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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_rwalk.wasp
Title produced by softwareLaw of Averages
Date of computationMon, 01 Dec 2008 08:52:54 -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/t1228146833ga7pw4rs0evygww.htm/, Retrieved Sun, 05 May 2024 14:26:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26959, Retrieved Sun, 05 May 2024 14:26:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact190

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...] [2008-12-01 15:52:54] [fdd9b7950d7c195d4d8aeb0c9bacacc6] [Current]
Feedback Forum
2008-12-05 14:33:30 [Vincent Vanden Poel] [reply] 
Je hebt deze vraag goed opgelost. Je had misschien nog wel kunnen verduidelijken welke differentiatie we moeten doorvoeren (gewoon of seizoenaal?). In dit geval is er sprake van een gewone differentiatie (d=1).
Ook had je de algemene formule voor de modelvergelijking kunnen geven.

Zoals je zei geeft de Variance Reduction Matrix de waarden weer nadat er gedifferentieerd is. Het werkt volgens volgende formule: Nabla^d * NablaS^D * Yt = et waarbij d = # keer gewoon gedifferentieerd en D = # keer seizoenaal gedifferentieerd. Deze laatste waarde wordt gebruikt om seizoenaliteit te verwijderen.
De 2e kolom geeft de bijhorende varianties weer. Dit is het risico/ de volatiliteit dat in de tijdreeksen zit. Deze waarde moet zo klein mogelijk zijn opdat men veel zou kunnen verklaren. We moeten ons dus de vraag stellen welke differentiatie nodig is om zoveel mogelijk van de tijdreeks te verklaren. Hier is de kleinste variantie 1 bij 1 maal gewoon differentiëren.

2008-12-06 14:57:14 [Jonas Janssens] [reply] 
Goede berekeningen en uitleg, maar je had nog kunnen vermelden hoe je ging differentiëren: niet-seizonaal (=d) of seizonaal (=D)? In dit geval is d=1 en D=0, dus ga je niet-seizonaal differentiëren, dit wil zeggen dat je de niet-seizonale trend eruit gaat halen.
2008-12-06 16:11:15 [Steven Vanhooreweghe] [reply] 
dit klopt, maar misschien had je kunnen zeggen welk soort differentiatie je moet doen. In dit geval d=1 dus een niet-seizoenale differntiatie. tevens had je wat meer kunnen zeggen over getrimde variantie. Dat bekomen we door na de differentiatie de extremen weg te laten en dan opnieuw de variantie te berekenen.
2008-12-07 12:09:18 [006ad2c49b6a7c2ad6ab685cfc1dae56] [reply] 
De ‘d’ in de eerste kolom is het aantal keer dat je differentieert, de gewone differentiatie. De ‘D’ geeft informatie over de seizoenaliteit, de seizoenale differentiatie. De kleinste variantie vinden we in de tabel bij d=1 en D=0, hier is de variantie 1 en zijn de gegevens 1 keer gedifferentieerd.

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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 time0 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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26959&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]0 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=26959&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26959&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 time0 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)39.477498997996Range24Trim Var.29.0581704567839
V(Y[t],d=1,D=0)1.00168207901747Range2Trim Var.NA
V(Y[t],d=2,D=0)1.9476861167002Range4Trim Var.0
V(Y[t],d=3,D=0)5.65320958006101Range8Trim Var.2.73877833719598
V(Y[t],d=0,D=1)10.5677449759316Range18Trim Var.4.46230762542388
V(Y[t],d=1,D=1)2.11507423462705Range4Trim Var.0
V(Y[t],d=2,D=1)3.99998302999448Range8Trim Var.2.23932824836077
V(Y[t],d=3,D=1)11.3388429752066Range16Trim Var.6.70792842379327
V(Y[t],d=0,D=2)25.8589119858470Range30Trim Var.12.3638907971402
V(Y[t],d=1,D=2)6.50631134799023Range8Trim Var.2.80074085507023
V(Y[t],d=2,D=2)12.3042791768138Range16Trim Var.6.33970111468465
V(Y[t],d=3,D=2)34.6523811230157Range30Trim Var.21.2736468670598

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 39.477498997996 & Range & 24 & Trim Var. & 29.0581704567839 \tabularnewline
V(Y[t],d=1,D=0) & 1.00168207901747 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.9476861167002 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.65320958006101 & Range & 8 & Trim Var. & 2.73877833719598 \tabularnewline
V(Y[t],d=0,D=1) & 10.5677449759316 & Range & 18 & Trim Var. & 4.46230762542388 \tabularnewline
V(Y[t],d=1,D=1) & 2.11507423462705 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.99998302999448 & Range & 8 & Trim Var. & 2.23932824836077 \tabularnewline
V(Y[t],d=3,D=1) & 11.3388429752066 & Range & 16 & Trim Var. & 6.70792842379327 \tabularnewline
V(Y[t],d=0,D=2) & 25.8589119858470 & Range & 30 & Trim Var. & 12.3638907971402 \tabularnewline
V(Y[t],d=1,D=2) & 6.50631134799023 & Range & 8 & Trim Var. & 2.80074085507023 \tabularnewline
V(Y[t],d=2,D=2) & 12.3042791768138 & Range & 16 & Trim Var. & 6.33970111468465 \tabularnewline
V(Y[t],d=3,D=2) & 34.6523811230157 & Range & 30 & Trim Var. & 21.2736468670598 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26959&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]39.477498997996[/C][C]Range[/C][C]24[/C][C]Trim Var.[/C][C]29.0581704567839[/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]1.9476861167002[/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]5.65320958006101[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.73877833719598[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]10.5677449759316[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]4.46230762542388[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.11507423462705[/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]2.23932824836077[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.3388429752066[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.70792842379327[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]25.8589119858470[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]12.3638907971402[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.50631134799023[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.80074085507023[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.3042791768138[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.33970111468465[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]34.6523811230157[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]21.2736468670598[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26959&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26959&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)39.477498997996Range24Trim Var.29.0581704567839
V(Y[t],d=1,D=0)1.00168207901747Range2Trim Var.NA
V(Y[t],d=2,D=0)1.9476861167002Range4Trim Var.0
V(Y[t],d=3,D=0)5.65320958006101Range8Trim Var.2.73877833719598
V(Y[t],d=0,D=1)10.5677449759316Range18Trim Var.4.46230762542388
V(Y[t],d=1,D=1)2.11507423462705Range4Trim Var.0
V(Y[t],d=2,D=1)3.99998302999448Range8Trim Var.2.23932824836077
V(Y[t],d=3,D=1)11.3388429752066Range16Trim Var.6.70792842379327
V(Y[t],d=0,D=2)25.8589119858470Range30Trim Var.12.3638907971402
V(Y[t],d=1,D=2)6.50631134799023Range8Trim Var.2.80074085507023
V(Y[t],d=2,D=2)12.3042791768138Range16Trim Var.6.33970111468465
V(Y[t],d=3,D=2)34.6523811230157Range30Trim Var.21.2736468670598


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')