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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 05:54:22 -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/t1228136119goc09j8rzm4x5fm.htm/, Retrieved Sun, 05 May 2024 16:13:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26904, Retrieved Sun, 05 May 2024 16:13:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact204

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, Q3] [2008-12-01 12:54:22] [a16dfd7e948381d8b6391003c5d09447] [Current]
Feedback Forum
2008-12-04 09:23:18 [Julie Govaerts] [reply] 
d= niet saisonaal differentiëren
D = saisonaal differentiëren
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
2008-12-07 14:37:43 [Stephanie Vanderlinden] [reply] 
Correct verklaring.
2008-12-08 14:06:55 [Jonas Janssens] [reply] 
Zoals hierboven vermeld, staat d voor de niet-seizonale differentiatie en D voor de seizonale differentiatie. Dit had je verkeerd geïnterpreteerd.
Voor de rest is deze vraag goed opgelost.
2008-12-10 09:16:43 [b5935c41f1031f8c061510fc5ad27e97] [reply] 
Q3:De interpretatie van d&D heeft studente verkeerd geinterpreteerd : d wijst op niet-seizoenale differentiatie en D wijst op een seizoenale differentiatie. De uitleg over hoe we met behulp van variance reduction matrix de reekst stationair kunnen maken is goed gedaan.Er kan ook geoordeeld worden aan de hand van getrimde variantie om te kontroleren , want die laat de grootste en de kleinste observaties eruit.

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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=26904&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=26904&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26904&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)29.6817795591182Range26Trim Var.19.7591303600584
V(Y[t],d=1,D=0)1.00190742931646Range2Trim Var.NA
V(Y[t],d=2,D=0)1.93158953722334Range4Trim Var.0
V(Y[t],d=3,D=0)5.58064516129032Range8Trim Var.2.74703915010820
V(Y[t],d=0,D=1)12.6654997138722Range20Trim Var.6.02255062944718
V(Y[t],d=1,D=1)1.9999830996865Range4Trim Var.0
V(Y[t],d=2,D=1)3.84329896907217Range8Trim Var.2.32018561484919
V(Y[t],d=3,D=1)11.1322143648292Range16Trim Var.6.25295148496587
V(Y[t],d=0,D=2)26.7789473684211Range30Trim Var.13.1847398200068
V(Y[t],d=1,D=2)5.8395913835221Range8Trim Var.2.80500037427951
V(Y[t],d=2,D=2)11.0613107822410Range16Trim Var.6.60288095582213
V(Y[t],d=3,D=2)31.9152542372881Range28Trim Var.21.1437436072281

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 29.6817795591182 & Range & 26 & Trim Var. & 19.7591303600584 \tabularnewline
V(Y[t],d=1,D=0) & 1.00190742931646 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.93158953722334 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.58064516129032 & Range & 8 & Trim Var. & 2.74703915010820 \tabularnewline
V(Y[t],d=0,D=1) & 12.6654997138722 & Range & 20 & Trim Var. & 6.02255062944718 \tabularnewline
V(Y[t],d=1,D=1) & 1.9999830996865 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.84329896907217 & Range & 8 & Trim Var. & 2.32018561484919 \tabularnewline
V(Y[t],d=3,D=1) & 11.1322143648292 & Range & 16 & Trim Var. & 6.25295148496587 \tabularnewline
V(Y[t],d=0,D=2) & 26.7789473684211 & Range & 30 & Trim Var. & 13.1847398200068 \tabularnewline
V(Y[t],d=1,D=2) & 5.8395913835221 & Range & 8 & Trim Var. & 2.80500037427951 \tabularnewline
V(Y[t],d=2,D=2) & 11.0613107822410 & Range & 16 & Trim Var. & 6.60288095582213 \tabularnewline
V(Y[t],d=3,D=2) & 31.9152542372881 & Range & 28 & Trim Var. & 21.1437436072281 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26904&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]29.6817795591182[/C][C]Range[/C][C]26[/C][C]Trim Var.[/C][C]19.7591303600584[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00190742931646[/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]1.93158953722334[/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]2.74703915010820[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.6654997138722[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]6.02255062944718[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.9999830996865[/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]3.84329896907217[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.32018561484919[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.1322143648292[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.25295148496587[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]26.7789473684211[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]13.1847398200068[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.8395913835221[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.80500037427951[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.0613107822410[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.60288095582213[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]31.9152542372881[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]21.1437436072281[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26904&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26904&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)29.6817795591182Range26Trim Var.19.7591303600584
V(Y[t],d=1,D=0)1.00190742931646Range2Trim Var.NA
V(Y[t],d=2,D=0)1.93158953722334Range4Trim Var.0
V(Y[t],d=3,D=0)5.58064516129032Range8Trim Var.2.74703915010820
V(Y[t],d=0,D=1)12.6654997138722Range20Trim Var.6.02255062944718
V(Y[t],d=1,D=1)1.9999830996865Range4Trim Var.0
V(Y[t],d=2,D=1)3.84329896907217Range8Trim Var.2.32018561484919
V(Y[t],d=3,D=1)11.1322143648292Range16Trim Var.6.25295148496587
V(Y[t],d=0,D=2)26.7789473684211Range30Trim Var.13.1847398200068
V(Y[t],d=1,D=2)5.8395913835221Range8Trim Var.2.80500037427951
V(Y[t],d=2,D=2)11.0613107822410Range16Trim Var.6.60288095582213
V(Y[t],d=3,D=2)31.9152542372881Range28Trim Var.21.1437436072281


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')