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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 computationFri, 28 Nov 2008 12:30:37 -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/28/t1227900766luh7prcj9cg5x4a.htm/, Retrieved Sun, 19 May 2024 12:40:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26166, Retrieved Sun, 19 May 2024 12:40:01 +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] [Non Stationary Ti...] [2008-11-28 19:30:37] [4b953869c7238aca4b6e0cfb0c5cddd6] [Current]
Feedback Forum
2008-12-03 16:00:52 [Ken Van den Heuvel] [reply] 
Je stelt: 'De eerste kolom van deze tabel is de backshift operator met de waarde uitgedrukt in de tweede kolom (176.86). De range is de variantie van de tijdreeks en geeft dusdanig de grootte van de spreiding aan. De beste oplossing is degene met de kleinste variantie. We vinden deze bij d=1 (2e rij, 1.00132795711906). We bekomen deze oplossing na 1 keer te differenciëren.
Waarom weten we nu zeker dat dit de correcte oplossing is? Doordat we eerst de reeks gesimuleerd hebben.'

1) de waarde van de backshiftoperator staat niet in de 2de kolom, dit is de waarde van de variantie.
2) range is niet hetzelfde als variantie. Variantie is de spreiding van de reeks, range is de kleinste waarde afgetrokken van de grootste waarde.
3) Mbt de juistheid van de oplossing, een loutere voorafgaande simulatie lijkt mij onvoldoende.
Wanneer een niet-seizoenale random-walk niet-seizoenaal gedifferentieerd word, dan word deze stationair. Uit je berekening blijkt dat we 1 maal niet-seizoenaal moeten differentiëren om de kleinste variantie te krijgen. Maw, de reeks wordt stationair door niet-seizoenaal te differentiëren => de reeks was dus om te beginnen niet-seizoenaal. Dit staaft de stelling van geen seizoenaliteit nog verder.
2008-12-08 21:36:52 [4db2e62d895b4fb371d0fef3013b569f] [reply] 
Correcte oplossing

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=26166&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=26166&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26166&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)176.862669338677Range46Trim Var.141.616553287982
V(Y[t],d=1,D=0)1.00132795711906Range2Trim Var.NA
V(Y[t],d=2,D=0)1.97987927565392Range4Trim Var.0
V(Y[t],d=3,D=0)5.92740312844811Range8Trim Var.2.64031372549020
V(Y[t],d=0,D=1)13.8749789611876Range20Trim Var.6.57721804511278
V(Y[t],d=1,D=1)1.91767857293753Range4Trim Var.0
V(Y[t],d=2,D=1)3.93400364855119Range8Trim Var.2.22879867439934
V(Y[t],d=3,D=1)11.8097639942064Range16Trim Var.6.27863319219989
V(Y[t],d=0,D=2)19.5787881468377Range26Trim Var.9.40320733104238
V(Y[t],d=1,D=2)5.68776371308017Range8Trim Var.2.60809940863837
V(Y[t],d=2,D=2)11.7631956896013Range16Trim Var.6.2602234228788
V(Y[t],d=3,D=2)35.40670799441Range30Trim Var.20.00900079061

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 176.862669338677 & Range & 46 & Trim Var. & 141.616553287982 \tabularnewline
V(Y[t],d=1,D=0) & 1.00132795711906 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.97987927565392 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.92740312844811 & Range & 8 & Trim Var. & 2.64031372549020 \tabularnewline
V(Y[t],d=0,D=1) & 13.8749789611876 & Range & 20 & Trim Var. & 6.57721804511278 \tabularnewline
V(Y[t],d=1,D=1) & 1.91767857293753 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.93400364855119 & Range & 8 & Trim Var. & 2.22879867439934 \tabularnewline
V(Y[t],d=3,D=1) & 11.8097639942064 & Range & 16 & Trim Var. & 6.27863319219989 \tabularnewline
V(Y[t],d=0,D=2) & 19.5787881468377 & Range & 26 & Trim Var. & 9.40320733104238 \tabularnewline
V(Y[t],d=1,D=2) & 5.68776371308017 & Range & 8 & Trim Var. & 2.60809940863837 \tabularnewline
V(Y[t],d=2,D=2) & 11.7631956896013 & Range & 16 & Trim Var. & 6.2602234228788 \tabularnewline
V(Y[t],d=3,D=2) & 35.40670799441 & Range & 30 & Trim Var. & 20.00900079061 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26166&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]176.862669338677[/C][C]Range[/C][C]46[/C][C]Trim Var.[/C][C]141.616553287982[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00132795711906[/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]1.97987927565392[/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]5.92740312844811[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.64031372549020[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]13.8749789611876[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]6.57721804511278[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.91767857293753[/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]3.93400364855119[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.22879867439934[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.8097639942064[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.27863319219989[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]19.5787881468377[/C][C]Range[/C][C]26[/C][C]Trim Var.[/C][C]9.40320733104238[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.68776371308017[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.60809940863837[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.7631956896013[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.2602234228788[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]35.40670799441[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]20.00900079061[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26166&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26166&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)176.862669338677Range46Trim Var.141.616553287982
V(Y[t],d=1,D=0)1.00132795711906Range2Trim Var.NA
V(Y[t],d=2,D=0)1.97987927565392Range4Trim Var.0
V(Y[t],d=3,D=0)5.92740312844811Range8Trim Var.2.64031372549020
V(Y[t],d=0,D=1)13.8749789611876Range20Trim Var.6.57721804511278
V(Y[t],d=1,D=1)1.91767857293753Range4Trim Var.0
V(Y[t],d=2,D=1)3.93400364855119Range8Trim Var.2.22879867439934
V(Y[t],d=3,D=1)11.8097639942064Range16Trim Var.6.27863319219989
V(Y[t],d=0,D=2)19.5787881468377Range26Trim Var.9.40320733104238
V(Y[t],d=1,D=2)5.68776371308017Range8Trim Var.2.60809940863837
V(Y[t],d=2,D=2)11.7631956896013Range16Trim Var.6.2602234228788
V(Y[t],d=3,D=2)35.40670799441Range30Trim Var.20.00900079061


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')