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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 05:54:10 -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/t1228136088q58byiep6vo4fqn.htm/, Retrieved Sun, 05 May 2024 10:39:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26903, Retrieved Sun, 05 May 2024 10:39:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact175

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] [Workshop 7] [2008-12-01 12:54:10] [d300b7a0882cee7d84584ad37a3d4ede] [Current]
Feedback Forum
2008-12-06 09:53:56 [Loïque Verhasselt] [reply] 
Q3: Juist! Als ik de tijdreeks wil voorspellen, wat is dan de variantie?Variantie= risico in de tijdreeks, de volatiliteit = men wil er zoveel mogelijk van verklaren. Hoe meer men verklaart, hoe kleiner de variantie. Het is de bedoeling van de kleinste variantie te kiezen en zo te kijken welke differentiatie er nodig is. Hier is het d=1,D=0 met een variantie van ongeveer 1 zoals de student vermeld!
2008-12-06 10:19:31 [Britt Severijns] [reply] 
Zoals de student heeft vermeld gebruiken we D om de seizoenaliteit uit te grafiek te halen. Je vertelt ook dat d = aantal keer dat gedifferentieerd wordt. Je had nog kunnen vermelden dat dit gebruikt wordt om de lange termijn trend eruit te halen. De variantie stelt het risico in de tijdreeks voor als men de tijdreeks wil voorspellen. Hoe kleiner de variantie is hoe meer je kan verklaren. Dit had de student juist opgemerkt.
2008-12-06 13:24:30 [Nicolaj Wuyts] [reply] 
De uitleg en resultaten bij de tabel zijn correct.

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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'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=26903&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=26903&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26903&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)52.1758557114228Range39Trim Var.26.8806761817998
V(Y[t],d=1,D=0)1.00084506362122Range2Trim Var.NA
V(Y[t],d=2,D=0)2.02010456312170Range4Trim Var.0
V(Y[t],d=3,D=0)6.08869345102875Range8Trim Var.2.67607119314436
V(Y[t],d=0,D=1)11.9909617261925Range18Trim Var.7.06826661288696
V(Y[t],d=1,D=1)2.05754556747028Range4Trim Var.0
V(Y[t],d=2,D=1)4.18969072164948Range8Trim Var.2.36109037439204
V(Y[t],d=3,D=1)12.7684416801568Range16Trim Var.6.4
V(Y[t],d=0,D=2)26.0782308712959Range30Trim Var.12.0923847799990
V(Y[t],d=1,D=2)6.16026648900733Range8Trim Var.2.67415547415547
V(Y[t],d=2,D=2)12.6680047457204Range16Trim Var.6.92973640130477
V(Y[t],d=3,D=2)39.1863690113592Range32Trim Var.21.6581151370890

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 52.1758557114228 & Range & 39 & Trim Var. & 26.8806761817998 \tabularnewline
V(Y[t],d=1,D=0) & 1.00084506362122 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.02010456312170 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.08869345102875 & Range & 8 & Trim Var. & 2.67607119314436 \tabularnewline
V(Y[t],d=0,D=1) & 11.9909617261925 & Range & 18 & Trim Var. & 7.06826661288696 \tabularnewline
V(Y[t],d=1,D=1) & 2.05754556747028 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.18969072164948 & Range & 8 & Trim Var. & 2.36109037439204 \tabularnewline
V(Y[t],d=3,D=1) & 12.7684416801568 & Range & 16 & Trim Var. & 6.4 \tabularnewline
V(Y[t],d=0,D=2) & 26.0782308712959 & Range & 30 & Trim Var. & 12.0923847799990 \tabularnewline
V(Y[t],d=1,D=2) & 6.16026648900733 & Range & 8 & Trim Var. & 2.67415547415547 \tabularnewline
V(Y[t],d=2,D=2) & 12.6680047457204 & Range & 16 & Trim Var. & 6.92973640130477 \tabularnewline
V(Y[t],d=3,D=2) & 39.1863690113592 & Range & 32 & Trim Var. & 21.6581151370890 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26903&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]52.1758557114228[/C][C]Range[/C][C]39[/C][C]Trim Var.[/C][C]26.8806761817998[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00084506362122[/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]2.02010456312170[/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]6.08869345102875[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.67607119314436[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]11.9909617261925[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]7.06826661288696[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.05754556747028[/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]4.18969072164948[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.36109037439204[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.7684416801568[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.4[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]26.0782308712959[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]12.0923847799990[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.16026648900733[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.67415547415547[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.6680047457204[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.92973640130477[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]39.1863690113592[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]21.6581151370890[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26903&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26903&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)52.1758557114228Range39Trim Var.26.8806761817998
V(Y[t],d=1,D=0)1.00084506362122Range2Trim Var.NA
V(Y[t],d=2,D=0)2.02010456312170Range4Trim Var.0
V(Y[t],d=3,D=0)6.08869345102875Range8Trim Var.2.67607119314436
V(Y[t],d=0,D=1)11.9909617261925Range18Trim Var.7.06826661288696
V(Y[t],d=1,D=1)2.05754556747028Range4Trim Var.0
V(Y[t],d=2,D=1)4.18969072164948Range8Trim Var.2.36109037439204
V(Y[t],d=3,D=1)12.7684416801568Range16Trim Var.6.4
V(Y[t],d=0,D=2)26.0782308712959Range30Trim Var.12.0923847799990
V(Y[t],d=1,D=2)6.16026648900733Range8Trim Var.2.67415547415547
V(Y[t],d=2,D=2)12.6680047457204Range16Trim Var.6.92973640130477
V(Y[t],d=3,D=2)39.1863690113592Range32Trim Var.21.6581151370890


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')