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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 computationMon, 01 Dec 2008 12:21:20 -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/01/t12281593495id3lkftu75jir9.htm/, Retrieved Sun, 05 May 2024 18:11:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27219, Retrieved Sun, 05 May 2024 18:11:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact186

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] [non-stationary ti...] [2008-12-01 19:21:20] [e7b1048c2c3a353441b9143db4404b91] [Current]
Feedback Forum
2008-12-07 15:32:04 [Toon Wouters] [reply] 
Goede interpretatie. De variantie van de tijdreeks is het risico in de tijdreeks. We trachten de variantie zo klein mogelijk te maken, zo kan men meer verklaren.
2008-12-08 18:17:54 [Jasmine Hendrikx] [reply] 
Eigen evaluatie:
De berekening is goed uitgevoerd en de conclusie is goed. Het is inderdaad zo dat de VRM een overzicht geeft van alle varianties met een verschillende combinatie van d en D. Er wordt ook uitgelegd wat deze d en D juist doen. Hierbij zou er nog de volgende formule vermeld kunnen worden Nd* NsD*Yt=Et ( N is nabla, normaal wordt deze voorgesteld door een omgekeerde driehoek, D en d zijn exponenten van nabla(N) en s is een index). Kleine d is dan inderdaad het aantal keer dat we gewoon differentiëren en hoofdletter D heeft dan betrekking op het seizoenaal differentiëren. Als je met maandcijfers werkt, zal s altijd gelijk zijn aan 12. Het is ook juist dat je naar de combinatie van d en D moet kijken met de kleinste variantie, aangezien de variantie van de tijdreeks het risico/ de volatiliteit aangeeft die in de tijdreeks zit. Je wilt zoveel mogelijk verklaren, dus je neemt de kleinste variantie. Er zou nog bij mogen staan dat we uit de VRM kunnen afleiden dat de variantie het kleinst is bij D=0 en d=1.

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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'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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27219&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27219&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27219&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'George Udny Yule' @ 72.249.76.132






Variance Reduction Matrix
V(Y[t],d=0,D=0)131.028040080160Range48Trim Var.71.7914100590198
V(Y[t],d=1,D=0)0.99987927662554Range2Trim Var.NA
V(Y[t],d=2,D=0)1.98791140416798Range4Trim Var.0
V(Y[t],d=3,D=0)5.85483870967742Range8Trim Var.2.72017775308985
V(Y[t],d=0,D=1)12.2581209815868Range18Trim Var.5.86010820493579
V(Y[t],d=1,D=1)2.17277190491884Range4Trim Var.0
V(Y[t],d=2,D=1)4.42884900937593Range8Trim Var.2.27679646967619
V(Y[t],d=3,D=1)13.4214194427878Range16Trim Var.6.54964415339507
V(Y[t],d=0,D=2)24.2313135780628Range28Trim Var.14.9216066729114
V(Y[t],d=1,D=2)6.7586231401288Range8Trim Var.2.72284171015289
V(Y[t],d=2,D=2)13.8942739137028Range16Trim Var.6.62740560979739
V(Y[t],d=3,D=2)42.5677786935178Range32Trim Var.22.0375210281946

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 131.028040080160 & Range & 48 & Trim Var. & 71.7914100590198 \tabularnewline
V(Y[t],d=1,D=0) & 0.99987927662554 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.98791140416798 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.85483870967742 & Range & 8 & Trim Var. & 2.72017775308985 \tabularnewline
V(Y[t],d=0,D=1) & 12.2581209815868 & Range & 18 & Trim Var. & 5.86010820493579 \tabularnewline
V(Y[t],d=1,D=1) & 2.17277190491884 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.42884900937593 & Range & 8 & Trim Var. & 2.27679646967619 \tabularnewline
V(Y[t],d=3,D=1) & 13.4214194427878 & Range & 16 & Trim Var. & 6.54964415339507 \tabularnewline
V(Y[t],d=0,D=2) & 24.2313135780628 & Range & 28 & Trim Var. & 14.9216066729114 \tabularnewline
V(Y[t],d=1,D=2) & 6.7586231401288 & Range & 8 & Trim Var. & 2.72284171015289 \tabularnewline
V(Y[t],d=2,D=2) & 13.8942739137028 & Range & 16 & Trim Var. & 6.62740560979739 \tabularnewline
V(Y[t],d=3,D=2) & 42.5677786935178 & Range & 32 & Trim Var. & 22.0375210281946 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27219&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]131.028040080160[/C][C]Range[/C][C]48[/C][C]Trim Var.[/C][C]71.7914100590198[/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]1.98791140416798[/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]5.85483870967742[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.72017775308985[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.2581209815868[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]5.86010820493579[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.17277190491884[/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]4.42884900937593[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.27679646967619[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]13.4214194427878[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.54964415339507[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]24.2313135780628[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]14.9216066729114[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.7586231401288[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.72284171015289[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]13.8942739137028[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.62740560979739[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]42.5677786935178[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]22.0375210281946[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27219&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27219&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)131.028040080160Range48Trim Var.71.7914100590198
V(Y[t],d=1,D=0)0.99987927662554Range2Trim Var.NA
V(Y[t],d=2,D=0)1.98791140416798Range4Trim Var.0
V(Y[t],d=3,D=0)5.85483870967742Range8Trim Var.2.72017775308985
V(Y[t],d=0,D=1)12.2581209815868Range18Trim Var.5.86010820493579
V(Y[t],d=1,D=1)2.17277190491884Range4Trim Var.0
V(Y[t],d=2,D=1)4.42884900937593Range8Trim Var.2.27679646967619
V(Y[t],d=3,D=1)13.4214194427878Range16Trim Var.6.54964415339507
V(Y[t],d=0,D=2)24.2313135780628Range28Trim Var.14.9216066729114
V(Y[t],d=1,D=2)6.7586231401288Range8Trim Var.2.72284171015289
V(Y[t],d=2,D=2)13.8942739137028Range16Trim Var.6.62740560979739
V(Y[t],d=3,D=2)42.5677786935178Range32Trim Var.22.0375210281946


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')