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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 12:19:56 -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/t12281592575rspnwnhymq15yx.htm/, Retrieved Sun, 05 May 2024 20:01:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27214, Retrieved Sun, 05 May 2024 20:01:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact169

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] [Q1 Non Stationary...] [2008-12-01 19:19:56] [70ba55c7ff8e068610dc28fc16e6d1e2] [Current]
Feedback Forum
2008-12-03 10:19:17 [Romina Machiels] [reply] 
Correct beantwoord.
2008-12-06 15:46:14 [Kevin Engels] [reply] 
De student geeft het correcte antwoord. Op de Variance Reduction Matrix zien we in de eerste kolom V(Y[t],d=0,D=0) staan: dit is de variantie van functie Y(t) nadat je x aantal keer differentieert(= waarde van d aanpassen). De tweede kolom geeft de spreiding van de reeks weer. Wanneer we een eerste keer gingen differentiëren, hoopten we dat de eerste variantie van 54 zou verkleinen. Bij d=1 kwam men dan ook tot een waarde van 1,0005.
2008-12-08 19:57:15 [Ruben Jacobs] [reply] 
Waar de variatie het kleinst is, bekom je het meest adequate stationaire karakter. Door de lange termijn trend zo klein mogelijk te maken, kunnen we zoveel mogelijk van de tijdreeks verklaren. De bedoeling hier was dus om de optimale d en D te indentificeren. We zien dan dat de waarde optimaal is bij d=1 en D=0. Dit wil zeggen dat indien je de reeks 1 keer differentieert je het lange termijn effect kunt uitzuiveren.
Er is hier blijkbaar geen sprake van seizoenaliteit (want D = 0).

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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=27214&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=27214&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27214&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)61.6012985971944Range35Trim Var.40.4231621907593
V(Y[t],d=1,D=0)1.00055532752251Range2Trim Var.NA
V(Y[t],d=2,D=0)1.96378269617706Range4Trim Var.0
V(Y[t],d=3,D=0)6.03225806451613Range8Trim Var.2.48751507571358
V(Y[t],d=0,D=1)15.3831588514492Range20Trim Var.6.86512984307735
V(Y[t],d=1,D=1)2.04108466212048Range4Trim Var.0
V(Y[t],d=2,D=1)3.92577319587629Range8Trim Var.2.25272949170432
V(Y[t],d=3,D=1)11.6694214876033Range16Trim Var.6.44486236159759
V(Y[t],d=0,D=2)29.7991154356479Range24Trim Var.17.2064703744093
V(Y[t],d=1,D=2)6.08422829224961Range8Trim Var.2.75977211584111
V(Y[t],d=2,D=2)11.4418426240622Range16Trim Var.5.90172932330827
V(Y[t],d=3,D=2)33.1944673379439Range32Trim Var.20.0454143861944

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 61.6012985971944 & Range & 35 & Trim Var. & 40.4231621907593 \tabularnewline
V(Y[t],d=1,D=0) & 1.00055532752251 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.96378269617706 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.03225806451613 & Range & 8 & Trim Var. & 2.48751507571358 \tabularnewline
V(Y[t],d=0,D=1) & 15.3831588514492 & Range & 20 & Trim Var. & 6.86512984307735 \tabularnewline
V(Y[t],d=1,D=1) & 2.04108466212048 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.92577319587629 & Range & 8 & Trim Var. & 2.25272949170432 \tabularnewline
V(Y[t],d=3,D=1) & 11.6694214876033 & Range & 16 & Trim Var. & 6.44486236159759 \tabularnewline
V(Y[t],d=0,D=2) & 29.7991154356479 & Range & 24 & Trim Var. & 17.2064703744093 \tabularnewline
V(Y[t],d=1,D=2) & 6.08422829224961 & Range & 8 & Trim Var. & 2.75977211584111 \tabularnewline
V(Y[t],d=2,D=2) & 11.4418426240622 & Range & 16 & Trim Var. & 5.90172932330827 \tabularnewline
V(Y[t],d=3,D=2) & 33.1944673379439 & Range & 32 & Trim Var. & 20.0454143861944 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27214&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]61.6012985971944[/C][C]Range[/C][C]35[/C][C]Trim Var.[/C][C]40.4231621907593[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00055532752251[/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]1.96378269617706[/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]6.03225806451613[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.48751507571358[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]15.3831588514492[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]6.86512984307735[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.04108466212048[/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]3.92577319587629[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.25272949170432[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.6694214876033[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.44486236159759[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]29.7991154356479[/C][C]Range[/C][C]24[/C][C]Trim Var.[/C][C]17.2064703744093[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.08422829224961[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.75977211584111[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.4418426240622[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]5.90172932330827[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]33.1944673379439[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]20.0454143861944[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27214&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27214&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)61.6012985971944Range35Trim Var.40.4231621907593
V(Y[t],d=1,D=0)1.00055532752251Range2Trim Var.NA
V(Y[t],d=2,D=0)1.96378269617706Range4Trim Var.0
V(Y[t],d=3,D=0)6.03225806451613Range8Trim Var.2.48751507571358
V(Y[t],d=0,D=1)15.3831588514492Range20Trim Var.6.86512984307735
V(Y[t],d=1,D=1)2.04108466212048Range4Trim Var.0
V(Y[t],d=2,D=1)3.92577319587629Range8Trim Var.2.25272949170432
V(Y[t],d=3,D=1)11.6694214876033Range16Trim Var.6.44486236159759
V(Y[t],d=0,D=2)29.7991154356479Range24Trim Var.17.2064703744093
V(Y[t],d=1,D=2)6.08422829224961Range8Trim Var.2.75977211584111
V(Y[t],d=2,D=2)11.4418426240622Range16Trim Var.5.90172932330827
V(Y[t],d=3,D=2)33.1944673379439Range32Trim Var.20.0454143861944


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')