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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 computationSat, 29 Nov 2008 07:44:15 -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/29/t1227970223hxqpse60xf936sd.htm/, Retrieved Sat, 18 May 2024 22:46:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26302, Retrieved Sat, 18 May 2024 22:46:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsRandom Walk Simulation
Estimated Impact141

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] [law of averages] [2008-11-29 14:44:15] [35c75b0726318bf2908e4a56ed2df1a9] [Current]
Feedback Forum
2008-12-04 08:24:32 [Julie Govaerts] [reply] 
de vrm = bevat de variantie van de time-series na gedifferentieerd te hebben, zowel seasonal als niet-seasonaal --> als een time series goed gedifferentieerd is dan zal de variantie/spreiding dalen!
De tweede kolom toont ons de variantie nadat de time series een aantal keer gedifferentieerd zijn. De kleine d en grote D tonen aan hoe vaak er al gedifferentieerd is. Door te differentiëren zien we dat de variantie van de time series daalt (niet zoveel te vaker er gedifferntieert is zoveel te lager de varinatie maar het is de bedoeling van het juiste aantal te kiezen).
Variantie = risico, volatiliteit van de tijdsreeks = moet zo klein mogelijk zijn want dan kan er het meeste verklaard worden
Trimmed variance = als de outliers wegeglaten zijn

Uit de 2e kolom kunnen we afleiden dat de variantie het laagst is bij D=0 (seasonal) en d=1 (non-seasonal). We kunnen de VRM dus gebruiken om na te gaan welke seasonal en non-seasonal differentiatie we nodig hebben om de time series stationair te maken
2008-12-06 10:01:02 [Annemiek Hoofman] [reply] 
In dit model moeten we in de tabel zoeken achter de kleinste variantie. Dit is hier het geval als we de tijdreeks transformeren met d=1 en D=0. Als men denkt dat er veel extreme outliers in de tijdreeks zijn, is het beter om naar de getrimde variantie te zien. Ook hier is die het kleinst bij d=1 en D=0. Om de tijdreeks stationair te maken moet er 1 x niet-seizoenaal gedifferentieerd worden en seizoenaal differentiëren is niet nodig. Dit bewijst nogmaals dat er geen seizoenale trend in de tijdreeks zit.

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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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26302&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26302&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26302&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Variance Reduction Matrix
V(Y[t],d=0,D=0)42.0290340681363Range28Trim Var.27.6805901093087
V(Y[t],d=1,D=0)1.00168207901747Range2Trim Var.NA
V(Y[t],d=2,D=0)1.86720321931590Range4Trim Var.0
V(Y[t],d=3,D=0)5.54832219121179Range8Trim Var.2.46301131418625
V(Y[t],d=0,D=1)13.1262665365065Range20Trim Var.6.76068825958288
V(Y[t],d=1,D=1)2.09861332927726Range4Trim Var.0
V(Y[t],d=2,D=1)3.92570531585423Range8Trim Var.2.22038111019056
V(Y[t],d=3,D=1)11.6528925619835Range16Trim Var.6.4295294047831
V(Y[t],d=0,D=2)32.4689429455993Range32Trim Var.17.9728275557084
V(Y[t],d=1,D=2)6.48943371085943Range8Trim Var.2.61889628289993
V(Y[t],d=2,D=2)12.0084566596194Range16Trim Var.6.06088800359828
V(Y[t],d=3,D=2)35.1601390332175Range32Trim Var.20.7609040491383

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 42.0290340681363 & Range & 28 & Trim Var. & 27.6805901093087 \tabularnewline
V(Y[t],d=1,D=0) & 1.00168207901747 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.86720321931590 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.54832219121179 & Range & 8 & Trim Var. & 2.46301131418625 \tabularnewline
V(Y[t],d=0,D=1) & 13.1262665365065 & Range & 20 & Trim Var. & 6.76068825958288 \tabularnewline
V(Y[t],d=1,D=1) & 2.09861332927726 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.92570531585423 & Range & 8 & Trim Var. & 2.22038111019056 \tabularnewline
V(Y[t],d=3,D=1) & 11.6528925619835 & Range & 16 & Trim Var. & 6.4295294047831 \tabularnewline
V(Y[t],d=0,D=2) & 32.4689429455993 & Range & 32 & Trim Var. & 17.9728275557084 \tabularnewline
V(Y[t],d=1,D=2) & 6.48943371085943 & Range & 8 & Trim Var. & 2.61889628289993 \tabularnewline
V(Y[t],d=2,D=2) & 12.0084566596194 & Range & 16 & Trim Var. & 6.06088800359828 \tabularnewline
V(Y[t],d=3,D=2) & 35.1601390332175 & Range & 32 & Trim Var. & 20.7609040491383 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26302&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]42.0290340681363[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]27.6805901093087[/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]1.86720321931590[/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]5.54832219121179[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.46301131418625[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]13.1262665365065[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]6.76068825958288[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.09861332927726[/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]3.92570531585423[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.22038111019056[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.6528925619835[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.4295294047831[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]32.4689429455993[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]17.9728275557084[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.48943371085943[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.61889628289993[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.0084566596194[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.06088800359828[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]35.1601390332175[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]20.7609040491383[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26302&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26302&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)42.0290340681363Range28Trim Var.27.6805901093087
V(Y[t],d=1,D=0)1.00168207901747Range2Trim Var.NA
V(Y[t],d=2,D=0)1.86720321931590Range4Trim Var.0
V(Y[t],d=3,D=0)5.54832219121179Range8Trim Var.2.46301131418625
V(Y[t],d=0,D=1)13.1262665365065Range20Trim Var.6.76068825958288
V(Y[t],d=1,D=1)2.09861332927726Range4Trim Var.0
V(Y[t],d=2,D=1)3.92570531585423Range8Trim Var.2.22038111019056
V(Y[t],d=3,D=1)11.6528925619835Range16Trim Var.6.4295294047831
V(Y[t],d=0,D=2)32.4689429455993Range32Trim Var.17.9728275557084
V(Y[t],d=1,D=2)6.48943371085943Range8Trim Var.2.61889628289993
V(Y[t],d=2,D=2)12.0084566596194Range16Trim Var.6.06088800359828
V(Y[t],d=3,D=2)35.1601390332175Range32Trim Var.20.7609040491383


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')