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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 07:35:25 -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/t1228228935fuziw6tbe6dddcs.htm/, Retrieved Sun, 19 May 2024 08:50:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27877, Retrieved Sun, 19 May 2024 08:50:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact196

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] [W7Q3] [2008-12-02 14:35:25] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum
2008-12-08 15:38:19 [Kevin Vermeiren] [reply] 
Het antwoord van de student is correct. Het klopt dat er gezocht moet worden naar de kleinste variantie. Bijkomend had nog vermeld mogen worden waarom dit het geval is. We doen dit omdat de variantie van een tijdreeks duidt op het risico, de volatiliteit van de tijdreeks. Bijgevolg kunnen we zeggen dat hoe kleiner de variantie hoe meer we van de tijdreeks kunnen verklaren. Het klopt dat de parameters d en D ingesteld moeten worden op respectievelijk 1 en 0 om zo tot de beste differentiatie te komen. Verder is het goed dat de student vermeld dat deze methode gevoelig is voor outliers. Indien deze aanwezig zijn is het inderdaad beter te kijken naar de getrimde variantie.
2008-12-08 21:39:57 [] [reply] 
De Variance Reduction Matrix wordt gebruikt om op een snelle manier de varianties weer te geven en dusdanig dient men de kleinste variantie te kiezen, want des te kleiner de variantie, des te meer er kan verklaard worden van de tijdreeks. Men beschrijft de variantie ook wel als het risico of de volaliteit die eigen is aan de tijdreeks. Men moet kiezen voor de kleinste variantie omdat hierbij vermeldt staat welke de beste differentiatie is die we moeten nemen om een stationaire reeks te bekomen. Hier is dat bij d=1 en D=0.
2008-12-09 11:20:54 [Yannick Van Schil] [reply] 
alweer correct geantwoord, je moet inderdaad naar de kleinste variantie kijken omdat we daarmee de tijdreeks kunnen verklaren. Bij deze variantie is d= 1 en D = 0.
V(Y[t],d=1,D=0) 1.00055532752251 Range 2 Trim Var. NA

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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'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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27877&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27877&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27877&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'George Udny Yule' @ 72.249.76.132






Variance Reduction Matrix
V(Y[t],d=0,D=0)165.037675350701Range47Trim Var.123.451442453690
V(Y[t],d=1,D=0)1.00055532752251Range2Trim Var.NA
V(Y[t],d=2,D=0)2.02010456312170Range4Trim Var.0
V(Y[t],d=3,D=0)6Range8Trim Var.2.73386096256684
V(Y[t],d=0,D=1)13.6180529841452Range18Trim Var.7.34785026737968
V(Y[t],d=1,D=1)2.05761316872428Range4Trim Var.0
V(Y[t],d=2,D=1)4.37113402061856Range8Trim Var.2.30832882766403
V(Y[t],d=3,D=1)13.1735537190083Range16Trim Var.6.90449742446569
V(Y[t],d=0,D=2)24.8757187085360Range30Trim Var.12.8649132787064
V(Y[t],d=1,D=2)6.26160337552743Range8Trim Var.2.69727384146543
V(Y[t],d=2,D=2)13.6744007635971Range16Trim Var.6.9534810602436
V(Y[t],d=3,D=2)41.669473608772Range32Trim Var.22.8039646993348

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 165.037675350701 & Range & 47 & Trim Var. & 123.451442453690 \tabularnewline
V(Y[t],d=1,D=0) & 1.00055532752251 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.02010456312170 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6 & Range & 8 & Trim Var. & 2.73386096256684 \tabularnewline
V(Y[t],d=0,D=1) & 13.6180529841452 & Range & 18 & Trim Var. & 7.34785026737968 \tabularnewline
V(Y[t],d=1,D=1) & 2.05761316872428 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.37113402061856 & Range & 8 & Trim Var. & 2.30832882766403 \tabularnewline
V(Y[t],d=3,D=1) & 13.1735537190083 & Range & 16 & Trim Var. & 6.90449742446569 \tabularnewline
V(Y[t],d=0,D=2) & 24.8757187085360 & Range & 30 & Trim Var. & 12.8649132787064 \tabularnewline
V(Y[t],d=1,D=2) & 6.26160337552743 & Range & 8 & Trim Var. & 2.69727384146543 \tabularnewline
V(Y[t],d=2,D=2) & 13.6744007635971 & Range & 16 & Trim Var. & 6.9534810602436 \tabularnewline
V(Y[t],d=3,D=2) & 41.669473608772 & Range & 32 & Trim Var. & 22.8039646993348 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27877&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]165.037675350701[/C][C]Range[/C][C]47[/C][C]Trim Var.[/C][C]123.451442453690[/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]2.02010456312170[/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[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.73386096256684[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]13.6180529841452[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]7.34785026737968[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.05761316872428[/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]4.37113402061856[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.30832882766403[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]13.1735537190083[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.90449742446569[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]24.8757187085360[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]12.8649132787064[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.26160337552743[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.69727384146543[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]13.6744007635971[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.9534810602436[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]41.669473608772[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]22.8039646993348[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27877&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27877&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)165.037675350701Range47Trim Var.123.451442453690
V(Y[t],d=1,D=0)1.00055532752251Range2Trim Var.NA
V(Y[t],d=2,D=0)2.02010456312170Range4Trim Var.0
V(Y[t],d=3,D=0)6Range8Trim Var.2.73386096256684
V(Y[t],d=0,D=1)13.6180529841452Range18Trim Var.7.34785026737968
V(Y[t],d=1,D=1)2.05761316872428Range4Trim Var.0
V(Y[t],d=2,D=1)4.37113402061856Range8Trim Var.2.30832882766403
V(Y[t],d=3,D=1)13.1735537190083Range16Trim Var.6.90449742446569
V(Y[t],d=0,D=2)24.8757187085360Range30Trim Var.12.8649132787064
V(Y[t],d=1,D=2)6.26160337552743Range8Trim Var.2.69727384146543
V(Y[t],d=2,D=2)13.6744007635971Range16Trim Var.6.9534810602436
V(Y[t],d=3,D=2)41.669473608772Range32Trim Var.22.8039646993348


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')