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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 05:40:52 -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/Nov/28/t1227876275rpsmbknb6kw0c17.htm/, Retrieved Sun, 19 May 2024 11:14:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26050, Retrieved Sun, 19 May 2024 11:14:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact211

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] [Variance reductio...] [2008-11-28 12:40:52] [09074fbe368d26382bb94e5bb318a104] [Current]
Feedback Forum
2008-12-04 13:33:17 [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=0.
2008-12-08 19:16:11 [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.

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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=26050&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=26050&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26050&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)28.2291623246493Range27Trim Var.18.2300715890244
V(Y[t],d=1,D=0)1.00200400801603Range2Trim Var.NA
V(Y[t],d=2,D=0)1.90742850678367Range4Trim Var.0
V(Y[t],d=3,D=0)5.45966119296424Range8Trim Var.2.73073314913577
V(Y[t],d=0,D=1)11.9422358366715Range20Trim Var.5.99520383693046
V(Y[t],d=1,D=1)2.09874853178526Range4Trim Var.0
V(Y[t],d=2,D=1)3.82680412371134Range8Trim Var.0.963719170095267
V(Y[t],d=3,D=1)10.7602624179944Range16Trim Var.6.57707747892413
V(Y[t],d=0,D=2)26.5083414418399Range32Trim Var.11.2899583918586
V(Y[t],d=1,D=2)6.45567843659782Range8Trim Var.2.73310353106618
V(Y[t],d=2,D=2)11.4669449871098Range16Trim Var.6.51375053214134
V(Y[t],d=3,D=2)31.7371268857276Range30Trim Var.20.3227412205933

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 28.2291623246493 & Range & 27 & Trim Var. & 18.2300715890244 \tabularnewline
V(Y[t],d=1,D=0) & 1.00200400801603 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.90742850678367 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.45966119296424 & Range & 8 & Trim Var. & 2.73073314913577 \tabularnewline
V(Y[t],d=0,D=1) & 11.9422358366715 & Range & 20 & Trim Var. & 5.99520383693046 \tabularnewline
V(Y[t],d=1,D=1) & 2.09874853178526 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.82680412371134 & Range & 8 & Trim Var. & 0.963719170095267 \tabularnewline
V(Y[t],d=3,D=1) & 10.7602624179944 & Range & 16 & Trim Var. & 6.57707747892413 \tabularnewline
V(Y[t],d=0,D=2) & 26.5083414418399 & Range & 32 & Trim Var. & 11.2899583918586 \tabularnewline
V(Y[t],d=1,D=2) & 6.45567843659782 & Range & 8 & Trim Var. & 2.73310353106618 \tabularnewline
V(Y[t],d=2,D=2) & 11.4669449871098 & Range & 16 & Trim Var. & 6.51375053214134 \tabularnewline
V(Y[t],d=3,D=2) & 31.7371268857276 & Range & 30 & Trim Var. & 20.3227412205933 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26050&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]28.2291623246493[/C][C]Range[/C][C]27[/C][C]Trim Var.[/C][C]18.2300715890244[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00200400801603[/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]1.90742850678367[/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]5.45966119296424[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.73073314913577[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]11.9422358366715[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]5.99520383693046[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.09874853178526[/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]3.82680412371134[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]0.963719170095267[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]10.7602624179944[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.57707747892413[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]26.5083414418399[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]11.2899583918586[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.45567843659782[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.73310353106618[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.4669449871098[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.51375053214134[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]31.7371268857276[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]20.3227412205933[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26050&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26050&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)28.2291623246493Range27Trim Var.18.2300715890244
V(Y[t],d=1,D=0)1.00200400801603Range2Trim Var.NA
V(Y[t],d=2,D=0)1.90742850678367Range4Trim Var.0
V(Y[t],d=3,D=0)5.45966119296424Range8Trim Var.2.73073314913577
V(Y[t],d=0,D=1)11.9422358366715Range20Trim Var.5.99520383693046
V(Y[t],d=1,D=1)2.09874853178526Range4Trim Var.0
V(Y[t],d=2,D=1)3.82680412371134Range8Trim Var.0.963719170095267
V(Y[t],d=3,D=1)10.7602624179944Range16Trim Var.6.57707747892413
V(Y[t],d=0,D=2)26.5083414418399Range32Trim Var.11.2899583918586
V(Y[t],d=1,D=2)6.45567843659782Range8Trim Var.2.73310353106618
V(Y[t],d=2,D=2)11.4669449871098Range16Trim Var.6.51375053214134
V(Y[t],d=3,D=2)31.7371268857276Range30Trim Var.20.3227412205933


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')