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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 computationFri, 28 Nov 2008 05:56:39 -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/Nov/28/t1227877031yj0b28gkqaorbuw.htm/, Retrieved Sun, 19 May 2024 11:33:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26063, Retrieved Sun, 19 May 2024 11:33:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact200

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] [Q3] [2008-11-28 12:56:39] [6fc58909ffe15c247a4f6748c8841ab4] [Current]
-           [Law of Averages] [] [2008-12-01 21:36:50] [d2d412c7f4d35ffbf5ee5ee89db327d4]
Feedback Forum
2008-12-04 17:04:53 [Stijn Van de Velde] [reply] 
Correct.

Dit wil zeggen dat indien we de reeks 1x 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).
2008-12-08 00:45:30 [Kenny Simons] [reply] 
Deze vraag heeft de student correct opgelost.

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 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=26063&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=26063&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26063&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)18.2683126252505Range19Trim Var.12.08906397697
V(Y[t],d=1,D=0)1.00197181511618Range2Trim Var.NA
V(Y[t],d=2,D=0)1.95571824521426Range4Trim Var.0
V(Y[t],d=3,D=0)5.84675796715779Range8Trim Var.2.60567752130481
V(Y[t],d=0,D=1)10.8566331167738Range18Trim Var.4.04036345372357
V(Y[t],d=1,D=1)1.90919461556012Range4Trim Var.0
V(Y[t],d=2,D=1)3.54639175257732Range8Trim Var.0.919462137296532
V(Y[t],d=3,D=1)10.1735366788788Range16Trim Var.6.34340905411968
V(Y[t],d=0,D=2)21.7461831048209Range24Trim Var.11.9395551314926
V(Y[t],d=1,D=2)5.58585831667777Range8Trim Var.2.69541778975741
V(Y[t],d=2,D=2)10.1056904041891Range16Trim Var.5.87803521779425
V(Y[t],d=3,D=2)28.3728096893253Range28Trim Var.13.2765673758865

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 18.2683126252505 & Range & 19 & Trim Var. & 12.08906397697 \tabularnewline
V(Y[t],d=1,D=0) & 1.00197181511618 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.95571824521426 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.84675796715779 & Range & 8 & Trim Var. & 2.60567752130481 \tabularnewline
V(Y[t],d=0,D=1) & 10.8566331167738 & Range & 18 & Trim Var. & 4.04036345372357 \tabularnewline
V(Y[t],d=1,D=1) & 1.90919461556012 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.54639175257732 & Range & 8 & Trim Var. & 0.919462137296532 \tabularnewline
V(Y[t],d=3,D=1) & 10.1735366788788 & Range & 16 & Trim Var. & 6.34340905411968 \tabularnewline
V(Y[t],d=0,D=2) & 21.7461831048209 & Range & 24 & Trim Var. & 11.9395551314926 \tabularnewline
V(Y[t],d=1,D=2) & 5.58585831667777 & Range & 8 & Trim Var. & 2.69541778975741 \tabularnewline
V(Y[t],d=2,D=2) & 10.1056904041891 & Range & 16 & Trim Var. & 5.87803521779425 \tabularnewline
V(Y[t],d=3,D=2) & 28.3728096893253 & Range & 28 & Trim Var. & 13.2765673758865 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26063&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]18.2683126252505[/C][C]Range[/C][C]19[/C][C]Trim Var.[/C][C]12.08906397697[/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]1.95571824521426[/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]5.84675796715779[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.60567752130481[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]10.8566331167738[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]4.04036345372357[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.90919461556012[/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]3.54639175257732[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]0.919462137296532[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]10.1735366788788[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.34340905411968[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]21.7461831048209[/C][C]Range[/C][C]24[/C][C]Trim Var.[/C][C]11.9395551314926[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.58585831667777[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.69541778975741[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]10.1056904041891[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]5.87803521779425[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]28.3728096893253[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]13.2765673758865[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26063&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26063&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)18.2683126252505Range19Trim Var.12.08906397697
V(Y[t],d=1,D=0)1.00197181511618Range2Trim Var.NA
V(Y[t],d=2,D=0)1.95571824521426Range4Trim Var.0
V(Y[t],d=3,D=0)5.84675796715779Range8Trim Var.2.60567752130481
V(Y[t],d=0,D=1)10.8566331167738Range18Trim Var.4.04036345372357
V(Y[t],d=1,D=1)1.90919461556012Range4Trim Var.0
V(Y[t],d=2,D=1)3.54639175257732Range8Trim Var.0.919462137296532
V(Y[t],d=3,D=1)10.1735366788788Range16Trim Var.6.34340905411968
V(Y[t],d=0,D=2)21.7461831048209Range24Trim Var.11.9395551314926
V(Y[t],d=1,D=2)5.58585831667777Range8Trim Var.2.69541778975741
V(Y[t],d=2,D=2)10.1056904041891Range16Trim Var.5.87803521779425
V(Y[t],d=3,D=2)28.3728096893253Range28Trim Var.13.2765673758865


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')