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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 07:14:32 -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/t1228054582aj3dadq5upe2iv8.htm/, Retrieved Mon, 20 May 2024 08:39:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26511, Retrieved Mon, 20 May 2024 08:39:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact144

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...] [2008-11-30 14:14:32] [d6e9f26c3644bfc30f06303d9993b878] [Current]
Feedback Forum
2008-12-07 16:55:29 [Elias Van Deun] [reply] 
De Variance Reduction Matrix is een techniek die de verschillende differentie waarden test. Daarbij wordt ook de variantie getoond. De reeks met de kleinste variantie is het meest stationair. In dit voorbeeld is het d=1 en D=0.
2008-12-08 18:26:18 [Peter Melgers] [reply] 
d = het aantal keer dat we gewoon differentiëren.
D = het aantal keer dat we seizoenaal differentiëren

Bij d=0 en D=0 (in dit geval gaan we dus niet differentiëren) is de variantie 59,35. Deze variante duidt op de spreidingsgrootte van de reeks.

We hopen dat wanneer we gaan differentiëren de variantie (spreidingsgrootte) zal verkleinen.

De beste oplossing is bijgevolg de oplossing met de kleinste variantie. In dit geval is deze te vinden bij d=1 en D=0.

De variantie is dus zo klein mogelijk als we 1 keer gewoon gaan differentiëren.
Dit komt overeen met het random walk model.

Post a new message

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=26511&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=26511&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26511&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)106.830765531062Range44Trim Var.68.5681031224784
V(Y[t],d=1,D=0)0.995243499046285Range2Trim Var.NA
V(Y[t],d=2,D=0)2.00400798364484Range4Trim Var.0
V(Y[t],d=3,D=0)5.92740312844811Range8Trim Var.2.72440458647355
V(Y[t],d=0,D=1)12.0080620729121Range18Trim Var.3.975525405693
V(Y[t],d=1,D=1)1.99176954732510Range4Trim Var.0
V(Y[t],d=2,D=1)3.98348818463366Range8Trim Var.2.25469478357381
V(Y[t],d=3,D=1)11.8346425832836Range16Trim Var.6.2952682295412
V(Y[t],d=0,D=2)28.5216629809819Range30Trim Var.12.9493125954729
V(Y[t],d=1,D=2)6.08437041972019Range8Trim Var.2.59799922299922
V(Y[t],d=2,D=2)12.1437632135307Range16Trim Var.6.30048596799227
V(Y[t],d=3,D=2)36.2202673164439Range32Trim Var.20.0673267326733

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 106.830765531062 & Range & 44 & Trim Var. & 68.5681031224784 \tabularnewline
V(Y[t],d=1,D=0) & 0.995243499046285 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.00400798364484 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.92740312844811 & Range & 8 & Trim Var. & 2.72440458647355 \tabularnewline
V(Y[t],d=0,D=1) & 12.0080620729121 & Range & 18 & Trim Var. & 3.975525405693 \tabularnewline
V(Y[t],d=1,D=1) & 1.99176954732510 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.98348818463366 & Range & 8 & Trim Var. & 2.25469478357381 \tabularnewline
V(Y[t],d=3,D=1) & 11.8346425832836 & Range & 16 & Trim Var. & 6.2952682295412 \tabularnewline
V(Y[t],d=0,D=2) & 28.5216629809819 & Range & 30 & Trim Var. & 12.9493125954729 \tabularnewline
V(Y[t],d=1,D=2) & 6.08437041972019 & Range & 8 & Trim Var. & 2.59799922299922 \tabularnewline
V(Y[t],d=2,D=2) & 12.1437632135307 & Range & 16 & Trim Var. & 6.30048596799227 \tabularnewline
V(Y[t],d=3,D=2) & 36.2202673164439 & Range & 32 & Trim Var. & 20.0673267326733 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26511&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]106.830765531062[/C][C]Range[/C][C]44[/C][C]Trim Var.[/C][C]68.5681031224784[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.995243499046285[/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]2.00400798364484[/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]5.92740312844811[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.72440458647355[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.0080620729121[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]3.975525405693[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.99176954732510[/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]3.98348818463366[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.25469478357381[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.8346425832836[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.2952682295412[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]28.5216629809819[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]12.9493125954729[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.08437041972019[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.59799922299922[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.1437632135307[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.30048596799227[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]36.2202673164439[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]20.0673267326733[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26511&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26511&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)106.830765531062Range44Trim Var.68.5681031224784
V(Y[t],d=1,D=0)0.995243499046285Range2Trim Var.NA
V(Y[t],d=2,D=0)2.00400798364484Range4Trim Var.0
V(Y[t],d=3,D=0)5.92740312844811Range8Trim Var.2.72440458647355
V(Y[t],d=0,D=1)12.0080620729121Range18Trim Var.3.975525405693
V(Y[t],d=1,D=1)1.99176954732510Range4Trim Var.0
V(Y[t],d=2,D=1)3.98348818463366Range8Trim Var.2.25469478357381
V(Y[t],d=3,D=1)11.8346425832836Range16Trim Var.6.2952682295412
V(Y[t],d=0,D=2)28.5216629809819Range30Trim Var.12.9493125954729
V(Y[t],d=1,D=2)6.08437041972019Range8Trim Var.2.59799922299922
V(Y[t],d=2,D=2)12.1437632135307Range16Trim Var.6.30048596799227
V(Y[t],d=3,D=2)36.2202673164439Range32Trim Var.20.0673267326733


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')