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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 computationTue, 02 Dec 2008 10:35:25 -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/02/t1228239374vas2yho2vqq3t2k.htm/, Retrieved Sun, 19 May 2024 00:03:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28123, Retrieved Sun, 19 May 2024 00:03:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact149

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] [NonStationatyTime...] [2008-12-02 17:35:25] [82f29a5d509ab8039aab37a0145f886d] [Current]
Feedback Forum
2008-12-05 14:26:14 [Angelique Van de Vijver] [reply] 
Goede berekening en vaststellingen van de student.
We zoeken hier dus inderdaad de differentiatie die de kleinste variantie weergeeft. Hoe kleiner de variantie is, hoe meer we kunnen verklaren. De variantie is het risico, de volatiliteit dat in de tijdreeks zit. Deze is dus het best zo klein mogelijk om goede voorspellingen te kunnen maken.
Ik zou ook nog vermelden dat we ‘d’ gebruiken om de LT-trend te elimineren(=niet-seizoenale differentiatie) en ‘D’ gebruiken we om seizoenaliteit te elimineren(=seizoenale differnetiatie). Deze differentiaties gebruiken we inderdaad om de tijdreeks stationair te maken.
Hier moeten we dus 1 keer niet-seizoenaal differentiëren (d=1;D=0) om tot een stationaire tijdreeks te komen.
Meestal zal de getrimde variantie ook het kleinst zijn bij de differentiatie met de kleinste variantie, maar hier kunnen we dit niet zeggen omdat er geen getrimde variantie weergegeven is bij deze differentiatie(d=1;D=0).
2008-12-08 19:13:10 [Stef Vermeiren] [reply] 
Correcte conclusie en berekeningen.

We moeten trachten de variantie zo klein mogelijk te houden. De ‘D’= 0 en de ‘d’=1. De ‘d’ wijst erop dat er een lange termijn trend aanwezig was. Deze differentiaties gebruiken we om de tijdreeks stationair te maken.


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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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28123&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28123&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28123&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'George Udny Yule' @ 72.249.76.132






Variance Reduction Matrix
V(Y[t],d=0,D=0)31.1334509018036Range29Trim Var.18.9741250813512
V(Y[t],d=1,D=0)1.00084506362122Range2Trim Var.NA
V(Y[t],d=2,D=0)1.99597585513078Range4Trim Var.0
V(Y[t],d=3,D=0)5.9757902252223Range8Trim Var.2.66791873951628
V(Y[t],d=0,D=1)12.0929747197630Range16Trim Var.4.16662861665373
V(Y[t],d=1,D=1)1.94211642625971Range4Trim Var.0
V(Y[t],d=2,D=1)3.66178779008103Range8Trim Var.0.93767441860465
V(Y[t],d=3,D=1)10.9173383317713Range16Trim Var.6.23052763111977
V(Y[t],d=0,D=2)25.4201680672269Range30Trim Var.12.7977508078264
V(Y[t],d=1,D=2)5.67916500111037Range8Trim Var.2.66955929392252
V(Y[t],d=2,D=2)10.5961766621172Range16Trim Var.6.2152273338714
V(Y[t],d=3,D=2)31.6439961300032Range32Trim Var.19.5194198708019

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 31.1334509018036 & Range & 29 & Trim Var. & 18.9741250813512 \tabularnewline
V(Y[t],d=1,D=0) & 1.00084506362122 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.99597585513078 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.9757902252223 & Range & 8 & Trim Var. & 2.66791873951628 \tabularnewline
V(Y[t],d=0,D=1) & 12.0929747197630 & Range & 16 & Trim Var. & 4.16662861665373 \tabularnewline
V(Y[t],d=1,D=1) & 1.94211642625971 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.66178779008103 & Range & 8 & Trim Var. & 0.93767441860465 \tabularnewline
V(Y[t],d=3,D=1) & 10.9173383317713 & Range & 16 & Trim Var. & 6.23052763111977 \tabularnewline
V(Y[t],d=0,D=2) & 25.4201680672269 & Range & 30 & Trim Var. & 12.7977508078264 \tabularnewline
V(Y[t],d=1,D=2) & 5.67916500111037 & Range & 8 & Trim Var. & 2.66955929392252 \tabularnewline
V(Y[t],d=2,D=2) & 10.5961766621172 & Range & 16 & Trim Var. & 6.2152273338714 \tabularnewline
V(Y[t],d=3,D=2) & 31.6439961300032 & Range & 32 & Trim Var. & 19.5194198708019 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28123&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]31.1334509018036[/C][C]Range[/C][C]29[/C][C]Trim Var.[/C][C]18.9741250813512[/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]1.99597585513078[/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]5.9757902252223[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.66791873951628[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.0929747197630[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]4.16662861665373[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.94211642625971[/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]3.66178779008103[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]0.93767441860465[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]10.9173383317713[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.23052763111977[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]25.4201680672269[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]12.7977508078264[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.67916500111037[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.66955929392252[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]10.5961766621172[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.2152273338714[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]31.6439961300032[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]19.5194198708019[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28123&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28123&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)31.1334509018036Range29Trim Var.18.9741250813512
V(Y[t],d=1,D=0)1.00084506362122Range2Trim Var.NA
V(Y[t],d=2,D=0)1.99597585513078Range4Trim Var.0
V(Y[t],d=3,D=0)5.9757902252223Range8Trim Var.2.66791873951628
V(Y[t],d=0,D=1)12.0929747197630Range16Trim Var.4.16662861665373
V(Y[t],d=1,D=1)1.94211642625971Range4Trim Var.0
V(Y[t],d=2,D=1)3.66178779008103Range8Trim Var.0.93767441860465
V(Y[t],d=3,D=1)10.9173383317713Range16Trim Var.6.23052763111977
V(Y[t],d=0,D=2)25.4201680672269Range30Trim Var.12.7977508078264
V(Y[t],d=1,D=2)5.67916500111037Range8Trim Var.2.66955929392252
V(Y[t],d=2,D=2)10.5961766621172Range16Trim Var.6.2152273338714
V(Y[t],d=3,D=2)31.6439961300032Range32Trim Var.19.5194198708019


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')