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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 10:25:52 -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/t1228152381rrkcesijtiysclt.htm/, Retrieved Sun, 05 May 2024 16:50:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27025, Retrieved Sun, 05 May 2024 16:50:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact252

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 / 7] [2008-11-30 17:25:28] [4300be8b33fd3dcdacd2aa9800ceba23]
F           [Law of Averages] [q3 taak 7] [2008-12-01 17:25:52] [732c025e7dfb439ac3d0c7b7e70fa7a1] [Current]
Feedback Forum
2008-12-08 01:24:40 [Gregory Van Overmeiren] [reply] 
De Variance Reduction Matrix heb je nodig om verschillende differentiatiewaarden op een tijdreeks te zoeken en ze toont de daarbij gerelateerde variatie. Waar de variatie het kleinst is, noteren we het meest adequate stationaire karakter. Door de lange termijn trend zo klein mogelijk te maken, kunnen we zoveel mogelijk van de tijdreeks verklaren. We moesten hier dus de optimale d en D te indentificeren. We zien dan de waarde van d en D optimaal is bij 1.
2008-12-08 10:17:50 [Elias Van Deun] [reply] 
De Variance Reduction Matrix is een techniek die de verschillende differentie waarden test. Daarbij wordt ook de variantie getoond. De reeks met de kleinste variantie is het meest stationair. In dit voorbeeld is het d=1 en D=0.
2008-12-08 22:59:10 [Gregory Van Overmeiren] [reply] 
correctie : We zien dan de waarde van d=1 en D=0 optimaal 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=27025&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=27025&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27025&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)48.5914068136273Range28Trim Var.34.934027213097
V(Y[t],d=1,D=0)1.00181085061690Range2Trim Var.NA
V(Y[t],d=2,D=0)1.91549295774648Range4Trim Var.0
V(Y[t],d=3,D=0)5.69354838709677Range8Trim Var.2.58168776023416
V(Y[t],d=0,D=1)12.1112027468273Range18Trim Var.6.43633609858525
V(Y[t],d=1,D=1)2.05734276370827Range4Trim Var.0
V(Y[t],d=2,D=1)3.86802426710789Range8Trim Var.2.25214038298150
V(Y[t],d=3,D=1)11.2809746954077Range16Trim Var.6.8534961154273
V(Y[t],d=0,D=2)23.2817868199912Range28Trim Var.12.6124118615335
V(Y[t],d=1,D=2)5.94934932267377Range8Trim Var.2.91181695017311
V(Y[t],d=2,D=2)11.0950660565026Range16Trim Var.6.15354449837208
V(Y[t],d=3,D=2)32.1016949152542Range28Trim Var.16.4632016971279

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 48.5914068136273 & Range & 28 & Trim Var. & 34.934027213097 \tabularnewline
V(Y[t],d=1,D=0) & 1.00181085061690 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.91549295774648 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.69354838709677 & Range & 8 & Trim Var. & 2.58168776023416 \tabularnewline
V(Y[t],d=0,D=1) & 12.1112027468273 & Range & 18 & Trim Var. & 6.43633609858525 \tabularnewline
V(Y[t],d=1,D=1) & 2.05734276370827 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.86802426710789 & Range & 8 & Trim Var. & 2.25214038298150 \tabularnewline
V(Y[t],d=3,D=1) & 11.2809746954077 & Range & 16 & Trim Var. & 6.8534961154273 \tabularnewline
V(Y[t],d=0,D=2) & 23.2817868199912 & Range & 28 & Trim Var. & 12.6124118615335 \tabularnewline
V(Y[t],d=1,D=2) & 5.94934932267377 & Range & 8 & Trim Var. & 2.91181695017311 \tabularnewline
V(Y[t],d=2,D=2) & 11.0950660565026 & Range & 16 & Trim Var. & 6.15354449837208 \tabularnewline
V(Y[t],d=3,D=2) & 32.1016949152542 & Range & 28 & Trim Var. & 16.4632016971279 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27025&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]48.5914068136273[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]34.934027213097[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00181085061690[/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]1.91549295774648[/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]5.69354838709677[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.58168776023416[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.1112027468273[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]6.43633609858525[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.05734276370827[/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]3.86802426710789[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.25214038298150[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.2809746954077[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.8534961154273[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]23.2817868199912[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]12.6124118615335[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.94934932267377[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.91181695017311[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.0950660565026[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.15354449837208[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]32.1016949152542[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]16.4632016971279[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27025&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27025&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)48.5914068136273Range28Trim Var.34.934027213097
V(Y[t],d=1,D=0)1.00181085061690Range2Trim Var.NA
V(Y[t],d=2,D=0)1.91549295774648Range4Trim Var.0
V(Y[t],d=3,D=0)5.69354838709677Range8Trim Var.2.58168776023416
V(Y[t],d=0,D=1)12.1112027468273Range18Trim Var.6.43633609858525
V(Y[t],d=1,D=1)2.05734276370827Range4Trim Var.0
V(Y[t],d=2,D=1)3.86802426710789Range8Trim Var.2.25214038298150
V(Y[t],d=3,D=1)11.2809746954077Range16Trim Var.6.8534961154273
V(Y[t],d=0,D=2)23.2817868199912Range28Trim Var.12.6124118615335
V(Y[t],d=1,D=2)5.94934932267377Range8Trim Var.2.91181695017311
V(Y[t],d=2,D=2)11.0950660565026Range16Trim Var.6.15354449837208
V(Y[t],d=3,D=2)32.1016949152542Range28Trim Var.16.4632016971279


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')