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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_rwalk.wasp
Title produced by softwareLaw of Averages
Date of computationSat, 29 Nov 2008 06:12:17 -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/t1227964396cye7u90jfjzut7i.htm/, Retrieved Sun, 19 May 2024 05:37:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26256, Retrieved Sun, 19 May 2024 05:37:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact145

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...] [2008-11-29 13:12:17] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum
2008-12-08 19:39:56 [94a54c888ac7f7d6874c3108eb0e1808] [reply] 
De student geeft een juiste interpretatie. Het volgende is eventueel voor de aanvulling.
De 2de kolom geeft de varianties aan na differentiatie. De variantie van de tijdreeks drukt een soort van risico, volatiliteit uit. De bedoeling van het te differentiëren is om deze variantie te minimaliseren zodat we zoveel mogelijk van de tijdreeks kunnen verklaren. De kleine d wijst op een normale differentiatie (om een LT trend te verwijderen), de grote D wijst op een seizoenale differentiatie (om seizoenaliteit te verwijderen). De volgende formule wordt toegepast. NABLA d NABLADs Yt = et waarbij s gelijk is aan 12 omdat we werken met maandcijfers. De NABLA operator = Yt – Yt-1. Uit de matrix kunnen we afleiden dat de differentiatie optimaal is bij d=1 of D=1.
2008-12-08 20:04:57 [Vincent Dolhain] [reply] 
correct
2008-12-10 07:43:42 [Peter Van Doninck] [reply] 
Misschien kleine verbetering: d is het aantal keer dat er gedifferentieerd is op lange termijn. De student heeft de correcte argumentatie gegeven, maar heeft niet gezegd bij welke d en D de tijdreeks stationair is. Dit is het geval bij d=1 en D=0. Toch bestaat er hier geen getrimde variantie. Eveneens is de tijdreeks stationair bij d=1 en D=1. Dit is de correcte oplossing. De getrimde variantie is hier gelijk aan nul. De getrimde variantie geeft meestal een correcter beeld, omdat ze gezuiverd is van outliërs.

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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=26256&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=26256&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26256&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)54.6614669338677Range29Trim Var.39.7398635086311
V(Y[t],d=1,D=0)1.00110260682007Range2Trim Var.NA
V(Y[t],d=2,D=0)1.93962166573740Range4Trim Var.0
V(Y[t],d=3,D=0)5.76611280586746Range8Trim Var.2.60549923621719
V(Y[t],d=0,D=1)10.5728447840576Range18Trim Var.4.38726790450928
V(Y[t],d=1,D=1)2.06582672108568Range4Trim Var.0
V(Y[t],d=2,D=1)3.90101395782954Range8Trim Var.2.31801376917656
V(Y[t],d=3,D=1)11.5123796540854Range16Trim Var.6.56383225208526
V(Y[t],d=0,D=2)25.2260061919505Range28Trim Var.12.1262555322927
V(Y[t],d=1,D=2)6.20237175216522Range8Trim Var.2.76919839419839
V(Y[t],d=2,D=2)11.9407320184476Range16Trim Var.6.72531776439822
V(Y[t],d=3,D=2)35.6098828250976Range32Trim Var.20.007680798005

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 54.6614669338677 & Range & 29 & Trim Var. & 39.7398635086311 \tabularnewline
V(Y[t],d=1,D=0) & 1.00110260682007 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.93962166573740 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.76611280586746 & Range & 8 & Trim Var. & 2.60549923621719 \tabularnewline
V(Y[t],d=0,D=1) & 10.5728447840576 & Range & 18 & Trim Var. & 4.38726790450928 \tabularnewline
V(Y[t],d=1,D=1) & 2.06582672108568 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.90101395782954 & Range & 8 & Trim Var. & 2.31801376917656 \tabularnewline
V(Y[t],d=3,D=1) & 11.5123796540854 & Range & 16 & Trim Var. & 6.56383225208526 \tabularnewline
V(Y[t],d=0,D=2) & 25.2260061919505 & Range & 28 & Trim Var. & 12.1262555322927 \tabularnewline
V(Y[t],d=1,D=2) & 6.20237175216522 & Range & 8 & Trim Var. & 2.76919839419839 \tabularnewline
V(Y[t],d=2,D=2) & 11.9407320184476 & Range & 16 & Trim Var. & 6.72531776439822 \tabularnewline
V(Y[t],d=3,D=2) & 35.6098828250976 & Range & 32 & Trim Var. & 20.007680798005 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26256&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]54.6614669338677[/C][C]Range[/C][C]29[/C][C]Trim Var.[/C][C]39.7398635086311[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00110260682007[/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]1.93962166573740[/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]5.76611280586746[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.60549923621719[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]10.5728447840576[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]4.38726790450928[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.06582672108568[/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]3.90101395782954[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.31801376917656[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.5123796540854[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.56383225208526[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]25.2260061919505[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]12.1262555322927[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.20237175216522[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.76919839419839[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.9407320184476[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.72531776439822[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]35.6098828250976[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]20.007680798005[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26256&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26256&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)54.6614669338677Range29Trim Var.39.7398635086311
V(Y[t],d=1,D=0)1.00110260682007Range2Trim Var.NA
V(Y[t],d=2,D=0)1.93962166573740Range4Trim Var.0
V(Y[t],d=3,D=0)5.76611280586746Range8Trim Var.2.60549923621719
V(Y[t],d=0,D=1)10.5728447840576Range18Trim Var.4.38726790450928
V(Y[t],d=1,D=1)2.06582672108568Range4Trim Var.0
V(Y[t],d=2,D=1)3.90101395782954Range8Trim Var.2.31801376917656
V(Y[t],d=3,D=1)11.5123796540854Range16Trim Var.6.56383225208526
V(Y[t],d=0,D=2)25.2260061919505Range28Trim Var.12.1262555322927
V(Y[t],d=1,D=2)6.20237175216522Range8Trim Var.2.76919839419839
V(Y[t],d=2,D=2)11.9407320184476Range16Trim Var.6.72531776439822
V(Y[t],d=3,D=2)35.6098828250976Range32Trim Var.20.007680798005


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')