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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 10:18:52 -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/t12281519615nkot2zfk0fm2kl.htm/, Retrieved Sun, 05 May 2024 13:43:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27005, Retrieved Sun, 05 May 2024 13:43:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact204

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] [] [2008-12-01 17:18:52] [c0a347e3519123f7eef62b705326dad9] [Current]
Feedback Forum
2008-12-07 14:50:38 [Roland Feldman] [reply] 
De VRM gaat trachten om de spreading van de tijdreeks te verkleinen door te differentieren, d staat voor een gewone differentiatie tewijl D staat voor een seizonale differentiatie. De eerste kolom in de matrix geeft aan hoe vaak er gewoon gedifferentieerd is en hoe vaak seizonaal gedifferentieerd. De 2e kolom geeft de variantie van onze tijdreeks weer, we moeten zoals eerder vermeld kijken naar de kleinste spreiding om een zo stationair mogelijke tijdreeks te bekomen, de optimale spreiding bekomen we bij 1.0018108, dus na 1 keer gewoon te differentiëren en geen enkele keer seizonaal.
2008-12-09 07:06:39 [Bonifer Spillemaeckers] [reply] 
De student begrijpt ook wel deze vraagstelling.

We gaan hier door differentiatie de spreiding van de dataset verkleinen. We kijken naar waar de variatie het kleinst is om zo de dataset het meest stationair te maken. Doordat we de LT-trend zo klein mogelijk proberen te maken, kunnen we toch de dataset beter proberen te verklaren. We gaan hier dus zoeken naar de optimale d en D (optimale waarde d = 1, optimale waarde D = 0). Inderdaad, als we de dataset 1 maal differentiëren, zien we dat we hier de meest optimale spreiding bekomen.

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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=27005&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=27005&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27005&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)45.033122244489Range28Trim Var.27.3801829372738
V(Y[t],d=1,D=0)0.999074454129142Range2Trim Var.NA
V(Y[t],d=2,D=0)2.01207243460765Range4Trim Var.0
V(Y[t],d=3,D=0)6.0483870967742Range8Trim Var.2.69530185780947
V(Y[t],d=0,D=1)11.5269633419733Range18Trim Var.6.42796532005165
V(Y[t],d=1,D=1)2.04936581573588Range4Trim Var.0
V(Y[t],d=2,D=1)4.26390055576768Range8Trim Var.2.40870553471985
V(Y[t],d=3,D=1)12.9255516741927Range16Trim Var.6.80743769223954
V(Y[t],d=0,D=2)23.0142945599292Range28Trim Var.11.9740234957362
V(Y[t],d=1,D=2)6.06735065511881Range8Trim Var.2.80853794031579
V(Y[t],d=2,D=2)13.0822918618032Range16Trim Var.6.59907139492632
V(Y[t],d=3,D=2)39.805066829111Range30Trim Var.22.5518731619997

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 45.033122244489 & Range & 28 & Trim Var. & 27.3801829372738 \tabularnewline
V(Y[t],d=1,D=0) & 0.999074454129142 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.01207243460765 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.0483870967742 & Range & 8 & Trim Var. & 2.69530185780947 \tabularnewline
V(Y[t],d=0,D=1) & 11.5269633419733 & Range & 18 & Trim Var. & 6.42796532005165 \tabularnewline
V(Y[t],d=1,D=1) & 2.04936581573588 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.26390055576768 & Range & 8 & Trim Var. & 2.40870553471985 \tabularnewline
V(Y[t],d=3,D=1) & 12.9255516741927 & Range & 16 & Trim Var. & 6.80743769223954 \tabularnewline
V(Y[t],d=0,D=2) & 23.0142945599292 & Range & 28 & Trim Var. & 11.9740234957362 \tabularnewline
V(Y[t],d=1,D=2) & 6.06735065511881 & Range & 8 & Trim Var. & 2.80853794031579 \tabularnewline
V(Y[t],d=2,D=2) & 13.0822918618032 & Range & 16 & Trim Var. & 6.59907139492632 \tabularnewline
V(Y[t],d=3,D=2) & 39.805066829111 & Range & 30 & Trim Var. & 22.5518731619997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27005&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]45.033122244489[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]27.3801829372738[/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]2.01207243460765[/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]6.0483870967742[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.69530185780947[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]11.5269633419733[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]6.42796532005165[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.04936581573588[/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]4.26390055576768[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.40870553471985[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.9255516741927[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.80743769223954[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]23.0142945599292[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]11.9740234957362[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.06735065511881[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.80853794031579[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]13.0822918618032[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.59907139492632[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]39.805066829111[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]22.5518731619997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27005&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27005&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)45.033122244489Range28Trim Var.27.3801829372738
V(Y[t],d=1,D=0)0.999074454129142Range2Trim Var.NA
V(Y[t],d=2,D=0)2.01207243460765Range4Trim Var.0
V(Y[t],d=3,D=0)6.0483870967742Range8Trim Var.2.69530185780947
V(Y[t],d=0,D=1)11.5269633419733Range18Trim Var.6.42796532005165
V(Y[t],d=1,D=1)2.04936581573588Range4Trim Var.0
V(Y[t],d=2,D=1)4.26390055576768Range8Trim Var.2.40870553471985
V(Y[t],d=3,D=1)12.9255516741927Range16Trim Var.6.80743769223954
V(Y[t],d=0,D=2)23.0142945599292Range28Trim Var.11.9740234957362
V(Y[t],d=1,D=2)6.06735065511881Range8Trim Var.2.80853794031579
V(Y[t],d=2,D=2)13.0822918618032Range16Trim Var.6.59907139492632
V(Y[t],d=3,D=2)39.805066829111Range30Trim Var.22.5518731619997


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')