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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 09:21:07 -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/t1228148509yv38vao5eq5bmce.htm/, Retrieved Sun, 05 May 2024 10:43:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26969, Retrieved Sun, 05 May 2024 10:43:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVariance reduction matrix
Estimated Impact178

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] [Non Stationary ti...] [2008-12-01 16:21:07] [3bdbbe597ac6c61989658933956ee6ac] [Current]
Feedback Forum
2008-12-06 14:16:58 [Thomas Plasschaert] [reply] 
De VRM gaat trachten om de spreading van de tijdreeks te verkleinen door te differentiëren, 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 differentiëren en geen enkele keer seizonaal
Als men denkt dat er veel extreme outliers in de tijdreeks zijn, is het beter om naar de getrimde variantie te zien. Ook hier is die het kleinst bij d=1 en D=0.

2008-12-08 14:21:28 [Sam De Cuyper] [reply] 
Juiste berekend maar de interpretatie kon ruimer. Je zou dus kunnen zeggen dat hoe kleiner de variantie is hoe meer er verklaard wordt. Dan luidt enkel nog de vraag welke differentiatie je moet toepassen om een zo klein mogelijke variantie te bekomen. Indien we in tabel 1 kleine d gelijk stellen aan 1, kunnen we zien dat de variantie daar het kleinst is. In dit geval wordt er het meest verklaard.
Een nadeel is wel dat de variantie gevoelig is voor outliers en misschien vertekende resultaten kan opleveren.
2008-12-09 23:23:12 [Peter Van Doninck] [reply] 
Goede opsomming van de gebruikte variabelen. We differentiëren echter wél seizoenaal! d en D zijn beiden gelijk aan 1! De reden waarom we de kleinste variantie nemen kan ook nog toegevoegd worden. Hoe kleiner deze waarde is, hoe meer je gaat kunnen verklaren. De getrimde variantie kan ook nuttig zijn: hier houden we geen rekening met de outliërs.

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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=26969&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=26969&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26969&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)55.8534829659319Range29Trim Var.41.8625972970661
V(Y[t],d=1,D=0)1.00132795711906Range2Trim Var.NA
V(Y[t],d=2,D=0)2.11668403998287Range4Trim Var.0
V(Y[t],d=3,D=0)6.4757902252223Range8Trim Var.2.76722532588454
V(Y[t],d=0,D=1)12.5873194869896Range16Trim Var.6.71135038782098
V(Y[t],d=1,D=1)2.04108466212048Range4Trim Var.0
V(Y[t],d=2,D=1)4.44534385473675Range8Trim Var.2.19702012805461
V(Y[t],d=3,D=1)13.6446110590440Range16Trim Var.6.44439116652015
V(Y[t],d=0,D=2)21.9366828836798Range26Trim Var.11.6094772399783
V(Y[t],d=1,D=2)6.0241794359316Range8Trim Var.2.7551758133421
V(Y[t],d=2,D=2)13.4968287526427Range16Trim Var.6.2136015720548
V(Y[t],d=3,D=2)41.4237288135593Range32Trim Var.22.1936957989303

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 55.8534829659319 & Range & 29 & Trim Var. & 41.8625972970661 \tabularnewline
V(Y[t],d=1,D=0) & 1.00132795711906 & 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) & 6.4757902252223 & Range & 8 & Trim Var. & 2.76722532588454 \tabularnewline
V(Y[t],d=0,D=1) & 12.5873194869896 & Range & 16 & Trim Var. & 6.71135038782098 \tabularnewline
V(Y[t],d=1,D=1) & 2.04108466212048 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.44534385473675 & Range & 8 & Trim Var. & 2.19702012805461 \tabularnewline
V(Y[t],d=3,D=1) & 13.6446110590440 & Range & 16 & Trim Var. & 6.44439116652015 \tabularnewline
V(Y[t],d=0,D=2) & 21.9366828836798 & Range & 26 & Trim Var. & 11.6094772399783 \tabularnewline
V(Y[t],d=1,D=2) & 6.0241794359316 & Range & 8 & Trim Var. & 2.7551758133421 \tabularnewline
V(Y[t],d=2,D=2) & 13.4968287526427 & Range & 16 & Trim Var. & 6.2136015720548 \tabularnewline
V(Y[t],d=3,D=2) & 41.4237288135593 & Range & 32 & Trim Var. & 22.1936957989303 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26969&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]55.8534829659319[/C][C]Range[/C][C]29[/C][C]Trim Var.[/C][C]41.8625972970661[/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]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]6.4757902252223[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.76722532588454[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.5873194869896[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.71135038782098[/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]4.44534385473675[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.19702012805461[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]13.6446110590440[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.44439116652015[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]21.9366828836798[/C][C]Range[/C][C]26[/C][C]Trim Var.[/C][C]11.6094772399783[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.0241794359316[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.7551758133421[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]13.4968287526427[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.2136015720548[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]41.4237288135593[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]22.1936957989303[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26969&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26969&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)55.8534829659319Range29Trim Var.41.8625972970661
V(Y[t],d=1,D=0)1.00132795711906Range2Trim Var.NA
V(Y[t],d=2,D=0)2.11668403998287Range4Trim Var.0
V(Y[t],d=3,D=0)6.4757902252223Range8Trim Var.2.76722532588454
V(Y[t],d=0,D=1)12.5873194869896Range16Trim Var.6.71135038782098
V(Y[t],d=1,D=1)2.04108466212048Range4Trim Var.0
V(Y[t],d=2,D=1)4.44534385473675Range8Trim Var.2.19702012805461
V(Y[t],d=3,D=1)13.6446110590440Range16Trim Var.6.44439116652015
V(Y[t],d=0,D=2)21.9366828836798Range26Trim Var.11.6094772399783
V(Y[t],d=1,D=2)6.0241794359316Range8Trim Var.2.7551758133421
V(Y[t],d=2,D=2)13.4968287526427Range16Trim Var.6.2136015720548
V(Y[t],d=3,D=2)41.4237288135593Range32Trim Var.22.1936957989303


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')