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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 15:51:09 -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/t1228085526f5ogrl8hlmg7or6.htm/, Retrieved Sun, 19 May 2024 00:03:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26782, Retrieved Sun, 19 May 2024 00:03:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact197

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] [14a75ec03b2c0d8ddd8b141a7b1594fd] [Current]
F             [Law of Averages] [Non stationary ti...] [2008-12-01 23:10:57] [cf9c64468d04c2c4dd548cc66b4e3677]
F             [Law of Averages] [] [2008-12-02 07:00:00] [74be16979710d4c4e7c6647856088456]
Feedback Forum
2008-12-07 22:19:52 [Kenny Simons] [reply] 
Hier heb ik de juiste techniek gebruikt, en heb ik de bekomen grafiek goed geïnterpreteerd.

Je hebt de VRM matrix nodig om verschillende differentiatie waarden op een tijdreeks te zoeken en 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 inderdaad dat de waarde van d en D optimaal is bij 1.
2008-12-08 00:43:32 [Kenny Simons] [reply] 
Correctie:

De waarde is optimaal bij d=1 en D=0.
Dit wil zeggen dat indien we de reeks 1 keer differentiëren (door bij 'd' 1 in te vullen) 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 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=26782&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=26782&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26782&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)65.5729699398798Range39Trim Var.38.3692436223540
V(Y[t],d=1,D=0)1.00055532752251Range2Trim Var.NA
V(Y[t],d=2,D=0)1.98791140416798Range4Trim Var.0
V(Y[t],d=3,D=0)5.90322580645161Range8Trim Var.2.63570178904001
V(Y[t],d=0,D=1)14.3252432086714Range20Trim Var.6.36340392137007
V(Y[t],d=1,D=1)2.09046737816987Range4Trim Var.0
V(Y[t],d=2,D=1)4.09072164948454Range8Trim Var.2.18099599182378
V(Y[t],d=3,D=1)12.4296839055977Range16Trim Var.6.52541311364841
V(Y[t],d=0,D=2)35.4719504643963Range34Trim Var.20.3710611677479
V(Y[t],d=1,D=2)6.44718632023096Range8Trim Var.2.67890288080041
V(Y[t],d=2,D=2)12.5412083745908Range16Trim Var.6.69022682002185
V(Y[t],d=3,D=2)38.4745762711864Range32Trim Var.21.2669392301558

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 65.5729699398798 & Range & 39 & Trim Var. & 38.3692436223540 \tabularnewline
V(Y[t],d=1,D=0) & 1.00055532752251 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.98791140416798 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.90322580645161 & Range & 8 & Trim Var. & 2.63570178904001 \tabularnewline
V(Y[t],d=0,D=1) & 14.3252432086714 & Range & 20 & Trim Var. & 6.36340392137007 \tabularnewline
V(Y[t],d=1,D=1) & 2.09046737816987 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.09072164948454 & Range & 8 & Trim Var. & 2.18099599182378 \tabularnewline
V(Y[t],d=3,D=1) & 12.4296839055977 & Range & 16 & Trim Var. & 6.52541311364841 \tabularnewline
V(Y[t],d=0,D=2) & 35.4719504643963 & Range & 34 & Trim Var. & 20.3710611677479 \tabularnewline
V(Y[t],d=1,D=2) & 6.44718632023096 & Range & 8 & Trim Var. & 2.67890288080041 \tabularnewline
V(Y[t],d=2,D=2) & 12.5412083745908 & Range & 16 & Trim Var. & 6.69022682002185 \tabularnewline
V(Y[t],d=3,D=2) & 38.4745762711864 & Range & 32 & Trim Var. & 21.2669392301558 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26782&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]65.5729699398798[/C][C]Range[/C][C]39[/C][C]Trim Var.[/C][C]38.3692436223540[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00055532752251[/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]1.98791140416798[/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]5.90322580645161[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.63570178904001[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]14.3252432086714[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]6.36340392137007[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.09046737816987[/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]4.09072164948454[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.18099599182378[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.4296839055977[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.52541311364841[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]35.4719504643963[/C][C]Range[/C][C]34[/C][C]Trim Var.[/C][C]20.3710611677479[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.44718632023096[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.67890288080041[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.5412083745908[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.69022682002185[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]38.4745762711864[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]21.2669392301558[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26782&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26782&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)65.5729699398798Range39Trim Var.38.3692436223540
V(Y[t],d=1,D=0)1.00055532752251Range2Trim Var.NA
V(Y[t],d=2,D=0)1.98791140416798Range4Trim Var.0
V(Y[t],d=3,D=0)5.90322580645161Range8Trim Var.2.63570178904001
V(Y[t],d=0,D=1)14.3252432086714Range20Trim Var.6.36340392137007
V(Y[t],d=1,D=1)2.09046737816987Range4Trim Var.0
V(Y[t],d=2,D=1)4.09072164948454Range8Trim Var.2.18099599182378
V(Y[t],d=3,D=1)12.4296839055977Range16Trim Var.6.52541311364841
V(Y[t],d=0,D=2)35.4719504643963Range34Trim Var.20.3710611677479
V(Y[t],d=1,D=2)6.44718632023096Range8Trim Var.2.67890288080041
V(Y[t],d=2,D=2)12.5412083745908Range16Trim Var.6.69022682002185
V(Y[t],d=3,D=2)38.4745762711864Range32Trim Var.21.2669392301558


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')