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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 computationSun, 30 Nov 2008 08:21:40 -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/30/t12280585833k4sbtauj0fln6i.htm/, Retrieved Tue, 28 May 2024 04:06:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26561, Retrieved Tue, 28 May 2024 04:06:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsq3
Estimated Impact157

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] [2008-11-30 15:21:40] [da22167fec87ac24b182b1311f73761c] [Current]
Feedback Forum
2008-12-06 12:49:02 [Ken Wright] [reply] 
d staat voor aantal keren dat er niet-seizoenaal wordt gedifferentieerd. Deze wordt gebruikt om bijvoorbeeld een LT trend uit je tijdreeksen te halen. In de tabel kan je eigenlijk beter zien naar de trimmed variance, hier laat het model de invloed van outliers achterwegen. Dus als je een tijdreeks hebt met veel outliers kan je best hier gebruik van maken. De variantie wilt zeggen het risico of volatiteit dat er in de tijdreeks zit, dit moet zo klein mogelijk zijn om het meeste te kunnen verklaren. Dus de 2e kolom met variantie, geeft de variantie weer nadat er gedifferentieerd is. 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=1.

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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=26561&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=26561&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26561&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)30.0427094188377Range29Trim Var.16.2847001272669
V(Y[t],d=1,D=0)1.00152111451819Range2Trim Var.NA
V(Y[t],d=2,D=0)2.17303822937626Range4Trim Var.0
V(Y[t],d=3,D=0)6.66933861231908Range8Trim Var.2.84966520731393
V(Y[t],d=0,D=1)10.6684619786582Range18Trim Var.5.66729617439163
V(Y[t],d=1,D=1)1.99984789717849Range4Trim Var.0
V(Y[t],d=2,D=1)4.4783335454584Range8Trim Var.2.33337706482199
V(Y[t],d=3,D=1)13.6197665502258Range16Trim Var.6.70826193072649
V(Y[t],d=0,D=2)21.4542061034940Range26Trim Var.10.8535279805353
V(Y[t],d=1,D=2)6.13500333111259Range8Trim Var.2.59775685632419
V(Y[t],d=2,D=2)13.7080846736425Range16Trim Var.6.33944840664550
V(Y[t],d=3,D=2)41.3047980793349Range32Trim Var.21.056384025182

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 30.0427094188377 & Range & 29 & Trim Var. & 16.2847001272669 \tabularnewline
V(Y[t],d=1,D=0) & 1.00152111451819 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.17303822937626 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.66933861231908 & Range & 8 & Trim Var. & 2.84966520731393 \tabularnewline
V(Y[t],d=0,D=1) & 10.6684619786582 & Range & 18 & Trim Var. & 5.66729617439163 \tabularnewline
V(Y[t],d=1,D=1) & 1.99984789717849 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.4783335454584 & Range & 8 & Trim Var. & 2.33337706482199 \tabularnewline
V(Y[t],d=3,D=1) & 13.6197665502258 & Range & 16 & Trim Var. & 6.70826193072649 \tabularnewline
V(Y[t],d=0,D=2) & 21.4542061034940 & Range & 26 & Trim Var. & 10.8535279805353 \tabularnewline
V(Y[t],d=1,D=2) & 6.13500333111259 & Range & 8 & Trim Var. & 2.59775685632419 \tabularnewline
V(Y[t],d=2,D=2) & 13.7080846736425 & Range & 16 & Trim Var. & 6.33944840664550 \tabularnewline
V(Y[t],d=3,D=2) & 41.3047980793349 & Range & 32 & Trim Var. & 21.056384025182 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26561&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]30.0427094188377[/C][C]Range[/C][C]29[/C][C]Trim Var.[/C][C]16.2847001272669[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00152111451819[/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]2.17303822937626[/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]6.66933861231908[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.84966520731393[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]10.6684619786582[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]5.66729617439163[/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]4.4783335454584[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.33337706482199[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]13.6197665502258[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.70826193072649[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]21.4542061034940[/C][C]Range[/C][C]26[/C][C]Trim Var.[/C][C]10.8535279805353[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.13500333111259[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.59775685632419[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]13.7080846736425[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.33944840664550[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]41.3047980793349[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]21.056384025182[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26561&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26561&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)30.0427094188377Range29Trim Var.16.2847001272669
V(Y[t],d=1,D=0)1.00152111451819Range2Trim Var.NA
V(Y[t],d=2,D=0)2.17303822937626Range4Trim Var.0
V(Y[t],d=3,D=0)6.66933861231908Range8Trim Var.2.84966520731393
V(Y[t],d=0,D=1)10.6684619786582Range18Trim Var.5.66729617439163
V(Y[t],d=1,D=1)1.99984789717849Range4Trim Var.0
V(Y[t],d=2,D=1)4.4783335454584Range8Trim Var.2.33337706482199
V(Y[t],d=3,D=1)13.6197665502258Range16Trim Var.6.70826193072649
V(Y[t],d=0,D=2)21.4542061034940Range26Trim Var.10.8535279805353
V(Y[t],d=1,D=2)6.13500333111259Range8Trim Var.2.59775685632419
V(Y[t],d=2,D=2)13.7080846736425Range16Trim Var.6.33944840664550
V(Y[t],d=3,D=2)41.3047980793349Range32Trim Var.21.056384025182


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')