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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 13:36:59 -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/t122816384875zlqdgyzeeycdv.htm/, Retrieved Sun, 12 May 2024 10:43:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27358, Retrieved Sun, 12 May 2024 10:43:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact172

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 Random Walk Si...] [2008-12-01 20:36:59] [35348cd8592af0baf5f138bd59921307] [Current]
Feedback Forum
2008-12-03 15:34:17 [Ken Van den Heuvel] [reply] 
VRM test verschillende differentie waarden op de reeks en toont vervolgens de bijhorende variantie. Een reeks benaderd het beste het stationaire karakter wanneer de variantie het kleinst is, maw wanneer de mean stationair is.

Uit de tabel blijkt dat bij d=1 en D=0 de variantie het kleinst is met 1.00181085061690.

d = het aantal keer dat de reeks niet-seizoenaal gedifferentieerd is.
D = het aantal keer dat de reeks seizoenaal gedifferentieerd is.

Wanneer een niet-seizoenale random-walk niet-seizoenaal gedifferentieerd word, dan word deze stationair. Uit onze berekening blijkt dat we 1 maal niet-seizoenaal moeten differentiëren om de kleinste variantie te krijgen. Maw, onze reeks wordt stationair door niet-seizoenaal te differentiëren => onze reeks was dus om te beginnen niet-seizoenaal. Dit staaft de stelling van geen seizoenaliteit in Q1 nog verder.
2008-12-08 16:42:17 [Lindsay Heyndrickx] [reply] 
Dit is correct. Hier wordt gebruik gemaakt van de nabla operator. Dit wordt gebruikt om tijdreeksen stationair te maken. De kleine d laat de spreiding aanpassen de grote D zorgt voor de seizonalteit. S wordt hier steeds door 12 vervangen omdat we met maanden werken. De variantie moet hier zo klein mogelijk zijn want dit is het deel dat we niet kunnen verklaren. De beste waarde staat dus op de tweede rij waar de variantie = 1.00190742931646. De kleine d is hier dus gelijk aan 1 en de grote D is hier gelijk aan nul.

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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=27358&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=27358&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27358&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)109.166332665331Range42Trim Var.78.1118556121876
V(Y[t],d=1,D=0)0.999074454129142Range2Trim Var.NA
V(Y[t],d=2,D=0)2.04426559356137Range4Trim Var.0
V(Y[t],d=3,D=0)6.18546764457714Range8Trim Var.2.67440925537142
V(Y[t],d=0,D=1)10.6700609284007Range20Trim Var.3.81151315383381
V(Y[t],d=1,D=1)1.79396827811156Range4Trim Var.0
V(Y[t],d=2,D=1)3.63709643205634Range8Trim Var.2.12017791463519
V(Y[t],d=3,D=1)10.7851069268126Range16Trim Var.5.70544485634847
V(Y[t],d=0,D=2)18.3641751437417Range26Trim Var.6.14014721215045
V(Y[t],d=1,D=2)5.2067332889185Range8Trim Var.2.45329536094708
V(Y[t],d=2,D=2)10.6469166198339Range16Trim Var.6.00968523002421
V(Y[t],d=3,D=2)31.2626939477550Range32Trim Var.19.2599222057760

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 109.166332665331 & Range & 42 & Trim Var. & 78.1118556121876 \tabularnewline
V(Y[t],d=1,D=0) & 0.999074454129142 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.04426559356137 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.18546764457714 & Range & 8 & Trim Var. & 2.67440925537142 \tabularnewline
V(Y[t],d=0,D=1) & 10.6700609284007 & Range & 20 & Trim Var. & 3.81151315383381 \tabularnewline
V(Y[t],d=1,D=1) & 1.79396827811156 & 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) & 10.7851069268126 & Range & 16 & Trim Var. & 5.70544485634847 \tabularnewline
V(Y[t],d=0,D=2) & 18.3641751437417 & Range & 26 & Trim Var. & 6.14014721215045 \tabularnewline
V(Y[t],d=1,D=2) & 5.2067332889185 & Range & 8 & Trim Var. & 2.45329536094708 \tabularnewline
V(Y[t],d=2,D=2) & 10.6469166198339 & Range & 16 & Trim Var. & 6.00968523002421 \tabularnewline
V(Y[t],d=3,D=2) & 31.2626939477550 & Range & 32 & Trim Var. & 19.2599222057760 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27358&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]109.166332665331[/C][C]Range[/C][C]42[/C][C]Trim Var.[/C][C]78.1118556121876[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.999074454129142[/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]2.04426559356137[/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]6.18546764457714[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.67440925537142[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]10.6700609284007[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]3.81151315383381[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.79396827811156[/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]10.7851069268126[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]5.70544485634847[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]18.3641751437417[/C][C]Range[/C][C]26[/C][C]Trim Var.[/C][C]6.14014721215045[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.2067332889185[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.45329536094708[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]10.6469166198339[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.00968523002421[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]31.2626939477550[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]19.2599222057760[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27358&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27358&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)109.166332665331Range42Trim Var.78.1118556121876
V(Y[t],d=1,D=0)0.999074454129142Range2Trim Var.NA
V(Y[t],d=2,D=0)2.04426559356137Range4Trim Var.0
V(Y[t],d=3,D=0)6.18546764457714Range8Trim Var.2.67440925537142
V(Y[t],d=0,D=1)10.6700609284007Range20Trim Var.3.81151315383381
V(Y[t],d=1,D=1)1.79396827811156Range4Trim Var.0
V(Y[t],d=2,D=1)3.63709643205634Range8Trim Var.2.12017791463519
V(Y[t],d=3,D=1)10.7851069268126Range16Trim Var.5.70544485634847
V(Y[t],d=0,D=2)18.3641751437417Range26Trim Var.6.14014721215045
V(Y[t],d=1,D=2)5.2067332889185Range8Trim Var.2.45329536094708
V(Y[t],d=2,D=2)10.6469166198339Range16Trim Var.6.00968523002421
V(Y[t],d=3,D=2)31.2626939477550Range32Trim Var.19.2599222057760


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')