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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 12:48:11 -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/t1228160923fl659kbyaz8guk9.htm/, Retrieved Sun, 05 May 2024 14:31:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27267, Retrieved Sun, 05 May 2024 14:31:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact178

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] [2008-12-01 19:48:11] [5e2b1e7aa808f9f0d23fd35605d4968f] [Current]
Feedback Forum
2008-12-04 18:22:18 [Stéphanie Claes] [reply] 
Er werd geen interpretatie gegeven van de Variance Reduction Matrix.

Als we de tabel bekijken dan zien we in de tweede kolom de verschillende varianties (= hoe groot de spreiding is van de reeks). Het doel van het differentieren is om de variantie te minimaliseren, zodat zoveel mogelijk van de tijdreeks verklaard kan worden (wat niet verklaard kan worden kan best zo klein mogelijk zijn).

d = gewone differentiatie, om de lange termijntrend te verwijderen
D = seizoenale differentiatie, om de seizoenaliteit te verwijderen.

De kleinste variantie vinden we terug in de tweede rij: 1.00023339852396, waarbij d=1,D=0.
We gaan dus 1 keer gewoon differentiëren om de variantie zo klein mogelijk te maken (= Random Walk).

Post a new message

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=27267&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=27267&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27267&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)149.826468937876Range44Trim Var.120.045913740378
V(Y[t],d=1,D=0)1.00023339852396Range2Trim Var.NA
V(Y[t],d=2,D=0)1.92352508626054Range4Trim Var.0
V(Y[t],d=3,D=0)5.82258064516129Range8Trim Var.2.44710470100787
V(Y[t],d=0,D=1)14.5786346652304Range16Trim Var.7.7150974025974
V(Y[t],d=1,D=1)1.95878013537151Range4Trim Var.0
V(Y[t],d=2,D=1)3.99998302999448Range8Trim Var.2.20832913179389
V(Y[t],d=3,D=1)12.4131549799778Range16Trim Var.6.30197996068843
V(Y[t],d=0,D=2)23.2261831048209Range28Trim Var.11.4554409994913
V(Y[t],d=1,D=2)5.78895847212969Range8Trim Var.2.59230804548446
V(Y[t],d=2,D=2)11.9915433403806Range16Trim Var.6.77194671802279
V(Y[t],d=3,D=2)37.5503995413337Range32Trim Var.22.5824936205566

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 149.826468937876 & Range & 44 & Trim Var. & 120.045913740378 \tabularnewline
V(Y[t],d=1,D=0) & 1.00023339852396 & 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) & 5.82258064516129 & Range & 8 & Trim Var. & 2.44710470100787 \tabularnewline
V(Y[t],d=0,D=1) & 14.5786346652304 & Range & 16 & Trim Var. & 7.7150974025974 \tabularnewline
V(Y[t],d=1,D=1) & 1.95878013537151 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.99998302999448 & Range & 8 & Trim Var. & 2.20832913179389 \tabularnewline
V(Y[t],d=3,D=1) & 12.4131549799778 & Range & 16 & Trim Var. & 6.30197996068843 \tabularnewline
V(Y[t],d=0,D=2) & 23.2261831048209 & Range & 28 & Trim Var. & 11.4554409994913 \tabularnewline
V(Y[t],d=1,D=2) & 5.78895847212969 & Range & 8 & Trim Var. & 2.59230804548446 \tabularnewline
V(Y[t],d=2,D=2) & 11.9915433403806 & Range & 16 & Trim Var. & 6.77194671802279 \tabularnewline
V(Y[t],d=3,D=2) & 37.5503995413337 & Range & 32 & Trim Var. & 22.5824936205566 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27267&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]149.826468937876[/C][C]Range[/C][C]44[/C][C]Trim Var.[/C][C]120.045913740378[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00023339852396[/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]5.82258064516129[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.44710470100787[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]14.5786346652304[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]7.7150974025974[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.95878013537151[/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]3.99998302999448[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.20832913179389[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.4131549799778[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.30197996068843[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]23.2261831048209[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]11.4554409994913[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.78895847212969[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.59230804548446[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.9915433403806[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.77194671802279[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]37.5503995413337[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]22.5824936205566[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27267&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27267&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)149.826468937876Range44Trim Var.120.045913740378
V(Y[t],d=1,D=0)1.00023339852396Range2Trim Var.NA
V(Y[t],d=2,D=0)1.92352508626054Range4Trim Var.0
V(Y[t],d=3,D=0)5.82258064516129Range8Trim Var.2.44710470100787
V(Y[t],d=0,D=1)14.5786346652304Range16Trim Var.7.7150974025974
V(Y[t],d=1,D=1)1.95878013537151Range4Trim Var.0
V(Y[t],d=2,D=1)3.99998302999448Range8Trim Var.2.20832913179389
V(Y[t],d=3,D=1)12.4131549799778Range16Trim Var.6.30197996068843
V(Y[t],d=0,D=2)23.2261831048209Range28Trim Var.11.4554409994913
V(Y[t],d=1,D=2)5.78895847212969Range8Trim Var.2.59230804548446
V(Y[t],d=2,D=2)11.9915433403806Range16Trim Var.6.77194671802279
V(Y[t],d=3,D=2)37.5503995413337Range32Trim Var.22.5824936205566


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')