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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 12:09:36 -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/t12281585928qjoq6g6nfp3w6i.htm/, Retrieved Sun, 05 May 2024 13:12:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27186, Retrieved Sun, 05 May 2024 13:12:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact202

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] [] [2008-11-30 10:24:27] [a4ee3bef49b119f4bd2e925060c84f5e]
F           [Law of Averages] [] [2008-12-01 19:09:36] [db9a5fd0f9c3e1245d8075d8bb09236d] [Current]
Feedback Forum
2008-12-06 13:00:11 [90714a39acc78a7b2ecd294ecc6b2864] [reply] 
Een Variance Reduction Matrix is een tabel die de varianties van de tijdreeksen bevat na het onderzoeken van verschillende combinaties na seizonale en niet-seizonale differentiatie. De tabel helpt bij het vinden van de differentiatiecombinatie met de laagste variantie want die verklaart de tijdreeks het best.

Door gebruik te maken van de tabel besluit ik deze tijdreeks best éénmaal niet-seizonaal gedifferentieerd dient te worden. De drie maatstaven met de laagste waarde bevinden zich ter hoogte van d=1 en D=0.
2008-12-07 13:54:14 [Stijn Van de Velde] [reply] 
Juist, maar niet volledig.

d=1 wil zeggen dat er een lange termijn trend is, en dat we deze kunnen uitzuiveren door 1 maal te differentiëren.
D=0 wil zeggen dat er geen seizoenaliteit is, en dat we die er dus niet moeten uitzuiveren.

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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=27186&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=27186&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27186&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)124.245194388778Range38Trim Var.99.6651850680165
V(Y[t],d=1,D=0)0.997078494338074Range2Trim Var.NA
V(Y[t],d=2,D=0)2.14084507042254Range4Trim Var.0
V(Y[t],d=3,D=0)6.34675796715779Range8Trim Var.2.97354777895605
V(Y[t],d=0,D=1)9.49506850237318Range16Trim Var.4.17574016176601
V(Y[t],d=1,D=1)2.04088185835847Range4Trim Var.0
V(Y[t],d=2,D=1)4.43711340206186Range8Trim Var.2.41981027242634
V(Y[t],d=3,D=1)13.1652722160688Range16Trim Var.6.56315338474722
V(Y[t],d=0,D=2)17.9281379920389Range24Trim Var.7.25925593233026
V(Y[t],d=1,D=2)6.10970464135021Range8Trim Var.2.77904731761355
V(Y[t],d=2,D=2)13.2684811018635Range16Trim Var.6.68219696969697
V(Y[t],d=3,D=2)39.0675099437417Range30Trim Var.22.6118204488778

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 124.245194388778 & Range & 38 & Trim Var. & 99.6651850680165 \tabularnewline
V(Y[t],d=1,D=0) & 0.997078494338074 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.14084507042254 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.34675796715779 & Range & 8 & Trim Var. & 2.97354777895605 \tabularnewline
V(Y[t],d=0,D=1) & 9.49506850237318 & Range & 16 & Trim Var. & 4.17574016176601 \tabularnewline
V(Y[t],d=1,D=1) & 2.04088185835847 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.43711340206186 & Range & 8 & Trim Var. & 2.41981027242634 \tabularnewline
V(Y[t],d=3,D=1) & 13.1652722160688 & Range & 16 & Trim Var. & 6.56315338474722 \tabularnewline
V(Y[t],d=0,D=2) & 17.9281379920389 & Range & 24 & Trim Var. & 7.25925593233026 \tabularnewline
V(Y[t],d=1,D=2) & 6.10970464135021 & Range & 8 & Trim Var. & 2.77904731761355 \tabularnewline
V(Y[t],d=2,D=2) & 13.2684811018635 & Range & 16 & Trim Var. & 6.68219696969697 \tabularnewline
V(Y[t],d=3,D=2) & 39.0675099437417 & Range & 30 & Trim Var. & 22.6118204488778 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27186&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]124.245194388778[/C][C]Range[/C][C]38[/C][C]Trim Var.[/C][C]99.6651850680165[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.997078494338074[/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]2.14084507042254[/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]6.34675796715779[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.97354777895605[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]9.49506850237318[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]4.17574016176601[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.04088185835847[/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]4.43711340206186[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.41981027242634[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]13.1652722160688[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.56315338474722[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]17.9281379920389[/C][C]Range[/C][C]24[/C][C]Trim Var.[/C][C]7.25925593233026[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.10970464135021[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.77904731761355[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]13.2684811018635[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.68219696969697[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]39.0675099437417[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]22.6118204488778[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27186&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27186&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)124.245194388778Range38Trim Var.99.6651850680165
V(Y[t],d=1,D=0)0.997078494338074Range2Trim Var.NA
V(Y[t],d=2,D=0)2.14084507042254Range4Trim Var.0
V(Y[t],d=3,D=0)6.34675796715779Range8Trim Var.2.97354777895605
V(Y[t],d=0,D=1)9.49506850237318Range16Trim Var.4.17574016176601
V(Y[t],d=1,D=1)2.04088185835847Range4Trim Var.0
V(Y[t],d=2,D=1)4.43711340206186Range8Trim Var.2.41981027242634
V(Y[t],d=3,D=1)13.1652722160688Range16Trim Var.6.56315338474722
V(Y[t],d=0,D=2)17.9281379920389Range24Trim Var.7.25925593233026
V(Y[t],d=1,D=2)6.10970464135021Range8Trim Var.2.77904731761355
V(Y[t],d=2,D=2)13.2684811018635Range16Trim Var.6.68219696969697
V(Y[t],d=3,D=2)39.0675099437417Range30Trim Var.22.6118204488778


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')