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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 computationMon, 01 Dec 2008 08:40:39 -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/t1228146069kr8pr2lpz0o6091.htm/, Retrieved Sun, 05 May 2024 14:20:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26949, Retrieved Sun, 05 May 2024 14:20:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact218

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] [] [2008-12-01 15:40:39] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum
2008-12-06 13:00:04 [Maarten Van Gucht] [reply] 
De student heeft hier een verkeerde berekening gemaakt, je moest hier de variantie reductiematrix berekenen.
We krijgen hier een gesimuleerde random walk. De variantie moeten we hier zo klein mogelijk maken, door deze manier kunnen we meer verklaren. (variantie= risico dat in de tijdreeks zit).
d= aantal keren differentiëren
D = heeft betrekking tot het seizoenaal differentiëren.
De variantie van de tijdreeks weerspiegelt het risico of de volatiliteit van/in de tijdreeks. Als je de variantie zo klein mogelijk kan houden kan men meer verklaren over de tijdreeks.
de getrimde variantie is de variantie na het differentiëren en hier worden de extreme waarden ook weggelaten.
de kleinste variantie in dit voorbeeld kunnen we zien bij d=1 en D=0
als vb d=2 dan gaan we 2 keer differentiëren, ...
2008-12-10 09:24:50 [Peter Van Doninck] [reply] 
De student heeft de vraag verkeerd opgelost. Hij diende de variantie reductiematrix te berekenen en te interpreteren. Dit heeft hij echter niet gedaan! Bijkomend is de verkregen reductiematrix niet correct! We moeten de waarden van d en D kiezen waar de variantie het kleinste is, zodat er meer verklaard kan worden. De getrimde variantie is ook belangrijk, omdat ze de outliërs niet meerekent.

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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=26949&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=26949&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26949&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)28.2871182364729Range23Trim Var.19.0822289316171
V(Y[t],d=1,D=0)1.00132795711906Range2Trim Var.NA
V(Y[t],d=2,D=0)1.97181482469112Range4Trim Var.0
V(Y[t],d=3,D=0)5.98387096774194Range8Trim Var.2.53646817549257
V(Y[t],d=0,D=1)13.9101053623725Range22Trim Var.5.73465346534653
V(Y[t],d=1,D=1)2.09861332927726Range4Trim Var.0
V(Y[t],d=2,D=1)4.18142632896356Range8Trim Var.2.38207382557891
V(Y[t],d=3,D=1)12.8263781204737Range16Trim Var.7.06343423584803
V(Y[t],d=0,D=2)29.2944183989385Range30Trim Var.15.3337530708739
V(Y[t],d=1,D=2)6.40490339773484Range8Trim Var.2.74049088073768
V(Y[t],d=2,D=2)12.8456481208910Range16Trim Var.6.84844824262674
V(Y[t],d=3,D=2)39.3978571684524Range32Trim Var.23.6703092531475

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 28.2871182364729 & Range & 23 & Trim Var. & 19.0822289316171 \tabularnewline
V(Y[t],d=1,D=0) & 1.00132795711906 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.97181482469112 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.98387096774194 & Range & 8 & Trim Var. & 2.53646817549257 \tabularnewline
V(Y[t],d=0,D=1) & 13.9101053623725 & Range & 22 & Trim Var. & 5.73465346534653 \tabularnewline
V(Y[t],d=1,D=1) & 2.09861332927726 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.18142632896356 & Range & 8 & Trim Var. & 2.38207382557891 \tabularnewline
V(Y[t],d=3,D=1) & 12.8263781204737 & Range & 16 & Trim Var. & 7.06343423584803 \tabularnewline
V(Y[t],d=0,D=2) & 29.2944183989385 & Range & 30 & Trim Var. & 15.3337530708739 \tabularnewline
V(Y[t],d=1,D=2) & 6.40490339773484 & Range & 8 & Trim Var. & 2.74049088073768 \tabularnewline
V(Y[t],d=2,D=2) & 12.8456481208910 & Range & 16 & Trim Var. & 6.84844824262674 \tabularnewline
V(Y[t],d=3,D=2) & 39.3978571684524 & Range & 32 & Trim Var. & 23.6703092531475 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26949&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]28.2871182364729[/C][C]Range[/C][C]23[/C][C]Trim Var.[/C][C]19.0822289316171[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00132795711906[/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]1.97181482469112[/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]5.98387096774194[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.53646817549257[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]13.9101053623725[/C][C]Range[/C][C]22[/C][C]Trim Var.[/C][C]5.73465346534653[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.09861332927726[/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]4.18142632896356[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.38207382557891[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.8263781204737[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]7.06343423584803[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]29.2944183989385[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]15.3337530708739[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.40490339773484[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.74049088073768[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.8456481208910[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.84844824262674[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]39.3978571684524[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]23.6703092531475[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26949&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26949&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)28.2871182364729Range23Trim Var.19.0822289316171
V(Y[t],d=1,D=0)1.00132795711906Range2Trim Var.NA
V(Y[t],d=2,D=0)1.97181482469112Range4Trim Var.0
V(Y[t],d=3,D=0)5.98387096774194Range8Trim Var.2.53646817549257
V(Y[t],d=0,D=1)13.9101053623725Range22Trim Var.5.73465346534653
V(Y[t],d=1,D=1)2.09861332927726Range4Trim Var.0
V(Y[t],d=2,D=1)4.18142632896356Range8Trim Var.2.38207382557891
V(Y[t],d=3,D=1)12.8263781204737Range16Trim Var.7.06343423584803
V(Y[t],d=0,D=2)29.2944183989385Range30Trim Var.15.3337530708739
V(Y[t],d=1,D=2)6.40490339773484Range8Trim Var.2.74049088073768
V(Y[t],d=2,D=2)12.8456481208910Range16Trim Var.6.84844824262674
V(Y[t],d=3,D=2)39.3978571684524Range32Trim Var.23.6703092531475


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')