d=3,D=2)42.0677249435625Range32Trim Var.25.5343837362997


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')