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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 computationSat, 29 Nov 2008 07:26:48 -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/Nov/29/t122796889601v68nynqlkcrj1.htm/, Retrieved Sun, 19 May 2024 07:21:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26294, Retrieved Sun, 19 May 2024 07:21:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact144

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] [Q3 workshop 4] [2008-11-29 14:26:48] [56fd94b954e08a6655cb7790b21ee404] [Current]
Feedback Forum
2008-12-06 14:43:18 [Ken Wright] [reply] 
De student heeft deze vraag niet helemaal goed beantwoord. d staat voor het aantal keer niet seizoenaal differentieren, de student stelt als de waarde bijvoorbeeld 3 is, dat de tijdreeks met 3 periodel wordt vertraagd, dit is niet waar het wilt zeggen dat de tijdreeks 3x na elkaar niet seizoenaal word gedifferentierd. De 2e kolom geeft de variantie weer na differentiatie, de variantie toont het risico of de volaliteit van de tijdreeks aan, deze kan best zo klein mogelijk zijn. Als je tijdreeks met veel outliers te maken heeft, kan er best gebruik gemaakt worden van de trimmed variance, deze 'knipt' de staarten eraf, dus de extreme outliers.
2008-12-08 16:03:37 [Birgit Van Dyck] [reply] 
De Variance Reduction Matrix geeft de waarden weer nadat er gedifferentieerd is. De gewone differentatie = d en de seizoenale differentiatie = D. D wordt gebruikt om seizoenaliteit te verwijderen. De 2de kolom bevat de varianties die het risico en de volatiliteit in de tijdreeks weergeeft. Deze waarden moeten zo klein mogelijk zijn. De kleinste variantie vinden we terug bij d= 1 en D= 0. De variantie is hier gelijk aan 1 en er is dus 1 keer gedifferentieerd.

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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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26294&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26294&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26294&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Variance Reduction Matrix
V(Y[t],d=0,D=0)33.0476793587174Range28Trim Var.21.8957080676182
V(Y[t],d=1,D=0)1.00084506362122Range2Trim Var.NA
V(Y[t],d=2,D=0)2.05229772207542Range4Trim Var.0
V(Y[t],d=3,D=0)6.16933861231908Range8Trim Var.2.74761399787911
V(Y[t],d=0,D=1)11.4405359006295Range22Trim Var.6.12451662799691
V(Y[t],d=1,D=1)1.99149914230909Range4Trim Var.0
V(Y[t],d=2,D=1)3.93400364855119Range8Trim Var.2.38808611665677
V(Y[t],d=3,D=1)11.9338161370026Range16Trim Var.6.55182777744648
V(Y[t],d=0,D=2)28.3145510835913Range34Trim Var.13.5655316357565
V(Y[t],d=1,D=2)6.15145458583167Range8Trim Var.2.50783761723110
V(Y[t],d=2,D=2)12.2198553090517Range16Trim Var.6.84033327251718
V(Y[t],d=3,D=2)37.2283656430286Range32Trim Var.20.1708290827571

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 33.0476793587174 & Range & 28 & Trim Var. & 21.8957080676182 \tabularnewline
V(Y[t],d=1,D=0) & 1.00084506362122 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.05229772207542 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.16933861231908 & Range & 8 & Trim Var. & 2.74761399787911 \tabularnewline
V(Y[t],d=0,D=1) & 11.4405359006295 & Range & 22 & Trim Var. & 6.12451662799691 \tabularnewline
V(Y[t],d=1,D=1) & 1.99149914230909 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.93400364855119 & Range & 8 & Trim Var. & 2.38808611665677 \tabularnewline
V(Y[t],d=3,D=1) & 11.9338161370026 & Range & 16 & Trim Var. & 6.55182777744648 \tabularnewline
V(Y[t],d=0,D=2) & 28.3145510835913 & Range & 34 & Trim Var. & 13.5655316357565 \tabularnewline
V(Y[t],d=1,D=2) & 6.15145458583167 & Range & 8 & Trim Var. & 2.50783761723110 \tabularnewline
V(Y[t],d=2,D=2) & 12.2198553090517 & Range & 16 & Trim Var. & 6.84033327251718 \tabularnewline
V(Y[t],d=3,D=2) & 37.2283656430286 & Range & 32 & Trim Var. & 20.1708290827571 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26294&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]33.0476793587174[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]21.8957080676182[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00084506362122[/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]2.05229772207542[/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]6.16933861231908[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.74761399787911[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]11.4405359006295[/C][C]Range[/C][C]22[/C][C]Trim Var.[/C][C]6.12451662799691[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.99149914230909[/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]3.93400364855119[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.38808611665677[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.9338161370026[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.55182777744648[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]28.3145510835913[/C][C]Range[/C][C]34[/C][C]Trim Var.[/C][C]13.5655316357565[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.15145458583167[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.50783761723110[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.2198553090517[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.84033327251718[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]37.2283656430286[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]20.1708290827571[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26294&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26294&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)33.0476793587174Range28Trim Var.21.8957080676182
V(Y[t],d=1,D=0)1.00084506362122Range2Trim Var.NA
V(Y[t],d=2,D=0)2.05229772207542Range4Trim Var.0
V(Y[t],d=3,D=0)6.16933861231908Range8Trim Var.2.74761399787911
V(Y[t],d=0,D=1)11.4405359006295Range22Trim Var.6.12451662799691
V(Y[t],d=1,D=1)1.99149914230909Range4Trim Var.0
V(Y[t],d=2,D=1)3.93400364855119Range8Trim Var.2.38808611665677
V(Y[t],d=3,D=1)11.9338161370026Range16Trim Var.6.55182777744648
V(Y[t],d=0,D=2)28.3145510835913Range34Trim Var.13.5655316357565
V(Y[t],d=1,D=2)6.15145458583167Range8Trim Var.2.50783761723110
V(Y[t],d=2,D=2)12.2198553090517Range16Trim Var.6.84033327251718
V(Y[t],d=3,D=2)37.2283656430286Range32Trim Var.20.1708290827571


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')