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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 12:52:59 -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/t1228161250hgfelqa83bqwltu.htm/, Retrieved Sun, 05 May 2024 13:05:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27275, Retrieved Sun, 05 May 2024 13:05:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact215

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 Ti...] [2008-12-01 19:52:59] [284c7cdb9fcda2adcbb08e211682c8d6] [Current]
Feedback Forum
2008-12-08 01:23:46 [Kenny Simons] [reply] 
Je hebt de VRM matrix nodig om verschillende differentiatie waarden op een tijdreeks te zoeken en de VRM toont de daarbij gerelateerde variatie. Waar de variatie het kleinst is, noteren we het meest adequate stationaire karakter. Door de lange termijn trend zo klein mogelijk te maken, kunnen we zoveel mogelijk van de tijdreeks verklaren. De bedoeling hier was dus om de optimale d en D te indentificeren. We zien dan dat de waarde optimaal is bij d=1 en D=0. Dit wil zeggen dat indien we de reeks 1 keer differentiëren we het lange termijn effect kunnen uitzuiveren.
Er is hier blijkbaar geen sprake van seizoenaliteit (want D = 0).

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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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27275&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27275&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27275&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Variance Reduction Matrix
V(Y[t],d=0,D=0)182.645691382766Range50Trim Var.136.427847346452
V(Y[t],d=1,D=0)0.997625773635625Range2Trim Var.NA
V(Y[t],d=2,D=0)2.13278061945973Range4Trim Var.0
V(Y[t],d=3,D=0)6.45966119296424Range8Trim Var.2.85552477685442
V(Y[t],d=0,D=1)10.3329013363854Range16Trim Var.4.86074961308122
V(Y[t],d=1,D=1)2.04936581573588Range4Trim Var.0
V(Y[t],d=2,D=1)4.4123541640151Range8Trim Var.2.25628242590494
V(Y[t],d=3,D=1)13.4379483684076Range16Trim Var.6.56104273770577
V(Y[t],d=0,D=2)20.4782308712959Range24Trim Var.13.0774566216156
V(Y[t],d=1,D=2)6.21896513435487Range8Trim Var.2.67549319895926
V(Y[t],d=2,D=2)13.4968287526427Range16Trim Var.6.37791013925152
V(Y[t],d=3,D=2)41.2457447952127Range32Trim Var.21.5284687891372

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 182.645691382766 & Range & 50 & Trim Var. & 136.427847346452 \tabularnewline
V(Y[t],d=1,D=0) & 0.997625773635625 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.13278061945973 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.45966119296424 & Range & 8 & Trim Var. & 2.85552477685442 \tabularnewline
V(Y[t],d=0,D=1) & 10.3329013363854 & Range & 16 & Trim Var. & 4.86074961308122 \tabularnewline
V(Y[t],d=1,D=1) & 2.04936581573588 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.4123541640151 & Range & 8 & Trim Var. & 2.25628242590494 \tabularnewline
V(Y[t],d=3,D=1) & 13.4379483684076 & Range & 16 & Trim Var. & 6.56104273770577 \tabularnewline
V(Y[t],d=0,D=2) & 20.4782308712959 & Range & 24 & Trim Var. & 13.0774566216156 \tabularnewline
V(Y[t],d=1,D=2) & 6.21896513435487 & Range & 8 & Trim Var. & 2.67549319895926 \tabularnewline
V(Y[t],d=2,D=2) & 13.4968287526427 & Range & 16 & Trim Var. & 6.37791013925152 \tabularnewline
V(Y[t],d=3,D=2) & 41.2457447952127 & Range & 32 & Trim Var. & 21.5284687891372 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27275&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]182.645691382766[/C][C]Range[/C][C]50[/C][C]Trim Var.[/C][C]136.427847346452[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.997625773635625[/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]2.13278061945973[/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]6.45966119296424[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.85552477685442[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]10.3329013363854[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]4.86074961308122[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.04936581573588[/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]4.4123541640151[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.25628242590494[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]13.4379483684076[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.56104273770577[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]20.4782308712959[/C][C]Range[/C][C]24[/C][C]Trim Var.[/C][C]13.0774566216156[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.21896513435487[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.67549319895926[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]13.4968287526427[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.37791013925152[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]41.2457447952127[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]21.5284687891372[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27275&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27275&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)182.645691382766Range50Trim Var.136.427847346452
V(Y[t],d=1,D=0)0.997625773635625Range2Trim Var.NA
V(Y[t],d=2,D=0)2.13278061945973Range4Trim Var.0
V(Y[t],d=3,D=0)6.45966119296424Range8Trim Var.2.85552477685442
V(Y[t],d=0,D=1)10.3329013363854Range16Trim Var.4.86074961308122
V(Y[t],d=1,D=1)2.04936581573588Range4Trim Var.0
V(Y[t],d=2,D=1)4.4123541640151Range8Trim Var.2.25628242590494
V(Y[t],d=3,D=1)13.4379483684076Range16Trim Var.6.56104273770577
V(Y[t],d=0,D=2)20.4782308712959Range24Trim Var.13.0774566216156
V(Y[t],d=1,D=2)6.21896513435487Range8Trim Var.2.67549319895926
V(Y[t],d=2,D=2)13.4968287526427Range16Trim Var.6.37791013925152
V(Y[t],d=3,D=2)41.2457447952127Range32Trim Var.21.5284687891372


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')