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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 computationSat, 29 Nov 2008 03:16:19 -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/29/t1227953811m8zxxwi89dsb79m.htm/, Retrieved Sun, 19 May 2024 04:00:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26184, Retrieved Sun, 19 May 2024 04:00:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsjulie govaerts
Estimated Impact183

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] [VRM] [2008-11-29 10:16:19] [ff1af8c6f1c2f1c0e8def9bfc9355be9] [Current]
Feedback Forum
2008-12-06 13:32:33 [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.
2008-12-07 11:58:28 [Jolien Van Landeghem] [reply] 
Deze vraag werd goed opgelost. We gaan de variantie van de tijdreeks interpreteren als we het risico zo klein mogelijk wensen te houden (we willen een kleine variantie) deze vinden we, zoals de student vaststelde, voor d=1 en D:0 (logisch want dit werd zo gesimuleerd). De D is gelijk aan nul, want deze geeft aan hoeveel periodes we terug moeten gaan met seizoenaliteit, logisch aangezien seizoensinvloeden geen rol spelen in dit geval. De d=1 : we moeten 1 periode terugkijken om de kleinste variantie te krijgen.tie zo klein mogelijk maken, omdat we zo de tijdreeks beter kunnen verklaren.

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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=26184&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=26184&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26184&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)120.738260521042Range41Trim Var.89.5732580417465
V(Y[t],d=1,D=0)1.00023339852396Range2Trim Var.NA
V(Y[t],d=2,D=0)2.08449088102915Range4Trim Var.0
V(Y[t],d=3,D=0)6.37096774193548Range8Trim Var.2.66060043330238
V(Y[t],d=0,D=1)13.2590971824822Range16Trim Var.6.7347021855838
V(Y[t],d=1,D=1)2.07407407407407Range4Trim Var.0
V(Y[t],d=2,D=1)4.30515463917526Range8Trim Var.2.42833814847381
V(Y[t],d=3,D=1)13.1651358950328Range16Trim Var.6.9541604010025
V(Y[t],d=0,D=2)22.9281026094648Range28Trim Var.9.77309016333407
V(Y[t],d=1,D=2)6.29528758605374Range8Trim Var.2.74139587266885
V(Y[t],d=2,D=2)12.8371379381094Range16Trim Var.6.8271915888454
V(Y[t],d=3,D=2)39.2372164689863Range32Trim Var.21.6985040276180

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 120.738260521042 & Range & 41 & Trim Var. & 89.5732580417465 \tabularnewline
V(Y[t],d=1,D=0) & 1.00023339852396 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.08449088102915 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.37096774193548 & Range & 8 & Trim Var. & 2.66060043330238 \tabularnewline
V(Y[t],d=0,D=1) & 13.2590971824822 & Range & 16 & Trim Var. & 6.7347021855838 \tabularnewline
V(Y[t],d=1,D=1) & 2.07407407407407 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.30515463917526 & Range & 8 & Trim Var. & 2.42833814847381 \tabularnewline
V(Y[t],d=3,D=1) & 13.1651358950328 & Range & 16 & Trim Var. & 6.9541604010025 \tabularnewline
V(Y[t],d=0,D=2) & 22.9281026094648 & Range & 28 & Trim Var. & 9.77309016333407 \tabularnewline
V(Y[t],d=1,D=2) & 6.29528758605374 & Range & 8 & Trim Var. & 2.74139587266885 \tabularnewline
V(Y[t],d=2,D=2) & 12.8371379381094 & Range & 16 & Trim Var. & 6.8271915888454 \tabularnewline
V(Y[t],d=3,D=2) & 39.2372164689863 & Range & 32 & Trim Var. & 21.6985040276180 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26184&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]120.738260521042[/C][C]Range[/C][C]41[/C][C]Trim Var.[/C][C]89.5732580417465[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00023339852396[/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]2.08449088102915[/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]6.37096774193548[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.66060043330238[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]13.2590971824822[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.7347021855838[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.07407407407407[/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]4.30515463917526[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.42833814847381[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]13.1651358950328[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.9541604010025[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]22.9281026094648[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]9.77309016333407[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.29528758605374[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.74139587266885[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.8371379381094[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.8271915888454[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]39.2372164689863[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]21.6985040276180[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26184&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26184&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)120.738260521042Range41Trim Var.89.5732580417465
V(Y[t],d=1,D=0)1.00023339852396Range2Trim Var.NA
V(Y[t],d=2,D=0)2.08449088102915Range4Trim Var.0
V(Y[t],d=3,D=0)6.37096774193548Range8Trim Var.2.66060043330238
V(Y[t],d=0,D=1)13.2590971824822Range16Trim Var.6.7347021855838
V(Y[t],d=1,D=1)2.07407407407407Range4Trim Var.0
V(Y[t],d=2,D=1)4.30515463917526Range8Trim Var.2.42833814847381
V(Y[t],d=3,D=1)13.1651358950328Range16Trim Var.6.9541604010025
V(Y[t],d=0,D=2)22.9281026094648Range28Trim Var.9.77309016333407
V(Y[t],d=1,D=2)6.29528758605374Range8Trim Var.2.74139587266885
V(Y[t],d=2,D=2)12.8371379381094Range16Trim Var.6.8271915888454
V(Y[t],d=3,D=2)39.2372164689863Range32Trim Var.21.6985040276180


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')