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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 16:10:57 -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/t12281731017jrk86xmx392wq2.htm/, Retrieved Fri, 17 May 2024 05:14:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27518, Retrieved Fri, 17 May 2024 05:14:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact224

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] [] [2008-11-30 16:39:37] [4c8dfb519edec2da3492d7e6be9a5685]
F         [Law of Averages] [Q3_VRM] [2008-11-30 22:51:09] [6816386b1f3c2f6c0c9f2aa1e5bc9362]
F             [Law of Averages] [Non stationary ti...] [2008-12-01 23:10:57] [e4cb5a8878d0401c2e8d19a1768b515b] [Current]
Feedback Forum
2008-12-08 22:07:17 [Jeroen Michel] [reply] 
De test die hier wordt gebruikt (VRM test), wordt gebruikt om de verschillende waarden die een reeks bevat te onderzoeken. Voorts wordt in een tabel weergegeven wat de varianties zijn bij de waarden d en D.

d = het aantal keer dat de reeks niet-seizoenaal gedifferentieerd is.
D = het aantal keer dat de reeks seizoenaal gedifferentieerd is.

Wanneer we de bijbehorende tabel bekijken bij deze output zien we dat de kleinste variantie bestaat bij d:1 en D:0.

Er moet dus een niet-seizoenale randam-walk getrokken worden om deze tijdreeks stationair te maken. Dit verklaart bovenstaand resultaat en de conclusie van de student.

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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=27518&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=27518&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27518&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)36.7072384769539Range28Trim Var.22.9373974041892
V(Y[t],d=1,D=0)1.00190742931646Range2Trim Var.NA
V(Y[t],d=2,D=0)2.16497377841345Range4Trim Var.0
V(Y[t],d=3,D=0)6.83062893489972Range8Trim Var.2.66272229939463
V(Y[t],d=0,D=1)14.5842394048541Range18Trim Var.6.47464668154323
V(Y[t],d=1,D=1)2.07380366905806Range4Trim Var.0
V(Y[t],d=2,D=1)4.55257731958763Range8Trim Var.2.42542787286064
V(Y[t],d=3,D=1)14.3553548606969Range16Trim Var.6.36773034949579
V(Y[t],d=0,D=2)25.5770720919947Range26Trim Var.12.6329923273657
V(Y[t],d=1,D=2)6.13486120364202Range8Trim Var.2.8512888301388
V(Y[t],d=2,D=2)13.5729208481637Range16Trim Var.6.59935722004688
V(Y[t],d=3,D=2)42.7203210663991Range32Trim Var.28.0271462504242

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 36.7072384769539 & Range & 28 & Trim Var. & 22.9373974041892 \tabularnewline
V(Y[t],d=1,D=0) & 1.00190742931646 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.16497377841345 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.83062893489972 & Range & 8 & Trim Var. & 2.66272229939463 \tabularnewline
V(Y[t],d=0,D=1) & 14.5842394048541 & Range & 18 & Trim Var. & 6.47464668154323 \tabularnewline
V(Y[t],d=1,D=1) & 2.07380366905806 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.55257731958763 & Range & 8 & Trim Var. & 2.42542787286064 \tabularnewline
V(Y[t],d=3,D=1) & 14.3553548606969 & Range & 16 & Trim Var. & 6.36773034949579 \tabularnewline
V(Y[t],d=0,D=2) & 25.5770720919947 & Range & 26 & Trim Var. & 12.6329923273657 \tabularnewline
V(Y[t],d=1,D=2) & 6.13486120364202 & Range & 8 & Trim Var. & 2.8512888301388 \tabularnewline
V(Y[t],d=2,D=2) & 13.5729208481637 & Range & 16 & Trim Var. & 6.59935722004688 \tabularnewline
V(Y[t],d=3,D=2) & 42.7203210663991 & Range & 32 & Trim Var. & 28.0271462504242 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27518&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]36.7072384769539[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]22.9373974041892[/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]2.16497377841345[/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]6.83062893489972[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.66272229939463[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]14.5842394048541[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]6.47464668154323[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.07380366905806[/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]4.55257731958763[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.42542787286064[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]14.3553548606969[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.36773034949579[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]25.5770720919947[/C][C]Range[/C][C]26[/C][C]Trim Var.[/C][C]12.6329923273657[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.13486120364202[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.8512888301388[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]13.5729208481637[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.59935722004688[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]42.7203210663991[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]28.0271462504242[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27518&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27518&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)36.7072384769539Range28Trim Var.22.9373974041892
V(Y[t],d=1,D=0)1.00190742931646Range2Trim Var.NA
V(Y[t],d=2,D=0)2.16497377841345Range4Trim Var.0
V(Y[t],d=3,D=0)6.83062893489972Range8Trim Var.2.66272229939463
V(Y[t],d=0,D=1)14.5842394048541Range18Trim Var.6.47464668154323
V(Y[t],d=1,D=1)2.07380366905806Range4Trim Var.0
V(Y[t],d=2,D=1)4.55257731958763Range8Trim Var.2.42542787286064
V(Y[t],d=3,D=1)14.3553548606969Range16Trim Var.6.36773034949579
V(Y[t],d=0,D=2)25.5770720919947Range26Trim Var.12.6329923273657
V(Y[t],d=1,D=2)6.13486120364202Range8Trim Var.2.8512888301388
V(Y[t],d=2,D=2)13.5729208481637Range16Trim Var.6.59935722004688
V(Y[t],d=3,D=2)42.7203210663991Range32Trim Var.28.0271462504242


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')