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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 08:01:10 -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/30/t1228057379aheamy0lw7eonhe.htm/, Retrieved Sun, 19 May 2024 03:47:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26551, Retrieved Sun, 19 May 2024 03:47:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsreproductie vraag 3 Natalie De Wilde
Estimated Impact160

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] [Law of averages] [2008-11-30 15:01:10] [bb7e3816cefc365f4d7adcd50784b783] [Current]
Feedback Forum
2008-12-06 12:40:34 [Ken Wright] [reply] 
De bedoeling van het differentiëren is om deze variantie te minimaliseren zodat we zoveel mogelijk van de tijdreeks kunnen verklaren. Als jouw tijdreeks met veel outliers te maken heeft, kan je best beroep doen op de trimmed variance en hieruit de kleinste kiezen, deze neemt de aller grootste en aller kleinste gegevens niet mee in zijn berekening. d staat voor gewone differentiatie, dus om de LT trend uit je tijdreeks te halen. 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.
2008-12-09 17:22:38 [Julian De Ruyter] [reply] 
Je hebt dit juist opgelost en een correcte conclusie gegeven.
het is inderdaad zo dat men moet kijken naar de kleinste variantie om te weten hoe vaak men trendmatig en/of seizonaal moet differentieeren (in dit geval 1 keer trendmatig) kleinste variantie betekent het minste risico en dus het beste model. (hierbij d=1 en D=0 -> 1.00132795711906)

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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'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26551&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26551&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26551&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'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)52.5875751503006Range28Trim Var.36.2577504397611
V(Y[t],d=1,D=0)1.00132795711906Range2Trim Var.NA
V(Y[t],d=2,D=0)1.92352508626054Range4Trim Var.0
V(Y[t],d=3,D=0)5.65320958006101Range8Trim Var.2.62932900432900
V(Y[t],d=0,D=1)11.8350388797253Range16Trim Var.6.40438186135076
V(Y[t],d=1,D=1)2.20569371561842Range4Trim Var.0
V(Y[t],d=2,D=1)4.18969072164948Range8Trim Var.2.52235294117647
V(Y[t],d=3,D=1)12.3884127119366Range16Trim Var.7.30952772749712
V(Y[t],d=0,D=2)29.1377620521893Range26Trim Var.14.0559148936170
V(Y[t],d=1,D=2)6.96982456140351Range8Trim Var.2.71926002369759
V(Y[t],d=2,D=2)13.1923176421263Range16Trim Var.7.33015935471178
V(Y[t],d=3,D=2)38.7626401977998Range30Trim Var.22.9282250853264

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 52.5875751503006 & Range & 28 & Trim Var. & 36.2577504397611 \tabularnewline
V(Y[t],d=1,D=0) & 1.00132795711906 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.92352508626054 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.65320958006101 & Range & 8 & Trim Var. & 2.62932900432900 \tabularnewline
V(Y[t],d=0,D=1) & 11.8350388797253 & Range & 16 & Trim Var. & 6.40438186135076 \tabularnewline
V(Y[t],d=1,D=1) & 2.20569371561842 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.18969072164948 & Range & 8 & Trim Var. & 2.52235294117647 \tabularnewline
V(Y[t],d=3,D=1) & 12.3884127119366 & Range & 16 & Trim Var. & 7.30952772749712 \tabularnewline
V(Y[t],d=0,D=2) & 29.1377620521893 & Range & 26 & Trim Var. & 14.0559148936170 \tabularnewline
V(Y[t],d=1,D=2) & 6.96982456140351 & Range & 8 & Trim Var. & 2.71926002369759 \tabularnewline
V(Y[t],d=2,D=2) & 13.1923176421263 & Range & 16 & Trim Var. & 7.33015935471178 \tabularnewline
V(Y[t],d=3,D=2) & 38.7626401977998 & Range & 30 & Trim Var. & 22.9282250853264 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26551&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]52.5875751503006[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]36.2577504397611[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00132795711906[/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]1.92352508626054[/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]5.65320958006101[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.62932900432900[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]11.8350388797253[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.40438186135076[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.20569371561842[/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]4.18969072164948[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.52235294117647[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.3884127119366[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]7.30952772749712[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]29.1377620521893[/C][C]Range[/C][C]26[/C][C]Trim Var.[/C][C]14.0559148936170[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.96982456140351[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.71926002369759[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]13.1923176421263[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]7.33015935471178[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]38.7626401977998[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]22.9282250853264[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26551&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26551&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)52.5875751503006Range28Trim Var.36.2577504397611
V(Y[t],d=1,D=0)1.00132795711906Range2Trim Var.NA
V(Y[t],d=2,D=0)1.92352508626054Range4Trim Var.0
V(Y[t],d=3,D=0)5.65320958006101Range8Trim Var.2.62932900432900
V(Y[t],d=0,D=1)11.8350388797253Range16Trim Var.6.40438186135076
V(Y[t],d=1,D=1)2.20569371561842Range4Trim Var.0
V(Y[t],d=2,D=1)4.18969072164948Range8Trim Var.2.52235294117647
V(Y[t],d=3,D=1)12.3884127119366Range16Trim Var.7.30952772749712
V(Y[t],d=0,D=2)29.1377620521893Range26Trim Var.14.0559148936170
V(Y[t],d=1,D=2)6.96982456140351Range8Trim Var.2.71926002369759
V(Y[t],d=2,D=2)13.1923176421263Range16Trim Var.7.33015935471178
V(Y[t],d=3,D=2)38.7626401977998Range30Trim Var.22.9282250853264


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')