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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 computationSat, 29 Nov 2008 06:09:10 -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/29/t1227964208cy2oyickdic3pvb.htm/, Retrieved Mon, 20 May 2024 10:32:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26254, Retrieved Mon, 20 May 2024 10:32:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact154

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 Variantiereduc...] [2008-11-29 13:09:10] [d7f41258beeebb8716e3f5d39f3cdc01] [Current]
Feedback Forum
2008-12-08 19:24:26 [Jef Keersmaekers] [reply] 
De VRM gaat trachten om de spreading van de tijdreeks te verkleinen door te differentiëren, d staat voor een gewone differentiatie tewijl D staat voor een seizonale differentiatie. De eerste kolom in de matrix geeft aan hoe vaak er gewoon gedifferentieerd is en hoe vaak seizonaal gedifferentieerd. De 2e kolom geeft de variantie van onze tijdreeks weer, we moeten zoals eerder vermeld kijken naar de kleinste spreiding om een zo stationair mogelijke tijdreeks te bekomen, de optimale spreiding bekomen we bij 1.00152, dus na 1 keer gewoon te differentiëren en geen enkele keer seizonaal.

De Variance reduction matrix techniek wordt gebruikt om de variantie/spreiding te verkleinen om op die manier een zo stationair mogelijke trend te verkrijgen (een tijdreeks zonder trend of verandering van spreiding).

Door differentiatie kan men de variantie laten dalen. Maar men kan op 2 manieren differentiëren, d = gewone differentiatie en D = seizoenale differentiatie. Als we dit eenmaal weten moeten we enkel nog weten hoeveel keer deze differentiatie net moet uitgevoerd worden. Al deze gegevens kunnen we uit de tabel aflezen.

Uit de variance reduction tabel kunnen we zien dat de variantie het kleinst is bij V(Y[t],d=1,D=0) ,namelijk 1.00168207901747. Dit betekent dat als we de reeks 1 keer gewoon differentiëren we het lange termijn effect kunnen uitzuiveren en op die manier een meer stabiel gemiddelde verkrijgen.

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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 time0 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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26254&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]0 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=26254&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26254&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 time0 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)59.3568096192385Range34Trim Var.39.0947059844949
V(Y[t],d=1,D=0)1.00084506362122Range2Trim Var.NA
V(Y[t],d=2,D=0)1.95571824521426Range4Trim Var.0
V(Y[t],d=3,D=0)5.89514506393198Range8Trim Var.2.55655116055684
V(Y[t],d=0,D=1)12.8529302857912Range18Trim Var.7.21154273549262
V(Y[t],d=1,D=1)1.99957749216248Range4Trim Var.0
V(Y[t],d=2,D=1)3.91750880319036Range8Trim Var.2.20997514498757
V(Y[t],d=3,D=1)11.6528925619835Range16Trim Var.6.30466160464515
V(Y[t],d=0,D=2)23.6349049093322Range24Trim Var.13.8492694853599
V(Y[t],d=1,D=2)5.85625582944704Range8Trim Var.2.71628388353652
V(Y[t],d=2,D=2)11.5602358587345Range16Trim Var.6.62983571807101
V(Y[t],d=3,D=2)34.2539506217078Range32Trim Var.20.749013771762

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 59.3568096192385 & Range & 34 & Trim Var. & 39.0947059844949 \tabularnewline
V(Y[t],d=1,D=0) & 1.00084506362122 & 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) & 5.89514506393198 & Range & 8 & Trim Var. & 2.55655116055684 \tabularnewline
V(Y[t],d=0,D=1) & 12.8529302857912 & Range & 18 & Trim Var. & 7.21154273549262 \tabularnewline
V(Y[t],d=1,D=1) & 1.99957749216248 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.91750880319036 & Range & 8 & Trim Var. & 2.20997514498757 \tabularnewline
V(Y[t],d=3,D=1) & 11.6528925619835 & Range & 16 & Trim Var. & 6.30466160464515 \tabularnewline
V(Y[t],d=0,D=2) & 23.6349049093322 & Range & 24 & Trim Var. & 13.8492694853599 \tabularnewline
V(Y[t],d=1,D=2) & 5.85625582944704 & Range & 8 & Trim Var. & 2.71628388353652 \tabularnewline
V(Y[t],d=2,D=2) & 11.5602358587345 & Range & 16 & Trim Var. & 6.62983571807101 \tabularnewline
V(Y[t],d=3,D=2) & 34.2539506217078 & Range & 32 & Trim Var. & 20.749013771762 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26254&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]59.3568096192385[/C][C]Range[/C][C]34[/C][C]Trim Var.[/C][C]39.0947059844949[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00084506362122[/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]5.89514506393198[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.55655116055684[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.8529302857912[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]7.21154273549262[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.99957749216248[/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]3.91750880319036[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.20997514498757[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.6528925619835[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.30466160464515[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]23.6349049093322[/C][C]Range[/C][C]24[/C][C]Trim Var.[/C][C]13.8492694853599[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.85625582944704[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.71628388353652[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.5602358587345[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.62983571807101[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]34.2539506217078[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]20.749013771762[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26254&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26254&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)59.3568096192385Range34Trim Var.39.0947059844949
V(Y[t],d=1,D=0)1.00084506362122Range2Trim Var.NA
V(Y[t],d=2,D=0)1.95571824521426Range4Trim Var.0
V(Y[t],d=3,D=0)5.89514506393198Range8Trim Var.2.55655116055684
V(Y[t],d=0,D=1)12.8529302857912Range18Trim Var.7.21154273549262
V(Y[t],d=1,D=1)1.99957749216248Range4Trim Var.0
V(Y[t],d=2,D=1)3.91750880319036Range8Trim Var.2.20997514498757
V(Y[t],d=3,D=1)11.6528925619835Range16Trim Var.6.30466160464515
V(Y[t],d=0,D=2)23.6349049093322Range24Trim Var.13.8492694853599
V(Y[t],d=1,D=2)5.85625582944704Range8Trim Var.2.71628388353652
V(Y[t],d=2,D=2)11.5602358587345Range16Trim Var.6.62983571807101
V(Y[t],d=3,D=2)34.2539506217078Range32Trim Var.20.749013771762


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 500 ; par2 = 0.5 ;
Parameters (R input):
par1 = 500 ; par2 = 0.5 ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')