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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 15:12:15 -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/t1228169588elol1180jw1kege.htm/, Retrieved Sun, 05 May 2024 15:21:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27451, Retrieved Sun, 05 May 2024 15:21:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsNon Stationary Time Series
Estimated Impact207

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] [Q3 t7] [2008-11-26 16:36:25] [8eb83367d7ce233bbf617141d324189b]
F           [Law of Averages] [question 3 Varian...] [2008-12-01 22:12:15] [3efbb18563b4564408d69b3c9a8e9a6e] [Current]
Feedback Forum
2008-12-08 19:42:53 [Romina Battain] [reply] 
De variantie van de reeks is het kleinst bij V(Y[t],d=1,D=0). In de 2de kolom van de tabel zien we hier immers het laagste getal. Dit wil zeggen dat indien we de reeks 1x differentiëren we het lange termijn effect kunnen uitzuiveren, en zo een meer stabiel gemiddelde krijgen van de reeks.
2008-12-09 07:34:09 [An De Koninck] [reply] 
De student heeft hier een heel goede uitleg gegeven. Hij heeft eerst de elementen d en D goed verklaard.
Ik kan hier verder geen commentaar op geven.

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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 time0 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 & 0 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27451&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]0 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=27451&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27451&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 time0 seconds
R Server'George Udny Yule' @ 72.249.76.132






Variance Reduction Matrix
V(Y[t],d=0,D=0)59.0785571142285Range33Trim Var.36.5075783282434
V(Y[t],d=1,D=0)1.00110260682007Range2Trim Var.NA
V(Y[t],d=2,D=0)1.99597585513078Range4Trim Var.0
V(Y[t],d=3,D=0)5.83864477185695Range8Trim Var.2.7676959228264
V(Y[t],d=0,D=1)12.3604369340559Range18Trim Var.6.35498053008416
V(Y[t],d=1,D=1)1.85183495153835Range4Trim Var.0
V(Y[t],d=2,D=1)3.91750880319036Range8Trim Var.2.10189013254456
V(Y[t],d=3,D=1)11.6446110590440Range16Trim Var.6.14965710537301
V(Y[t],d=0,D=2)16.1380451127820Range22Trim Var.6.09699290780142
V(Y[t],d=1,D=2)5.40926493448812Range8Trim Var.2.46897371243080
V(Y[t],d=2,D=2)11.5264092202567Range16Trim Var.5.85185372707366
V(Y[t],d=3,D=2)34.2964489196259Range30Trim Var.21.0959916589435

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 59.0785571142285 & Range & 33 & Trim Var. & 36.5075783282434 \tabularnewline
V(Y[t],d=1,D=0) & 1.00110260682007 & 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) & 5.83864477185695 & Range & 8 & Trim Var. & 2.7676959228264 \tabularnewline
V(Y[t],d=0,D=1) & 12.3604369340559 & Range & 18 & Trim Var. & 6.35498053008416 \tabularnewline
V(Y[t],d=1,D=1) & 1.85183495153835 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.91750880319036 & Range & 8 & Trim Var. & 2.10189013254456 \tabularnewline
V(Y[t],d=3,D=1) & 11.6446110590440 & Range & 16 & Trim Var. & 6.14965710537301 \tabularnewline
V(Y[t],d=0,D=2) & 16.1380451127820 & Range & 22 & Trim Var. & 6.09699290780142 \tabularnewline
V(Y[t],d=1,D=2) & 5.40926493448812 & Range & 8 & Trim Var. & 2.46897371243080 \tabularnewline
V(Y[t],d=2,D=2) & 11.5264092202567 & Range & 16 & Trim Var. & 5.85185372707366 \tabularnewline
V(Y[t],d=3,D=2) & 34.2964489196259 & Range & 30 & Trim Var. & 21.0959916589435 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27451&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]59.0785571142285[/C][C]Range[/C][C]33[/C][C]Trim Var.[/C][C]36.5075783282434[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00110260682007[/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]5.83864477185695[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.7676959228264[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.3604369340559[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]6.35498053008416[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.85183495153835[/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]3.91750880319036[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.10189013254456[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.6446110590440[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.14965710537301[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]16.1380451127820[/C][C]Range[/C][C]22[/C][C]Trim Var.[/C][C]6.09699290780142[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.40926493448812[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.46897371243080[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.5264092202567[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]5.85185372707366[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]34.2964489196259[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]21.0959916589435[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27451&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27451&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)59.0785571142285Range33Trim Var.36.5075783282434
V(Y[t],d=1,D=0)1.00110260682007Range2Trim Var.NA
V(Y[t],d=2,D=0)1.99597585513078Range4Trim Var.0
V(Y[t],d=3,D=0)5.83864477185695Range8Trim Var.2.7676959228264
V(Y[t],d=0,D=1)12.3604369340559Range18Trim Var.6.35498053008416
V(Y[t],d=1,D=1)1.85183495153835Range4Trim Var.0
V(Y[t],d=2,D=1)3.91750880319036Range8Trim Var.2.10189013254456
V(Y[t],d=3,D=1)11.6446110590440Range16Trim Var.6.14965710537301
V(Y[t],d=0,D=2)16.1380451127820Range22Trim Var.6.09699290780142
V(Y[t],d=1,D=2)5.40926493448812Range8Trim Var.2.46897371243080
V(Y[t],d=2,D=2)11.5264092202567Range16Trim Var.5.85185372707366
V(Y[t],d=3,D=2)34.2964489196259Range30Trim Var.21.0959916589435


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')