FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 14:18:33 -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/t12281664089mm9awy58g90tft.htm/, Retrieved Sun, 05 May 2024 14:39:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27412, Retrieved Sun, 05 May 2024 14:39:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact188

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] [Stefan Temmerman] [2008-12-01 21:18:33] [30f7cb12a8cb61e43b87da59ece37a2f] [Current]
Feedback Forum
2008-12-06 14:39:06 [Natalie De Wilde] [reply] 
In de tweede kolom zien we inderdaad de variantie, dit is de tijdreeks nadat deze een aantal keer gedifferentieerd is. D is seizoenaal differentiëren en d is niet seizoenaal differentiëren (wordt inderdaad gebruikt om de lange termijn trend weg te werken).
We moeten zoeken naar de kleinst mogelijk variantie, hoe kleiner deze is, hoe meer we kunnen verklaren.
Hier zien we de kleinste variantie bij d=1 en D=0. We kunnen ook kijken naar de Trim Var, hier moeten we opnieuw op zoek gaan naar de kleinste waarde, dikwijls komt dit overeen met de Variantie. In deze tabel staat er bij d=1 en D=0 geen Trim Var weergegeven.
2008-12-07 10:28:08 [Lana Van Wesemael] [reply] 
De d stelt het aantal keer voor dat men differentieert, hierdoor probeert men de lange termijn trend uit een reeks te halen. De D stelt het aantal keer voor dat men seizoenaal differentieert. Via deze transformatie probeert men de seizoenaliteit uit de reeks te filteren. Deze differentiaties worden toegepast om de tijdreeks stationair te maken.
2008-12-07 21:05:29 [Stefan Temmerman] [reply] 
De beste waarden om te differentiëren zijn d=1 en D=0. Deze maken de variantie het kleinst als we naar de VRM kijken.

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 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=27412&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=27412&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27412&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)55.0395831663327Range33Trim Var.35.9348919054801
V(Y[t],d=1,D=0)1.00023339852396Range2Trim Var.NA
V(Y[t],d=2,D=0)2.00400798364484Range4Trim Var.0
V(Y[t],d=3,D=0)5.94353216070617Range8Trim Var.2.72769343642418
V(Y[t],d=0,D=1)9.67514390547682Range16Trim Var.4.46858087598972
V(Y[t],d=1,D=1)1.91754337042952Range4Trim Var.0
V(Y[t],d=2,D=1)3.84329896907217Range8Trim Var.2.19063669592243
V(Y[t],d=3,D=1)11.3718326659283Range16Trim Var.6.40317602377428
V(Y[t],d=0,D=2)21.9347014595312Range26Trim Var.11.8760666682339
V(Y[t],d=1,D=2)5.74667554963358Range8Trim Var.2.44305168678428
V(Y[t],d=2,D=2)11.5770064495410Range16Trim Var.6.28055751021567
V(Y[t],d=3,D=2)34.2626939477550Range30Trim Var.19.5082698115921

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 55.0395831663327 & Range & 33 & Trim Var. & 35.9348919054801 \tabularnewline
V(Y[t],d=1,D=0) & 1.00023339852396 & 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) & 5.94353216070617 & Range & 8 & Trim Var. & 2.72769343642418 \tabularnewline
V(Y[t],d=0,D=1) & 9.67514390547682 & Range & 16 & Trim Var. & 4.46858087598972 \tabularnewline
V(Y[t],d=1,D=1) & 1.91754337042952 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.84329896907217 & Range & 8 & Trim Var. & 2.19063669592243 \tabularnewline
V(Y[t],d=3,D=1) & 11.3718326659283 & Range & 16 & Trim Var. & 6.40317602377428 \tabularnewline
V(Y[t],d=0,D=2) & 21.9347014595312 & Range & 26 & Trim Var. & 11.8760666682339 \tabularnewline
V(Y[t],d=1,D=2) & 5.74667554963358 & Range & 8 & Trim Var. & 2.44305168678428 \tabularnewline
V(Y[t],d=2,D=2) & 11.5770064495410 & Range & 16 & Trim Var. & 6.28055751021567 \tabularnewline
V(Y[t],d=3,D=2) & 34.2626939477550 & Range & 30 & Trim Var. & 19.5082698115921 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27412&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]55.0395831663327[/C][C]Range[/C][C]33[/C][C]Trim Var.[/C][C]35.9348919054801[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00023339852396[/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]5.94353216070617[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.72769343642418[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]9.67514390547682[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]4.46858087598972[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.91754337042952[/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]3.84329896907217[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.19063669592243[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.3718326659283[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.40317602377428[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]21.9347014595312[/C][C]Range[/C][C]26[/C][C]Trim Var.[/C][C]11.8760666682339[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.74667554963358[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.44305168678428[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.5770064495410[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.28055751021567[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]34.2626939477550[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]19.5082698115921[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27412&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27412&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)55.0395831663327Range33Trim Var.35.9348919054801
V(Y[t],d=1,D=0)1.00023339852396Range2Trim Var.NA
V(Y[t],d=2,D=0)2.00400798364484Range4Trim Var.0
V(Y[t],d=3,D=0)5.94353216070617Range8Trim Var.2.72769343642418
V(Y[t],d=0,D=1)9.67514390547682Range16Trim Var.4.46858087598972
V(Y[t],d=1,D=1)1.91754337042952Range4Trim Var.0
V(Y[t],d=2,D=1)3.84329896907217Range8Trim Var.2.19063669592243
V(Y[t],d=3,D=1)11.3718326659283Range16Trim Var.6.40317602377428
V(Y[t],d=0,D=2)21.9347014595312Range26Trim Var.11.8760666682339
V(Y[t],d=1,D=2)5.74667554963358Range8Trim Var.2.44305168678428
V(Y[t],d=2,D=2)11.5770064495410Range16Trim Var.6.28055751021567
V(Y[t],d=3,D=2)34.2626939477550Range30Trim Var.19.5082698115921


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')