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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 04:11:33 -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/t122795714554psaa29y1h1hxw.htm/, Retrieved Sun, 19 May 2024 05:55:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26208, Retrieved Sun, 19 May 2024 05:55:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact177

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] [variance reductoi...] [2008-11-29 11:11:33] [32a7b12f2bdf14b45f7a9a96ba1ab98d] [Current]
Feedback Forum
2008-12-04 08:52:58 [Julie Govaerts] [reply] 
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 gedifferentieert is zoveel te lager de variantie 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 wegelaten 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
2008-12-04 13:52:42 [72e979bcc364082694890d2eccc1a66f] [reply] 
Ook deze opdracht werd correct uitgevoerd.

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=26208&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=26208&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26208&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)48.8027094188377Range30Trim Var.34.3326458788644
V(Y[t],d=1,D=0)1.00152111451819Range2Trim Var.NA
V(Y[t],d=2,D=0)1.90742850678367Range4Trim Var.0
V(Y[t],d=3,D=0)5.58064516129032Range8Trim Var.2.60968523650775
V(Y[t],d=0,D=1)12.9547749688626Range20Trim Var.6.29610972568579
V(Y[t],d=1,D=1)2.06582672108568Range4Trim Var.0
V(Y[t],d=2,D=1)4.00824742268041Range8Trim Var.2.24488157366519
V(Y[t],d=3,D=1)11.7933713896226Range16Trim Var.6.45505130799248
V(Y[t],d=0,D=2)24.0975851393189Range30Trim Var.12.2603613811199
V(Y[t],d=1,D=2)6.31923606484566Range8Trim Var.2.69390969255257
V(Y[t],d=2,D=2)12.2451717647479Range16Trim Var.6.17514591120729
V(Y[t],d=3,D=2)36.0507757910202Range28Trim Var.21.781426746944

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 48.8027094188377 & Range & 30 & Trim Var. & 34.3326458788644 \tabularnewline
V(Y[t],d=1,D=0) & 1.00152111451819 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.90742850678367 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.58064516129032 & Range & 8 & Trim Var. & 2.60968523650775 \tabularnewline
V(Y[t],d=0,D=1) & 12.9547749688626 & Range & 20 & Trim Var. & 6.29610972568579 \tabularnewline
V(Y[t],d=1,D=1) & 2.06582672108568 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.00824742268041 & Range & 8 & Trim Var. & 2.24488157366519 \tabularnewline
V(Y[t],d=3,D=1) & 11.7933713896226 & Range & 16 & Trim Var. & 6.45505130799248 \tabularnewline
V(Y[t],d=0,D=2) & 24.0975851393189 & Range & 30 & Trim Var. & 12.2603613811199 \tabularnewline
V(Y[t],d=1,D=2) & 6.31923606484566 & Range & 8 & Trim Var. & 2.69390969255257 \tabularnewline
V(Y[t],d=2,D=2) & 12.2451717647479 & Range & 16 & Trim Var. & 6.17514591120729 \tabularnewline
V(Y[t],d=3,D=2) & 36.0507757910202 & Range & 28 & Trim Var. & 21.781426746944 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26208&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]48.8027094188377[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]34.3326458788644[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00152111451819[/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]1.90742850678367[/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]5.58064516129032[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.60968523650775[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.9547749688626[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]6.29610972568579[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.06582672108568[/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]4.00824742268041[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.24488157366519[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.7933713896226[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.45505130799248[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]24.0975851393189[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]12.2603613811199[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.31923606484566[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.69390969255257[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.2451717647479[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.17514591120729[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]36.0507757910202[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]21.781426746944[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26208&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26208&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)48.8027094188377Range30Trim Var.34.3326458788644
V(Y[t],d=1,D=0)1.00152111451819Range2Trim Var.NA
V(Y[t],d=2,D=0)1.90742850678367Range4Trim Var.0
V(Y[t],d=3,D=0)5.58064516129032Range8Trim Var.2.60968523650775
V(Y[t],d=0,D=1)12.9547749688626Range20Trim Var.6.29610972568579
V(Y[t],d=1,D=1)2.06582672108568Range4Trim Var.0
V(Y[t],d=2,D=1)4.00824742268041Range8Trim Var.2.24488157366519
V(Y[t],d=3,D=1)11.7933713896226Range16Trim Var.6.45505130799248
V(Y[t],d=0,D=2)24.0975851393189Range30Trim Var.12.2603613811199
V(Y[t],d=1,D=2)6.31923606484566Range8Trim Var.2.69390969255257
V(Y[t],d=2,D=2)12.2451717647479Range16Trim Var.6.17514591120729
V(Y[t],d=3,D=2)36.0507757910202Range28Trim Var.21.781426746944


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')