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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 computationFri, 28 Nov 2008 11:04:02 -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/28/t1227895468cp9clp0wz7vt79f.htm/, Retrieved Mon, 20 May 2024 09:29:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26151, Retrieved Mon, 20 May 2024 09:29:21 +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] [17.3] [2008-11-28 18:04:02] [0458bd763b171003ec052ce63099d477] [Current]
Feedback Forum
2008-12-04 12:10:51 [Steven Vercammen] [reply] 
Dit klopt volledig.
De 2de kolom geeft de varianties aan na differentiatie. De variantie van de tijdreeks drukt een soort van risico, volatiliteit uit. De bedoeling van het differentiëren is om deze variantie te minimaliseren zodat we zoveel mogelijk van de tijdreeks kunnen verklaren. De kleine d wijst op een normale differentiatie (om een LT trend te verwijderen), de grote D wijst op een seizoenale differentiatie (om seizoenaliteit te verwijderen). De volgende formule wordt toegepast. NABLA d NABLADs Yt = et waarbij s gelijk is aan 12 omdat we werken met maandcijfers. De NABLA operator = Yt – Yt-1. Uit de matrix kunnen we afleiden dat de differentiatie optimaal is bij d=1 of D=1.
2008-12-08 18:02:27 [5faab2fc6fb120339944528a32d48a04] [reply] 
Het is inderdaad zo zoals de student zegt. De variantie van de tijdsreeks is het risico of de volatiliteit dat in het model zit. Hoe kleiner de variantie hoe meer we van de volatiliteit kan verklaren. De differentiatie die nogdig is om de meeste volatiliteit te verklaren is dus de kleinste. In dit geval horende bij lijn 2.
2008-12-09 09:51:21 [Katrien Smolders] [reply] 
Wat je zegt is volledig correct. Hoe kleiner de variantie, hoe meer je van de tijdreeks kan verklaren. In jou geval zijn de gegevens 1 keer normaal gedifferentieerd (om LT trend eruit te halen).

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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=26151&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=26151&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26151&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)61.5134428857715Range33Trim Var.43.1162349700726
V(Y[t],d=1,D=0)0.997625773635625Range2Trim Var.NA
V(Y[t],d=2,D=0)1.99597585513078Range4Trim Var.0
V(Y[t],d=3,D=0)6.0483870967742Range8Trim Var.2.60350106203765
V(Y[t],d=0,D=1)11.2923553371259Range18Trim Var.6.90617014330583
V(Y[t],d=1,D=1)1.95878013537151Range4Trim Var.0
V(Y[t],d=2,D=1)3.95049849391201Range8Trim Var.2.34211271594449
V(Y[t],d=3,D=1)12.1404788276391Range16Trim Var.6.49927523769747
V(Y[t],d=0,D=2)24.4872888102609Range26Trim Var.11.7891829689298
V(Y[t],d=1,D=2)5.9492071952032Range8Trim Var.2.55720841905365
V(Y[t],d=2,D=2)11.8899920607309Range16Trim Var.6.7322821171006
V(Y[t],d=3,D=2)36.4321854731788Range28Trim Var.21.6470347352700

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 61.5134428857715 & Range & 33 & Trim Var. & 43.1162349700726 \tabularnewline
V(Y[t],d=1,D=0) & 0.997625773635625 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.99597585513078 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.0483870967742 & Range & 8 & Trim Var. & 2.60350106203765 \tabularnewline
V(Y[t],d=0,D=1) & 11.2923553371259 & Range & 18 & Trim Var. & 6.90617014330583 \tabularnewline
V(Y[t],d=1,D=1) & 1.95878013537151 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.95049849391201 & Range & 8 & Trim Var. & 2.34211271594449 \tabularnewline
V(Y[t],d=3,D=1) & 12.1404788276391 & Range & 16 & Trim Var. & 6.49927523769747 \tabularnewline
V(Y[t],d=0,D=2) & 24.4872888102609 & Range & 26 & Trim Var. & 11.7891829689298 \tabularnewline
V(Y[t],d=1,D=2) & 5.9492071952032 & Range & 8 & Trim Var. & 2.55720841905365 \tabularnewline
V(Y[t],d=2,D=2) & 11.8899920607309 & Range & 16 & Trim Var. & 6.7322821171006 \tabularnewline
V(Y[t],d=3,D=2) & 36.4321854731788 & Range & 28 & Trim Var. & 21.6470347352700 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26151&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]61.5134428857715[/C][C]Range[/C][C]33[/C][C]Trim Var.[/C][C]43.1162349700726[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.997625773635625[/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]1.99597585513078[/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]2.60350106203765[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]11.2923553371259[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]6.90617014330583[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.95878013537151[/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]3.95049849391201[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.34211271594449[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.1404788276391[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.49927523769747[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]24.4872888102609[/C][C]Range[/C][C]26[/C][C]Trim Var.[/C][C]11.7891829689298[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.9492071952032[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.55720841905365[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.8899920607309[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.7322821171006[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]36.4321854731788[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]21.6470347352700[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26151&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26151&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)61.5134428857715Range33Trim Var.43.1162349700726
V(Y[t],d=1,D=0)0.997625773635625Range2Trim Var.NA
V(Y[t],d=2,D=0)1.99597585513078Range4Trim Var.0
V(Y[t],d=3,D=0)6.0483870967742Range8Trim Var.2.60350106203765
V(Y[t],d=0,D=1)11.2923553371259Range18Trim Var.6.90617014330583
V(Y[t],d=1,D=1)1.95878013537151Range4Trim Var.0
V(Y[t],d=2,D=1)3.95049849391201Range8Trim Var.2.34211271594449
V(Y[t],d=3,D=1)12.1404788276391Range16Trim Var.6.49927523769747
V(Y[t],d=0,D=2)24.4872888102609Range26Trim Var.11.7891829689298
V(Y[t],d=1,D=2)5.9492071952032Range8Trim Var.2.55720841905365
V(Y[t],d=2,D=2)11.8899920607309Range16Trim Var.6.7322821171006
V(Y[t],d=3,D=2)36.4321854731788Range28Trim Var.21.6470347352700


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')