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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 05:49:16 -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/t1227963571eayuhltk6pp63bl.htm/, Retrieved Sun, 19 May 2024 07:45:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26248, Retrieved Sun, 19 May 2024 07:45:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact210

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] [Random Walk] [2008-11-29 12:49:16] [9b05d7ef5dbcfba4217d280d9092f628] [Current]
-           [Law of Averages] [q1] [2008-12-01 18:43:46] [988ab43f527fc78aae41c84649095267]
-             [Law of Averages] [Q1] [2008-12-01 20:44:52] [fe7291e888d31b8c4db0b24d6c0f75c6]
-           [Law of Averages] [q2] [2008-12-01 18:45:24] [988ab43f527fc78aae41c84649095267]
F           [Law of Averages] [q3] [2008-12-01 18:47:27] [988ab43f527fc78aae41c84649095267]
-             [Law of Averages] [Q2] [2008-12-01 20:46:37] [fe7291e888d31b8c4db0b24d6c0f75c6]
-             [Law of Averages] [Q3] [2008-12-01 20:50:15] [fe7291e888d31b8c4db0b24d6c0f75c6]
-           [Law of Averages] [q4] [2008-12-01 18:49:21] [988ab43f527fc78aae41c84649095267]
Feedback Forum
2008-12-08 20:05:20 [David Buelens] [reply] 
Correct enige gevonde trend in een random walk is pure toeval. Op elk moment heeft de munt 50% kans op kop of munt, dus een trend kan niet bestaan in een random walk.
2008-12-08 20:11:24 [8e2cc0b2ef568da46d009b2f601285b2] [reply] 
Q3: correct de optimale seizoenale en niet-seizoenale diffirentiatie zijn af te lezen bij de kleinste variatie!
2008-12-08 20:13:44 [8e2cc0b2ef568da46d009b2f601285b2] [reply] 
De spectraal analyse ontbindt de tijdreeks in sinus en cosinus golven. Ze haalt deze regelmatige golfbewegingen dus uit de tijdreeks.
Uit het raw periodogram kunnen we het volgende aflezen:
x-as = frequentie van de golfbewegingen
y-as = hoe sterk deze golfbeweging voorkomt
we zien duidelijk dat de golfbewegingen met een lage frequentie het meest voorkomen in onze tijdreeks en dus dominant zijn.
Golfbewegingen met een lage frequentie impliceren een traag op en neergaande beweging en dus een lange periode beweging in de tijdreeks.
Conclusie: de tijdreeks gaat traag op en neer.
Uit het cumulatief periodogram kunnen we het volgende afleiden:
Wanneer we alle golfbewegingen nemen met een frequentie tussen nul en vijf, welk percentage van onze tijdreeks wordt dan bepaald door deze beweging?
Hier kunnen we duidelijk zien dat 95% van de spreiding van de tijdreeks wordt bepaald door een golfbeweging met een frequentie tussen 0.0 en 0.1.

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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=26248&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=26248&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26248&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)32.6256513026052Range22Trim Var.22.889409411517
V(Y[t],d=1,D=0)1.00181085061690Range2Trim Var.NA
V(Y[t],d=2,D=0)1.95571824521426Range4Trim Var.0
V(Y[t],d=3,D=0)5.69354838709677Range8Trim Var.2.71938631316870
V(Y[t],d=0,D=1)12.6593563806510Range20Trim Var.7.06221989406903
V(Y[t],d=1,D=1)1.96706128898691Range4Trim Var.0
V(Y[t],d=2,D=1)3.90927835051546Range8Trim Var.2.13568847852268
V(Y[t],d=3,D=1)11.5536508477464Range16Trim Var.5.89162561576355
V(Y[t],d=0,D=2)24.4090933215391Range32Trim Var.12.0356892230576
V(Y[t],d=1,D=2)5.86496113701976Range8Trim Var.2.60201176106469
V(Y[t],d=2,D=2)12.0338087974238Range16Trim Var.6.10569218890422
V(Y[t],d=3,D=2)36.1948973375856Range32Trim Var.19.1820945149564

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 32.6256513026052 & Range & 22 & Trim Var. & 22.889409411517 \tabularnewline
V(Y[t],d=1,D=0) & 1.00181085061690 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.95571824521426 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.69354838709677 & Range & 8 & Trim Var. & 2.71938631316870 \tabularnewline
V(Y[t],d=0,D=1) & 12.6593563806510 & Range & 20 & Trim Var. & 7.06221989406903 \tabularnewline
V(Y[t],d=1,D=1) & 1.96706128898691 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.90927835051546 & Range & 8 & Trim Var. & 2.13568847852268 \tabularnewline
V(Y[t],d=3,D=1) & 11.5536508477464 & Range & 16 & Trim Var. & 5.89162561576355 \tabularnewline
V(Y[t],d=0,D=2) & 24.4090933215391 & Range & 32 & Trim Var. & 12.0356892230576 \tabularnewline
V(Y[t],d=1,D=2) & 5.86496113701976 & Range & 8 & Trim Var. & 2.60201176106469 \tabularnewline
V(Y[t],d=2,D=2) & 12.0338087974238 & Range & 16 & Trim Var. & 6.10569218890422 \tabularnewline
V(Y[t],d=3,D=2) & 36.1948973375856 & Range & 32 & Trim Var. & 19.1820945149564 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26248&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]32.6256513026052[/C][C]Range[/C][C]22[/C][C]Trim Var.[/C][C]22.889409411517[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00181085061690[/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]1.95571824521426[/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]5.69354838709677[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.71938631316870[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.6593563806510[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]7.06221989406903[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.96706128898691[/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]3.90927835051546[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.13568847852268[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.5536508477464[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]5.89162561576355[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]24.4090933215391[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]12.0356892230576[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.86496113701976[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.60201176106469[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.0338087974238[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.10569218890422[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]36.1948973375856[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]19.1820945149564[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26248&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26248&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)32.6256513026052Range22Trim Var.22.889409411517
V(Y[t],d=1,D=0)1.00181085061690Range2Trim Var.NA
V(Y[t],d=2,D=0)1.95571824521426Range4Trim Var.0
V(Y[t],d=3,D=0)5.69354838709677Range8Trim Var.2.71938631316870
V(Y[t],d=0,D=1)12.6593563806510Range20Trim Var.7.06221989406903
V(Y[t],d=1,D=1)1.96706128898691Range4Trim Var.0
V(Y[t],d=2,D=1)3.90927835051546Range8Trim Var.2.13568847852268
V(Y[t],d=3,D=1)11.5536508477464Range16Trim Var.5.89162561576355
V(Y[t],d=0,D=2)24.4090933215391Range32Trim Var.12.0356892230576
V(Y[t],d=1,D=2)5.86496113701976Range8Trim Var.2.60201176106469
V(Y[t],d=2,D=2)12.0338087974238Range16Trim Var.6.10569218890422
V(Y[t],d=3,D=2)36.1948973375856Range32Trim Var.19.1820945149564


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 500 ; par2 = 0.5 ;
Parameters (R input):
par1 = 500 ; par2 = 0.5 ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')