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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 15:27:27 -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/t1228084137msy85j4mob75why.htm/, Retrieved Sun, 19 May 2024 05:43:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26773, Retrieved Sun, 19 May 2024 05:43:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact159

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] [] [2008-11-30 16:39:37] [4c8dfb519edec2da3492d7e6be9a5685]
F           [Law of Averages] [Q3] [2008-11-30 22:27:27] [e11d930c9e2984715c66c796cf63ef19] [Current]
Feedback Forum
2008-12-05 13:41:27 [Olivier Uyttendaele] [reply] 
Ik denk hier een goede uitleg gegeven te hebben aan de vraag, ik kan nog evenwel nog iets dieper ingaan op het doel van dit model.

De variance Reduction matrix is nodig om de verschillende differentie waarden op de reeks te zoeken en toont de bijhorende variatie.
Waar de variatie het kleinst is, heeft de reeks het beste stationaire karakter. Stationair betekent dat de lange termijn trend uit de zo klein mogelijk te maken zodoende zoveel mogelijk van de tijdreeks kunnen verklaren. Bedoeling hier is concreet gezegd om ‘d’ en ‘D’ te identificeren.



2008-12-07 13:52:40 [Steven Hulsmans] [reply] 
De variantie van de reeks is het kleinst bij V(Y[t],d=1,D=0). In de 2de kolom van de tabel zien we hier immers het laagste getal. Dit wil zeggen dat indien we de reeks 1x differentiëren we het lange termijn effect kunnen uitzuiveren, en zo een meer stabiel gemiddelde krijgen van de reeks. We moeten er wel rekening mee houden dan elke keer we opnieuw simuleren we elke keer een andere variantie bekomen.

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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=26773&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=26773&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26773&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)30.5370741482966Range25Trim Var.21.9324171801598
V(Y[t],d=1,D=0)1.00197181511618Range2Trim Var.NA
V(Y[t],d=2,D=0)1.87523534782995Range4Trim Var.0
V(Y[t],d=3,D=0)5.51612903225806Range8Trim Var.2.52164250043513
V(Y[t],d=0,D=1)11.6906453024540Range20Trim Var.6.56318237292608
V(Y[t],d=1,D=1)2.13991769547325Range4Trim Var.0
V(Y[t],d=2,D=1)3.98348818463366Range8Trim Var.2.25451720310766
V(Y[t],d=3,D=1)11.5867086989861Range16Trim Var.6.51198416855829
V(Y[t],d=0,D=2)26.4375762936754Range32Trim Var.12.0418125778740
V(Y[t],d=1,D=2)6.53164556962025Range8Trim Var.2.83747491896898
V(Y[t],d=2,D=2)12.3974630021142Range16Trim Var.6.5341068111849
V(Y[t],d=3,D=2)36.2456014619988Range32Trim Var.22.2796827479277

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 30.5370741482966 & Range & 25 & Trim Var. & 21.9324171801598 \tabularnewline
V(Y[t],d=1,D=0) & 1.00197181511618 & 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) & 5.51612903225806 & Range & 8 & Trim Var. & 2.52164250043513 \tabularnewline
V(Y[t],d=0,D=1) & 11.6906453024540 & Range & 20 & Trim Var. & 6.56318237292608 \tabularnewline
V(Y[t],d=1,D=1) & 2.13991769547325 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.98348818463366 & Range & 8 & Trim Var. & 2.25451720310766 \tabularnewline
V(Y[t],d=3,D=1) & 11.5867086989861 & Range & 16 & Trim Var. & 6.51198416855829 \tabularnewline
V(Y[t],d=0,D=2) & 26.4375762936754 & Range & 32 & Trim Var. & 12.0418125778740 \tabularnewline
V(Y[t],d=1,D=2) & 6.53164556962025 & Range & 8 & Trim Var. & 2.83747491896898 \tabularnewline
V(Y[t],d=2,D=2) & 12.3974630021142 & Range & 16 & Trim Var. & 6.5341068111849 \tabularnewline
V(Y[t],d=3,D=2) & 36.2456014619988 & Range & 32 & Trim Var. & 22.2796827479277 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26773&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]30.5370741482966[/C][C]Range[/C][C]25[/C][C]Trim Var.[/C][C]21.9324171801598[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00197181511618[/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]5.51612903225806[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.52164250043513[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]11.6906453024540[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]6.56318237292608[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.13991769547325[/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]3.98348818463366[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.25451720310766[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.5867086989861[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.51198416855829[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]26.4375762936754[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]12.0418125778740[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.53164556962025[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.83747491896898[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.3974630021142[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.5341068111849[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]36.2456014619988[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]22.2796827479277[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26773&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26773&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)30.5370741482966Range25Trim Var.21.9324171801598
V(Y[t],d=1,D=0)1.00197181511618Range2Trim Var.NA
V(Y[t],d=2,D=0)1.87523534782995Range4Trim Var.0
V(Y[t],d=3,D=0)5.51612903225806Range8Trim Var.2.52164250043513
V(Y[t],d=0,D=1)11.6906453024540Range20Trim Var.6.56318237292608
V(Y[t],d=1,D=1)2.13991769547325Range4Trim Var.0
V(Y[t],d=2,D=1)3.98348818463366Range8Trim Var.2.25451720310766
V(Y[t],d=3,D=1)11.5867086989861Range16Trim Var.6.51198416855829
V(Y[t],d=0,D=2)26.4375762936754Range32Trim Var.12.0418125778740
V(Y[t],d=1,D=2)6.53164556962025Range8Trim Var.2.83747491896898
V(Y[t],d=2,D=2)12.3974630021142Range16Trim Var.6.5341068111849
V(Y[t],d=3,D=2)36.2456014619988Range32Trim Var.22.2796827479277


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')