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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 04:09:28 -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/t1228043407uyn82osehwaplst.htm/, Retrieved Sun, 19 May 2024 12:40:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26431, Retrieved Sun, 19 May 2024 12:40:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact182

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 11:09:28] [dafd615cb3e0decc017580d68ecea30a] [Current]
Feedback Forum
2008-12-07 11:33:25 [Dana Molenberghs] [reply] 
De uitleg van Jeroen klopt helemaal. De d staat voor het aantal keren niet-seizonaal differentieren, terwijl de grote D voor het aantal keer seizoenaal differentieren staat (Hoe groter de variantie wordt (2de kolom), hoe groter de onzekerheid wordt. Daarom is de beste combinatie diegene met de kleinste variantie.)
Met de kleine d halen we de lange termijn trend uit de tijdreeks en met de grote D halen we de seizoenaliteit eruit. Zo maken we de tijdrijks stationair.

2008-12-08 21:04:53 [Jeroen Michel] [reply] 
De test die hier wordt gebruikt (VRM test), wordt gebruikt om de verschillende waarden die een reeks bevat te onderzoeken. Voorts wordt in een tabel weergegeven wat de varianties zijn bij de waarden d en D.

d = het aantal keer dat de reeks niet-seizoenaal gedifferentieerd is.
D = het aantal keer dat de reeks seizoenaal gedifferentieerd is.

Wanneer we de bijbehorende tabel bekijken bij deze output zien we dat de kleinste variantie bestaat bij d:1 en D:0.

Er moet dus een niet-seizoenale randam-walk getrokken worden om deze tijdreeks stationair te maken. Dit verklaart bovenstaand resultaat en de conclusie van de student.

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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'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=26431&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=26431&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26431&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)93.6068136272545Range35Trim Var.66.8119532769578
V(Y[t],d=1,D=0)0.997625773635625Range2Trim Var.NA
V(Y[t],d=2,D=0)2.02010456312170Range4Trim Var.0
V(Y[t],d=3,D=0)6.00804828973843Range8Trim Var.2.74042067736185
V(Y[t],d=0,D=1)9.85114619449961Range16Trim Var.4.56315338474722
V(Y[t],d=1,D=1)2.02462375677069Range4Trim Var.0
V(Y[t],d=2,D=1)4.30515463917526Range8Trim Var.2.20583464585439
V(Y[t],d=3,D=1)13.0412541535316Range16Trim Var.6.35383303823202
V(Y[t],d=0,D=2)19.4340203449801Range24Trim Var.10.9999773781246
V(Y[t],d=1,D=2)6.02524539196092Range8Trim Var.2.7832122126951
V(Y[t],d=2,D=2)12.8624187116975Range16Trim Var.6.86150490730643
V(Y[t],d=3,D=2)39.0677966101695Range32Trim Var.22.8642964194406

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 93.6068136272545 & Range & 35 & Trim Var. & 66.8119532769578 \tabularnewline
V(Y[t],d=1,D=0) & 0.997625773635625 & 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) & 6.00804828973843 & Range & 8 & Trim Var. & 2.74042067736185 \tabularnewline
V(Y[t],d=0,D=1) & 9.85114619449961 & Range & 16 & Trim Var. & 4.56315338474722 \tabularnewline
V(Y[t],d=1,D=1) & 2.02462375677069 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.30515463917526 & Range & 8 & Trim Var. & 2.20583464585439 \tabularnewline
V(Y[t],d=3,D=1) & 13.0412541535316 & Range & 16 & Trim Var. & 6.35383303823202 \tabularnewline
V(Y[t],d=0,D=2) & 19.4340203449801 & Range & 24 & Trim Var. & 10.9999773781246 \tabularnewline
V(Y[t],d=1,D=2) & 6.02524539196092 & Range & 8 & Trim Var. & 2.7832122126951 \tabularnewline
V(Y[t],d=2,D=2) & 12.8624187116975 & Range & 16 & Trim Var. & 6.86150490730643 \tabularnewline
V(Y[t],d=3,D=2) & 39.0677966101695 & Range & 32 & Trim Var. & 22.8642964194406 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26431&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]93.6068136272545[/C][C]Range[/C][C]35[/C][C]Trim Var.[/C][C]66.8119532769578[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.997625773635625[/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]6.00804828973843[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.74042067736185[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]9.85114619449961[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]4.56315338474722[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.02462375677069[/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]4.30515463917526[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.20583464585439[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]13.0412541535316[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.35383303823202[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]19.4340203449801[/C][C]Range[/C][C]24[/C][C]Trim Var.[/C][C]10.9999773781246[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.02524539196092[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.7832122126951[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.8624187116975[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.86150490730643[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]39.0677966101695[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]22.8642964194406[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26431&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26431&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)93.6068136272545Range35Trim Var.66.8119532769578
V(Y[t],d=1,D=0)0.997625773635625Range2Trim Var.NA
V(Y[t],d=2,D=0)2.02010456312170Range4Trim Var.0
V(Y[t],d=3,D=0)6.00804828973843Range8Trim Var.2.74042067736185
V(Y[t],d=0,D=1)9.85114619449961Range16Trim Var.4.56315338474722
V(Y[t],d=1,D=1)2.02462375677069Range4Trim Var.0
V(Y[t],d=2,D=1)4.30515463917526Range8Trim Var.2.20583464585439
V(Y[t],d=3,D=1)13.0412541535316Range16Trim Var.6.35383303823202
V(Y[t],d=0,D=2)19.4340203449801Range24Trim Var.10.9999773781246
V(Y[t],d=1,D=2)6.02524539196092Range8Trim Var.2.7832122126951
V(Y[t],d=2,D=2)12.8624187116975Range16Trim Var.6.86150490730643
V(Y[t],d=3,D=2)39.0677966101695Range32Trim Var.22.8642964194406


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')