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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_rwalk.wasp
Title produced by softwareLaw of Averages
Date of computationTue, 02 Dec 2008 11:24:41 -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/02/t1228242314si8vhktjeieywwa.htm/, Retrieved Sun, 19 May 2024 12:37:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28219, Retrieved Sun, 19 May 2024 12:37:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156

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] [] [2008-12-02 18:24:41] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum
2008-12-04 13:03:42 [Angelique Van de Vijver] [reply] 
Goede berekening en juiste conclusies van de student.
Goede uitleg over de differentiatie: d(LT-trend elimineren) en D(seizoenaliteit elimineren). Deze differentiatie gebruiken we dus inderdaad om de tijdreeks stationair te maken.
We zoeken dus inderdaad naar de differentiatie met de kleinste variantie, omdat we dan meer kunnen verklaren. De kleinste variantie vinden we als d=1 en D=0. (zonder seizoenale differentiatie dus)
De variantie is het risico, de volatiliteit dat in de tijdreeks zit. Deze is dus het best zo klein mogelijk om goede voorspellingen te kunnen maken.
2008-12-10 08:34:31 [Peter Van Doninck] [reply] 
Goede berekening en conclusie. Je kan er nog aan toevoegen dat de getrimde variantie betrouwbaarder is dan de gewone variantie wanneer je te maken hebt met outliërs. De variantie moet steeds klein genoeg zijn, om zo meer te kunnen verklaren. Enkel bij d en D gelijk aan 1 vinden we een getrimde variantie. Daarom nemen we ook deze waarden voor het differentiëren.

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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=28219&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=28219&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28219&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)26.1017074148297Range25Trim Var.14.5391144682301
V(Y[t],d=1,D=0)1.00023339852396Range2Trim Var.NA
V(Y[t],d=2,D=0)2.10058746050601Range4Trim Var.0
V(Y[t],d=3,D=0)6.5241773219965Range8Trim Var.2.63842389904713
V(Y[t],d=0,D=1)10.7145117312418Range14Trim Var.4.8957528957529
V(Y[t],d=1,D=1)1.95878013537151Range4Trim Var.0
V(Y[t],d=2,D=1)3.95049849391201Range8Trim Var.2.37395782512062
V(Y[t],d=3,D=1)12.2231234557383Range16Trim Var.6.39798525980519
V(Y[t],d=0,D=2)26.3740999557718Range24Trim Var.14.1420421011214
V(Y[t],d=1,D=2)5.82250055518543Range8Trim Var.2.66185714503143
V(Y[t],d=2,D=2)11.8393234672304Range16Trim Var.6.43795418193725
V(Y[t],d=3,D=2)37.0508474576271Range30Trim Var.22.1489509213647

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 26.1017074148297 & Range & 25 & Trim Var. & 14.5391144682301 \tabularnewline
V(Y[t],d=1,D=0) & 1.00023339852396 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.10058746050601 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.5241773219965 & Range & 8 & Trim Var. & 2.63842389904713 \tabularnewline
V(Y[t],d=0,D=1) & 10.7145117312418 & Range & 14 & Trim Var. & 4.8957528957529 \tabularnewline
V(Y[t],d=1,D=1) & 1.95878013537151 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.95049849391201 & Range & 8 & Trim Var. & 2.37395782512062 \tabularnewline
V(Y[t],d=3,D=1) & 12.2231234557383 & Range & 16 & Trim Var. & 6.39798525980519 \tabularnewline
V(Y[t],d=0,D=2) & 26.3740999557718 & Range & 24 & Trim Var. & 14.1420421011214 \tabularnewline
V(Y[t],d=1,D=2) & 5.82250055518543 & Range & 8 & Trim Var. & 2.66185714503143 \tabularnewline
V(Y[t],d=2,D=2) & 11.8393234672304 & Range & 16 & Trim Var. & 6.43795418193725 \tabularnewline
V(Y[t],d=3,D=2) & 37.0508474576271 & Range & 30 & Trim Var. & 22.1489509213647 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28219&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]26.1017074148297[/C][C]Range[/C][C]25[/C][C]Trim Var.[/C][C]14.5391144682301[/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]2.10058746050601[/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]6.5241773219965[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.63842389904713[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]10.7145117312418[/C][C]Range[/C][C]14[/C][C]Trim Var.[/C][C]4.8957528957529[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.95878013537151[/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]3.95049849391201[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.37395782512062[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.2231234557383[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.39798525980519[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]26.3740999557718[/C][C]Range[/C][C]24[/C][C]Trim Var.[/C][C]14.1420421011214[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.82250055518543[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.66185714503143[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.8393234672304[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.43795418193725[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]37.0508474576271[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]22.1489509213647[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28219&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28219&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)26.1017074148297Range25Trim Var.14.5391144682301
V(Y[t],d=1,D=0)1.00023339852396Range2Trim Var.NA
V(Y[t],d=2,D=0)2.10058746050601Range4Trim Var.0
V(Y[t],d=3,D=0)6.5241773219965Range8Trim Var.2.63842389904713
V(Y[t],d=0,D=1)10.7145117312418Range14Trim Var.4.8957528957529
V(Y[t],d=1,D=1)1.95878013537151Range4Trim Var.0
V(Y[t],d=2,D=1)3.95049849391201Range8Trim Var.2.37395782512062
V(Y[t],d=3,D=1)12.2231234557383Range16Trim Var.6.39798525980519
V(Y[t],d=0,D=2)26.3740999557718Range24Trim Var.14.1420421011214
V(Y[t],d=1,D=2)5.82250055518543Range8Trim Var.2.66185714503143
V(Y[t],d=2,D=2)11.8393234672304Range16Trim Var.6.43795418193725
V(Y[t],d=3,D=2)37.0508474576271Range30Trim Var.22.1489509213647


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')