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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 11:54:18 -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/t12281577051s6h8fzy21liwc7.htm/, Retrieved Sun, 05 May 2024 09:39:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27153, Retrieved Sun, 05 May 2024 09:39:13 +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] [q3 / 7] [2008-11-30 17:25:28] [4300be8b33fd3dcdacd2aa9800ceba23]
F           [Law of Averages] [Non Stationary Ti...] [2008-12-01 18:54:18] [1fa440a634ec541bd583650ead0404df] [Current]
Feedback Forum
2008-12-07 15:06:30 [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 differentieren en geen enkele keer seizonaal.
2008-12-08 23:00:17 [Gregory Van Overmeiren] [reply] 
Goed geantwoord. De Variance Reduction Matrix heb je nodig om verschillende differentiatie waarden op een tijdreeks te zoeken en ze toont de daarbij gerelateerde variatie. Waar de variatie het kleinst is, noteren we het meest adequate stationaire karakter. Door de lange termijn trend zo klein mogelijk te maken, kunnen we zoveel mogelijk van de tijdreeks verklaren. We moesten hier dus de optimale d en D indentificeren. We zien dan de waarde van d=1 en D=0 optimaal is.
2008-12-08 23:57:28 [Bonifer Spillemaeckers] [reply] 
Naar mijn mening geeft de student ook hier een correct antwoord.

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'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=27153&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=27153&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27153&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)74.8041042084168Range36Trim Var.48.8128820382436
V(Y[t],d=1,D=0)1.00132795711906Range2Trim Var.NA
V(Y[t],d=2,D=0)1.83501006036217Range4Trim Var.0
V(Y[t],d=3,D=0)5.31449990264166Range8Trim Var.2.5479920323845
V(Y[t],d=0,D=1)14.5554246473895Range18Trim Var.7.98178256112765
V(Y[t],d=1,D=1)2.00816285142089Range4Trim Var.0
V(Y[t],d=2,D=1)3.69477748080268Range8Trim Var.2.24850892526087
V(Y[t],d=3,D=1)10.7272727272727Range16Trim Var.6.12892269916125
V(Y[t],d=0,D=2)27.4420698805838Range28Trim Var.15.5661723818350
V(Y[t],d=1,D=2)6.17714412613813Range8Trim Var.2.61950400158087
V(Y[t],d=2,D=2)11.1881428354787Range16Trim Var.5.96659382985815
V(Y[t],d=3,D=2)32.4150929874225Range30Trim Var.20.407623528337

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 74.8041042084168 & Range & 36 & Trim Var. & 48.8128820382436 \tabularnewline
V(Y[t],d=1,D=0) & 1.00132795711906 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.83501006036217 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.31449990264166 & Range & 8 & Trim Var. & 2.5479920323845 \tabularnewline
V(Y[t],d=0,D=1) & 14.5554246473895 & Range & 18 & Trim Var. & 7.98178256112765 \tabularnewline
V(Y[t],d=1,D=1) & 2.00816285142089 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.69477748080268 & Range & 8 & Trim Var. & 2.24850892526087 \tabularnewline
V(Y[t],d=3,D=1) & 10.7272727272727 & Range & 16 & Trim Var. & 6.12892269916125 \tabularnewline
V(Y[t],d=0,D=2) & 27.4420698805838 & Range & 28 & Trim Var. & 15.5661723818350 \tabularnewline
V(Y[t],d=1,D=2) & 6.17714412613813 & Range & 8 & Trim Var. & 2.61950400158087 \tabularnewline
V(Y[t],d=2,D=2) & 11.1881428354787 & Range & 16 & Trim Var. & 5.96659382985815 \tabularnewline
V(Y[t],d=3,D=2) & 32.4150929874225 & Range & 30 & Trim Var. & 20.407623528337 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27153&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]74.8041042084168[/C][C]Range[/C][C]36[/C][C]Trim Var.[/C][C]48.8128820382436[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00132795711906[/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]1.83501006036217[/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]5.31449990264166[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.5479920323845[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]14.5554246473895[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]7.98178256112765[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.00816285142089[/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]3.69477748080268[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.24850892526087[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]10.7272727272727[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.12892269916125[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]27.4420698805838[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]15.5661723818350[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.17714412613813[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.61950400158087[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.1881428354787[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]5.96659382985815[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]32.4150929874225[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]20.407623528337[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27153&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27153&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)74.8041042084168Range36Trim Var.48.8128820382436
V(Y[t],d=1,D=0)1.00132795711906Range2Trim Var.NA
V(Y[t],d=2,D=0)1.83501006036217Range4Trim Var.0
V(Y[t],d=3,D=0)5.31449990264166Range8Trim Var.2.5479920323845
V(Y[t],d=0,D=1)14.5554246473895Range18Trim Var.7.98178256112765
V(Y[t],d=1,D=1)2.00816285142089Range4Trim Var.0
V(Y[t],d=2,D=1)3.69477748080268Range8Trim Var.2.24850892526087
V(Y[t],d=3,D=1)10.7272727272727Range16Trim Var.6.12892269916125
V(Y[t],d=0,D=2)27.4420698805838Range28Trim Var.15.5661723818350
V(Y[t],d=1,D=2)6.17714412613813Range8Trim Var.2.61950400158087
V(Y[t],d=2,D=2)11.1881428354787Range16Trim Var.5.96659382985815
V(Y[t],d=3,D=2)32.4150929874225Range30Trim Var.20.407623528337


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 500 ; par2 = 0.5 ;
Parameters (R input):
par1 = 500 ; par2 = 0.5 ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')