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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 computationMon, 01 Dec 2008 15:49:32 -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/t1228171845jy555xk7xzoohnf.htm/, Retrieved Sun, 05 May 2024 11:23:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27490, Retrieved Sun, 05 May 2024 11:23:28 +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] [] [2008-12-01 22:49:32] [75a00449045803b2332dacf227dc78d5] [Current]
Feedback Forum
2008-12-07 13:16:30 [Glenn De Maeyer] [reply] 
De variance Reduction matrix heb je nodig om de verschillende differentie waarden op de reeks te zoeken en toont je de bijhorende variatie.
Waar de variatie het kleinst is, heeft de reeks het beste stationaire karakter. Stationair betekent dat de lange termijn trend zo klein mogelijk te maken zodoende zoveel mogelijk van de tijdreeks kunnen verklaren. Bedoeling hier is concreet gezegd om ‘d’ en ‘D’ te identificeren.

Je moet de tabel als volgt interpreteren:


Kolom 1: Hier lees je af van wat de variatie berekend wordt.

d = 0 => het aantal keren dat we niet seizonaal differentiëren – LT trend eruit te halen
D = 0 => het aantal keren dat we wel seizonaal differentiëren

Kolom 2: In deze kolom zal je de laagste waarde moeten zoeken. De laagste waarde staat in de 2de rij (0.99862375353116). Je zal hier dus niet seizonaal differentiëren aangezien d=1 en D=0, dit is de meest gunstige waarde.

Kolom 4 + 5: Dit is de getrimde variatie. 5% van de kleinste en grootste waarden worden weggelaten en beïnvloeden bijgevolg het resultaat niet meer.
2008-12-07 15:25:29 [Chi-Kwong Man] [reply] 
In de eerste kolom van de variance reduction matrix vindt je de berekening van de variantie. De kleine 'd' staat voor differentiëren (lange termijn effect zuiveren,
waardoor men een stabieler gemiddelde krijgt). V(Y[t],d=1,D=0) betekent dat men '1x' differentiërt. De tweede kolom geeft de variantie weer (de kleinste kan men vinden in de tweede rij (0.99862375353116).
2008-12-08 14:07:25 [Bas van Keken] [reply] 
Ik lees in de tabel bij d=1 de waarde 0.99862375353116. Bij het maken van een herproductie kunt u allen een ander getal bekomen. De conclusie blijft echter dat bij 1 maal seizoenaal differentieren de waarde het kleinst blijft.
d = het aantal keer dat de reeks niet-seizoenaal gedifferentieerd is.
D = het aantal keer dat de reeks seizoenaal gedifferentieerd is.

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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=27490&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=27490&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27490&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)76.522741482966Range36Trim Var.55.9335781141843
V(Y[t],d=1,D=0)0.99862375353116Range2Trim Var.NA
V(Y[t],d=2,D=0)1.87523534782995Range4Trim Var.0
V(Y[t],d=3,D=0)5.45966119296424Range8Trim Var.2.59484556364352
V(Y[t],d=0,D=1)12.0300265930589Range16Trim Var.6.04664673630191
V(Y[t],d=1,D=1)2.12338918886945Range4Trim Var.0
V(Y[t],d=2,D=1)4.20618556701031Range8Trim Var.2.24769415237041
V(Y[t],d=3,D=1)12.6941467155150Range16Trim Var.7.15476706653177
V(Y[t],d=0,D=2)26.9380804953560Range26Trim Var.13.3060064935065
V(Y[t],d=1,D=2)6.46406395736176Range8Trim Var.2.77694235588972
V(Y[t],d=2,D=2)13.073924407454Range16Trim Var.6.4973411890148
V(Y[t],d=3,D=2)40.1183574013688Range30Trim Var.25.2855326345938

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 76.522741482966 & Range & 36 & Trim Var. & 55.9335781141843 \tabularnewline
V(Y[t],d=1,D=0) & 0.99862375353116 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.87523534782995 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.45966119296424 & Range & 8 & Trim Var. & 2.59484556364352 \tabularnewline
V(Y[t],d=0,D=1) & 12.0300265930589 & Range & 16 & Trim Var. & 6.04664673630191 \tabularnewline
V(Y[t],d=1,D=1) & 2.12338918886945 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.20618556701031 & Range & 8 & Trim Var. & 2.24769415237041 \tabularnewline
V(Y[t],d=3,D=1) & 12.6941467155150 & Range & 16 & Trim Var. & 7.15476706653177 \tabularnewline
V(Y[t],d=0,D=2) & 26.9380804953560 & Range & 26 & Trim Var. & 13.3060064935065 \tabularnewline
V(Y[t],d=1,D=2) & 6.46406395736176 & Range & 8 & Trim Var. & 2.77694235588972 \tabularnewline
V(Y[t],d=2,D=2) & 13.073924407454 & Range & 16 & Trim Var. & 6.4973411890148 \tabularnewline
V(Y[t],d=3,D=2) & 40.1183574013688 & Range & 30 & Trim Var. & 25.2855326345938 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27490&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]76.522741482966[/C][C]Range[/C][C]36[/C][C]Trim Var.[/C][C]55.9335781141843[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.99862375353116[/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]1.87523534782995[/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]5.45966119296424[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.59484556364352[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.0300265930589[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.04664673630191[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.12338918886945[/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]4.20618556701031[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.24769415237041[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.6941467155150[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]7.15476706653177[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]26.9380804953560[/C][C]Range[/C][C]26[/C][C]Trim Var.[/C][C]13.3060064935065[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.46406395736176[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.77694235588972[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]13.073924407454[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.4973411890148[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]40.1183574013688[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]25.2855326345938[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27490&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27490&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)76.522741482966Range36Trim Var.55.9335781141843
V(Y[t],d=1,D=0)0.99862375353116Range2Trim Var.NA
V(Y[t],d=2,D=0)1.87523534782995Range4Trim Var.0
V(Y[t],d=3,D=0)5.45966119296424Range8Trim Var.2.59484556364352
V(Y[t],d=0,D=1)12.0300265930589Range16Trim Var.6.04664673630191
V(Y[t],d=1,D=1)2.12338918886945Range4Trim Var.0
V(Y[t],d=2,D=1)4.20618556701031Range8Trim Var.2.24769415237041
V(Y[t],d=3,D=1)12.6941467155150Range16Trim Var.7.15476706653177
V(Y[t],d=0,D=2)26.9380804953560Range26Trim Var.13.3060064935065
V(Y[t],d=1,D=2)6.46406395736176Range8Trim Var.2.77694235588972
V(Y[t],d=2,D=2)13.073924407454Range16Trim Var.6.4973411890148
V(Y[t],d=3,D=2)40.1183574013688Range30Trim Var.25.2855326345938


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')