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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 08:53:29 -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/t12280604509kfcalfkudtcddw.htm/, Retrieved Sun, 19 May 2024 10:20:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26577, Retrieved Sun, 19 May 2024 10:20:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact164

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] [nonstationaryques...] [2008-11-30 15:53:29] [89a49ebb3ece8e9a225c7f9f53a14c57] [Current]
Feedback Forum
2008-12-07 09:13:45 [6066575aa30c0611e452e930b1dff53d] [reply] 
Deze vraag werd ook zeer goed beantwoord. Er werd duidelijk vermeld dat D staat voor seizoenaal differentiëren, dit is omdat er eventueel seizoenaliteit in de tijdreeks zit en dat de kleine d staat voor het aantal keer dat er gedifferentieerd werd. Verder werd er ook vermeld dat als ik een tijdreeks wil voorspellen, dat de variantie dan het risico voorstelt dat in de tijdreeks zit. We trachten dus de variantie zo klein mogelijk te maken. De kleinste variantie is 1 (bij d=1 en D=0). Dit is dus bij 1 keer differentiëren. Dit is logisch want we hebben het zo gesimuleerd.

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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=26577&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=26577&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26577&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)39.8037835671343Range26Trim Var.29.3692027839291
V(Y[t],d=1,D=0)1.00168207901747Range2Trim Var.NA
V(Y[t],d=2,D=0)1.88329979879276Range4Trim Var.0
V(Y[t],d=3,D=0)5.60482248328682Range8Trim Var.2.49799734802400
V(Y[t],d=0,D=1)13.9476217726462Range20Trim Var.6.0348703341048
V(Y[t],d=1,D=1)2.09053497942387Range4Trim Var.0
V(Y[t],d=2,D=1)4.11544694752026Range8Trim Var.2.39764705882353
V(Y[t],d=3,D=1)12.6363465962341Range16Trim Var.6.90251170710941
V(Y[t],d=0,D=2)29.8902078726227Range34Trim Var.13.1897803234317
V(Y[t],d=1,D=2)6.20237175216522Range8Trim Var.2.86731916925280
V(Y[t],d=2,D=2)12.6003514687648Range16Trim Var.6.55796440275011
V(Y[t],d=3,D=2)39.2881355932203Range32Trim Var.21.6519187415776

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 39.8037835671343 & Range & 26 & Trim Var. & 29.3692027839291 \tabularnewline
V(Y[t],d=1,D=0) & 1.00168207901747 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.88329979879276 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.60482248328682 & Range & 8 & Trim Var. & 2.49799734802400 \tabularnewline
V(Y[t],d=0,D=1) & 13.9476217726462 & Range & 20 & Trim Var. & 6.0348703341048 \tabularnewline
V(Y[t],d=1,D=1) & 2.09053497942387 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.11544694752026 & Range & 8 & Trim Var. & 2.39764705882353 \tabularnewline
V(Y[t],d=3,D=1) & 12.6363465962341 & Range & 16 & Trim Var. & 6.90251170710941 \tabularnewline
V(Y[t],d=0,D=2) & 29.8902078726227 & Range & 34 & Trim Var. & 13.1897803234317 \tabularnewline
V(Y[t],d=1,D=2) & 6.20237175216522 & Range & 8 & Trim Var. & 2.86731916925280 \tabularnewline
V(Y[t],d=2,D=2) & 12.6003514687648 & Range & 16 & Trim Var. & 6.55796440275011 \tabularnewline
V(Y[t],d=3,D=2) & 39.2881355932203 & Range & 32 & Trim Var. & 21.6519187415776 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26577&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]39.8037835671343[/C][C]Range[/C][C]26[/C][C]Trim Var.[/C][C]29.3692027839291[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00168207901747[/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]1.88329979879276[/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]5.60482248328682[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.49799734802400[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]13.9476217726462[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]6.0348703341048[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.09053497942387[/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]4.11544694752026[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.39764705882353[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.6363465962341[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.90251170710941[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]29.8902078726227[/C][C]Range[/C][C]34[/C][C]Trim Var.[/C][C]13.1897803234317[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.20237175216522[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.86731916925280[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.6003514687648[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.55796440275011[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]39.2881355932203[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]21.6519187415776[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26577&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26577&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)39.8037835671343Range26Trim Var.29.3692027839291
V(Y[t],d=1,D=0)1.00168207901747Range2Trim Var.NA
V(Y[t],d=2,D=0)1.88329979879276Range4Trim Var.0
V(Y[t],d=3,D=0)5.60482248328682Range8Trim Var.2.49799734802400
V(Y[t],d=0,D=1)13.9476217726462Range20Trim Var.6.0348703341048
V(Y[t],d=1,D=1)2.09053497942387Range4Trim Var.0
V(Y[t],d=2,D=1)4.11544694752026Range8Trim Var.2.39764705882353
V(Y[t],d=3,D=1)12.6363465962341Range16Trim Var.6.90251170710941
V(Y[t],d=0,D=2)29.8902078726227Range34Trim Var.13.1897803234317
V(Y[t],d=1,D=2)6.20237175216522Range8Trim Var.2.86731916925280
V(Y[t],d=2,D=2)12.6003514687648Range16Trim Var.6.55796440275011
V(Y[t],d=3,D=2)39.2881355932203Range32Trim Var.21.6519187415776


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')