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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 00:00:00 -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/t1228201222386aqk7rak0ytml.htm/, Retrieved Sat, 18 May 2024 07:28:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27553, Retrieved Sat, 18 May 2024 07:28:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact220

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 16:39:37] [4c8dfb519edec2da3492d7e6be9a5685]
F         [Law of Averages] [Q3_VRM] [2008-11-30 22:51:09] [6816386b1f3c2f6c0c9f2aa1e5bc9362]
F             [Law of Averages] [] [2008-12-02 07:00:00] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum
2008-12-06 09:19:34 [Siem Van Opstal] [reply] 
de student geeft geen conclusie bij zijn berekeningen.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 matric 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 1.00197181511618, dus na 1 keer gewoon te differentiëren en geen enkele keer seizonaal
2008-12-08 23:42:44 [Bonifer Spillemaeckers] [reply] 
De reproductie heb ik correct uitgevoerd, maar een conclusie heb ik niet echt getrokken. Ik heb enkel de kolommen een klein beetje verklaard.

Zoals Siem hierboven ook vermeldt, gaan we door differentiatie de spreiding van de dataset verkleinen. We kijken naar waar de variatie het kleinst is om zo de dataset het meest stationair te maken. Doordat we de LT-trend zo klein mogelijk proberen te maken, kunnen we toch de dataset beter proberen te verklaren. We gaan hier dus zoeken naar de optimale d en D (optimale waarde d = 1, optimale waarde D = 0). Inderdaad, als we de dataset 1 maal differentiëren, zien we dat we hier de meest optimale spreiding bekomen.

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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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27553&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27553&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27553&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'George Udny Yule' @ 72.249.76.132






Variance Reduction Matrix
V(Y[t],d=0,D=0)27.2656352705411Range21Trim Var.16.4082282077509
V(Y[t],d=1,D=0)1.00197181511618Range2Trim Var.NA
V(Y[t],d=2,D=0)2.07645875251509Range4Trim Var.0
V(Y[t],d=3,D=0)6.43548387096774Range8Trim Var.2.63041620509574
V(Y[t],d=0,D=1)9.347022587269Range14Trim Var.4.46116866970576
V(Y[t],d=1,D=1)1.9917019460711Range4Trim Var.0
V(Y[t],d=2,D=1)4.07415892410165Range8Trim Var.2.35529411764706
V(Y[t],d=3,D=1)12.5619834710744Range16Trim Var.6.87468239129393
V(Y[t],d=0,D=2)20.1475984077842Range20Trim Var.13.5737298915919
V(Y[t],d=1,D=2)6.2025138796358Range8Trim Var.2.46033629398603
V(Y[t],d=2,D=2)12.4397284591574Range16Trim Var.6.94409390309946
V(Y[t],d=3,D=2)37.864406779661Range32Trim Var.22.4249847206943

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 27.2656352705411 & Range & 21 & Trim Var. & 16.4082282077509 \tabularnewline
V(Y[t],d=1,D=0) & 1.00197181511618 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.07645875251509 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.43548387096774 & Range & 8 & Trim Var. & 2.63041620509574 \tabularnewline
V(Y[t],d=0,D=1) & 9.347022587269 & Range & 14 & Trim Var. & 4.46116866970576 \tabularnewline
V(Y[t],d=1,D=1) & 1.9917019460711 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.07415892410165 & Range & 8 & Trim Var. & 2.35529411764706 \tabularnewline
V(Y[t],d=3,D=1) & 12.5619834710744 & Range & 16 & Trim Var. & 6.87468239129393 \tabularnewline
V(Y[t],d=0,D=2) & 20.1475984077842 & Range & 20 & Trim Var. & 13.5737298915919 \tabularnewline
V(Y[t],d=1,D=2) & 6.2025138796358 & Range & 8 & Trim Var. & 2.46033629398603 \tabularnewline
V(Y[t],d=2,D=2) & 12.4397284591574 & Range & 16 & Trim Var. & 6.94409390309946 \tabularnewline
V(Y[t],d=3,D=2) & 37.864406779661 & Range & 32 & Trim Var. & 22.4249847206943 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27553&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]27.2656352705411[/C][C]Range[/C][C]21[/C][C]Trim Var.[/C][C]16.4082282077509[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00197181511618[/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]2.07645875251509[/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]6.43548387096774[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.63041620509574[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]9.347022587269[/C][C]Range[/C][C]14[/C][C]Trim Var.[/C][C]4.46116866970576[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.9917019460711[/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]4.07415892410165[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.35529411764706[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.5619834710744[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.87468239129393[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]20.1475984077842[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]13.5737298915919[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.2025138796358[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.46033629398603[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.4397284591574[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.94409390309946[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]37.864406779661[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]22.4249847206943[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27553&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27553&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)27.2656352705411Range21Trim Var.16.4082282077509
V(Y[t],d=1,D=0)1.00197181511618Range2Trim Var.NA
V(Y[t],d=2,D=0)2.07645875251509Range4Trim Var.0
V(Y[t],d=3,D=0)6.43548387096774Range8Trim Var.2.63041620509574
V(Y[t],d=0,D=1)9.347022587269Range14Trim Var.4.46116866970576
V(Y[t],d=1,D=1)1.9917019460711Range4Trim Var.0
V(Y[t],d=2,D=1)4.07415892410165Range8Trim Var.2.35529411764706
V(Y[t],d=3,D=1)12.5619834710744Range16Trim Var.6.87468239129393
V(Y[t],d=0,D=2)20.1475984077842Range20Trim Var.13.5737298915919
V(Y[t],d=1,D=2)6.2025138796358Range8Trim Var.2.46033629398603
V(Y[t],d=2,D=2)12.4397284591574Range16Trim Var.6.94409390309946
V(Y[t],d=3,D=2)37.864406779661Range32Trim Var.22.4249847206943


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')