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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 computationWed, 03 Dec 2008 04:13:27 -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/03/t12283028299xz807h3xjmy107.htm/, Retrieved Fri, 17 May 2024 18:37:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28615, Retrieved Fri, 17 May 2024 18:37:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact205

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] [2008-12-02 20:13:15] [17bd4671b42d569d890f7246b2ee4ecc]
F           [Law of Averages] [] [2008-12-03 11:13:27] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum
2008-12-05 15:11:49 [Vincent Vanden Poel] [reply] 
Uitleg?

De Variance Reduction Matrix geeft de waarden weer nadat er gedifferentieerd is. Het werkt volgens volgende formule: Nablad * NablaDS * Yt = et waarbij d = # keer gewoon gedifferentieerd en D = # keer seizoenaal gedifferentieerd. Deze laatste waarde wordt gebruikt om seizoenaliteit te verwijderen.
De 2e kolom geeft de bijhorende varianties weer. Dit is het risico/ de volatiliteit dat in de tijdreeksen zit. Deze waarde moet zo klein mogelijk zijn opdat men veel zou kunnen verklaren. We moeten ons dus de vraag stellen welke differentiatie nodig is om zoveel mogelijk van de tijdreeks te verklaren. Hier is de kleinste variantie 1 bij 1 maal gewoon differentiëren.

2008-12-09 23:47:03 [Gert-Jan Geudens] [reply] 
We moeten hier kiezen voor de kleinste variantie. In het geval van outliers kunnen we ons ook nog baseren op de getrimde variantie. De tijdreeksen zijn dan bewerkt met een logaritme zodat de 5% hoogste en laagste gegevens verwijderd zijn. De outliers en hun vertekend beeld op de variantie zijn dan verwijderd.

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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 time0 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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28615&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]0 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=28615&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28615&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 time0 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)25.9945330661323Range23Trim Var.16.3823232323232
V(Y[t],d=1,D=0)1.00110260682007Range2Trim Var.NA
V(Y[t],d=2,D=0)2.11668403998287Range4Trim Var.0
V(Y[t],d=3,D=0)6.51612903225806Range8Trim Var.2.74916917233740
V(Y[t],d=0,D=1)11.5489110310701Range16Trim Var.6.51717247702109
V(Y[t],d=1,D=1)1.99984789717849Range4Trim Var.0
V(Y[t],d=2,D=1)4.19792117432438Range8Trim Var.2.37086302454473
V(Y[t],d=3,D=1)12.6198176706143Range16Trim Var.6.72740515783366
V(Y[t],d=0,D=2)22.8706413091552Range26Trim Var.12.7476598776503
V(Y[t],d=1,D=2)6.0167177437264Range8Trim Var.2.63197262672078
V(Y[t],d=2,D=2)12.7863979803927Range16Trim Var.7.00249357619331
V(Y[t],d=3,D=2)38.1863690113592Range32Trim Var.22.4881053788131

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 25.9945330661323 & Range & 23 & Trim Var. & 16.3823232323232 \tabularnewline
V(Y[t],d=1,D=0) & 1.00110260682007 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.11668403998287 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.51612903225806 & Range & 8 & Trim Var. & 2.74916917233740 \tabularnewline
V(Y[t],d=0,D=1) & 11.5489110310701 & Range & 16 & Trim Var. & 6.51717247702109 \tabularnewline
V(Y[t],d=1,D=1) & 1.99984789717849 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.19792117432438 & Range & 8 & Trim Var. & 2.37086302454473 \tabularnewline
V(Y[t],d=3,D=1) & 12.6198176706143 & Range & 16 & Trim Var. & 6.72740515783366 \tabularnewline
V(Y[t],d=0,D=2) & 22.8706413091552 & Range & 26 & Trim Var. & 12.7476598776503 \tabularnewline
V(Y[t],d=1,D=2) & 6.0167177437264 & Range & 8 & Trim Var. & 2.63197262672078 \tabularnewline
V(Y[t],d=2,D=2) & 12.7863979803927 & Range & 16 & Trim Var. & 7.00249357619331 \tabularnewline
V(Y[t],d=3,D=2) & 38.1863690113592 & Range & 32 & Trim Var. & 22.4881053788131 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28615&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]25.9945330661323[/C][C]Range[/C][C]23[/C][C]Trim Var.[/C][C]16.3823232323232[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00110260682007[/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]2.11668403998287[/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]6.51612903225806[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.74916917233740[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]11.5489110310701[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.51717247702109[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.99984789717849[/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]4.19792117432438[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.37086302454473[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.6198176706143[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.72740515783366[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]22.8706413091552[/C][C]Range[/C][C]26[/C][C]Trim Var.[/C][C]12.7476598776503[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.0167177437264[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.63197262672078[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.7863979803927[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]7.00249357619331[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]38.1863690113592[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]22.4881053788131[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28615&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28615&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)25.9945330661323Range23Trim Var.16.3823232323232
V(Y[t],d=1,D=0)1.00110260682007Range2Trim Var.NA
V(Y[t],d=2,D=0)2.11668403998287Range4Trim Var.0
V(Y[t],d=3,D=0)6.51612903225806Range8Trim Var.2.74916917233740
V(Y[t],d=0,D=1)11.5489110310701Range16Trim Var.6.51717247702109
V(Y[t],d=1,D=1)1.99984789717849Range4Trim Var.0
V(Y[t],d=2,D=1)4.19792117432438Range8Trim Var.2.37086302454473
V(Y[t],d=3,D=1)12.6198176706143Range16Trim Var.6.72740515783366
V(Y[t],d=0,D=2)22.8706413091552Range26Trim Var.12.7476598776503
V(Y[t],d=1,D=2)6.0167177437264Range8Trim Var.2.63197262672078
V(Y[t],d=2,D=2)12.7863979803927Range16Trim Var.7.00249357619331
V(Y[t],d=3,D=2)38.1863690113592Range32Trim Var.22.4881053788131


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')