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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 computationTue, 02 Dec 2008 07:35:04 -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/02/t1228228541ftjcu79z7rn0xo9.htm/, Retrieved Sun, 19 May 2024 12:18:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27862, Retrieved Sun, 19 May 2024 12:18:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact174

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] [2008-12-02 14:35:04] [5bd06487453d0eec7a1bf04bf9f25085] [Current]
Feedback Forum
2008-12-04 10:18:11 [72e979bcc364082694890d2eccc1a66f] [reply] 
We moeten hier op zoek gaan naar de kleinste variantie en die vinden we bij d=1 en D=0. De student heeft deze opdracht correct uitgevoerd en heeft de tabel correct geïnterpreteerd.
2008-12-07 16:48:34 [Jolien Van Landeghem] [reply] 
We moeten voor een stationaire tijdreeks te bekomen inderdaad de kleinste variantie zoeken. We kunnen ook naar de trimmed variance kijken, die de extreme waarden weglaat. We gaan de variantie van de tijdreeks interpreteren als we het risico zo klein mogelijk wensen te houden (we willen een kleine variantie) deze vinden we, zoals de student correct vermeldde, voor d=1 en D:0 (logisch want dit werd zo gesimuleerd). De D is gelijk aan nul, want deze geeft aan hoeveel periodes we terug moeten gaan met seizoenaliteit, omdat seizoensinvloeden geen rol spelen in dit geval. De d=1 : we moeten 1 periode terugkijken om de kleinste variantie te krijgen. Deze vraag werd goed opgelost.
2008-12-08 17:28:03 [Hannes Van Hoof] [reply] 
In deze grafiek moet de differentiatie worden gezocht met met de kleinste variantie. Dit is hierbij d=1 en D=0. Dit is zeer logisch en konden we al van de vorige oef afleiden(in de autocorrelatie functie). Daar zagen we een trendmatig verloop zonder seizoenaliteit.

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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=27862&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=27862&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27862&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)75.5091142284569Range39Trim Var.52.1990240631751
V(Y[t],d=1,D=0)0.999492961827269Range2Trim Var.NA
V(Y[t],d=2,D=0)1.93962166573740Range4Trim Var.0
V(Y[t],d=3,D=0)5.62903225806452Range8Trim Var.2.69000239750659
V(Y[t],d=0,D=1)11.589574847679Range20Trim Var.4.25293617021277
V(Y[t],d=1,D=1)1.98352219433670Range4Trim Var.0
V(Y[t],d=2,D=1)3.73606550422129Range8Trim Var.0.956544850498339
V(Y[t],d=3,D=1)10.6280310130357Range16Trim Var.6.44319644839068
V(Y[t],d=0,D=2)24.4123485183547Range28Trim Var.13.5364863029764
V(Y[t],d=1,D=2)5.84808349988896Range8Trim Var.2.70471667960367
V(Y[t],d=2,D=2)11.2050561547176Range16Trim Var.6.28561745803125
V(Y[t],d=3,D=2)31.8049234958971Range30Trim Var.20.3349053910541

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 75.5091142284569 & Range & 39 & Trim Var. & 52.1990240631751 \tabularnewline
V(Y[t],d=1,D=0) & 0.999492961827269 & 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) & 5.62903225806452 & Range & 8 & Trim Var. & 2.69000239750659 \tabularnewline
V(Y[t],d=0,D=1) & 11.589574847679 & Range & 20 & Trim Var. & 4.25293617021277 \tabularnewline
V(Y[t],d=1,D=1) & 1.98352219433670 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.73606550422129 & Range & 8 & Trim Var. & 0.956544850498339 \tabularnewline
V(Y[t],d=3,D=1) & 10.6280310130357 & Range & 16 & Trim Var. & 6.44319644839068 \tabularnewline
V(Y[t],d=0,D=2) & 24.4123485183547 & Range & 28 & Trim Var. & 13.5364863029764 \tabularnewline
V(Y[t],d=1,D=2) & 5.84808349988896 & Range & 8 & Trim Var. & 2.70471667960367 \tabularnewline
V(Y[t],d=2,D=2) & 11.2050561547176 & Range & 16 & Trim Var. & 6.28561745803125 \tabularnewline
V(Y[t],d=3,D=2) & 31.8049234958971 & Range & 30 & Trim Var. & 20.3349053910541 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27862&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]75.5091142284569[/C][C]Range[/C][C]39[/C][C]Trim Var.[/C][C]52.1990240631751[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.999492961827269[/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]5.62903225806452[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.69000239750659[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]11.589574847679[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]4.25293617021277[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.98352219433670[/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]3.73606550422129[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]0.956544850498339[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]10.6280310130357[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.44319644839068[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]24.4123485183547[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]13.5364863029764[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.84808349988896[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.70471667960367[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.2050561547176[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.28561745803125[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]31.8049234958971[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]20.3349053910541[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27862&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27862&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)75.5091142284569Range39Trim Var.52.1990240631751
V(Y[t],d=1,D=0)0.999492961827269Range2Trim Var.NA
V(Y[t],d=2,D=0)1.93962166573740Range4Trim Var.0
V(Y[t],d=3,D=0)5.62903225806452Range8Trim Var.2.69000239750659
V(Y[t],d=0,D=1)11.589574847679Range20Trim Var.4.25293617021277
V(Y[t],d=1,D=1)1.98352219433670Range4Trim Var.0
V(Y[t],d=2,D=1)3.73606550422129Range8Trim Var.0.956544850498339
V(Y[t],d=3,D=1)10.6280310130357Range16Trim Var.6.44319644839068
V(Y[t],d=0,D=2)24.4123485183547Range28Trim Var.13.5364863029764
V(Y[t],d=1,D=2)5.84808349988896Range8Trim Var.2.70471667960367
V(Y[t],d=2,D=2)11.2050561547176Range16Trim Var.6.28561745803125
V(Y[t],d=3,D=2)31.8049234958971Range30Trim Var.20.3349053910541


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')