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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_variancereduction.wasp
Title produced by softwareVariance Reduction Matrix
Date of computationSun, 07 Dec 2008 02:41:29 -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/07/t1228642937uwgimosgo1e6hie.htm/, Retrieved Sun, 19 May 2024 09:40:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29830, Retrieved Sun, 19 May 2024 09:40:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact226

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Variance Reduction Matrix] [step 2] [2008-12-07 09:41:29] [a9e6d7cd6e144e8b311d9f96a24c5a25] [Current]
Feedback Forum
2008-12-13 11:20:29 [Ken Wright] [reply] 
Juist, deze calculator gaat trachten de verschillende waarden te zoeken om het best te kunnen differentiëren, dus de beste waarden voor d en D. In de eerste kolom van de geproduceerde tabel zien we de optimale waarden voor d en D. De tweede kolom geeft de bijhorende variantie weer, dus na differentiatie met de gegeven waarden d en D. Om de beste waarden voor d en D te achter halen moeten we kijken naar de rij met de kleinste variantie. . Men moet hier wel oppassen, bij de gewone spreiding wordt de invloed van outliers (=waarden die extreem afwijken van het gemiddelde) mee in acht genomen. Daarom kan men beter gebruikmaken van de trimmed variance, deze houdt namelijk geen rekening met outliers. Vandaar de naam trimmed, dit duidt erop dat de aller grootste waarden en kleinste er worden ‘afgeknipt’. . Deze calculator geeft eigenlijk alleen maar een aanwijzing hoe men moet differentiëren. Daarom wordt er nog extra gebruik gemaakt van de (partial) autocorrelatie en de spectral analysis.
2008-12-16 19:01:53 [Kevin Vermeiren] [reply] 
De student vermeldt terecht dat in de tabel de kleinste variantie gezocht moet worden. Bijgevolg vinden we inderdaad dat d=1 en D=1. Verder vermeldt de student correct dat hoe kleiner de variantie, hoe meer het model kan verklaren want de variantie geeft het risico, de volatiliteit van de tijdreeks weer. Hier had nog wel vermeld mogen worden dat indien er sprake is van outliers, er gewerkt dient te worden met de kolom met de getrimde varianties. In dit geval vinden we dan dezelfde resultaten.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2648,9
2669,6
3042,3
2604,2
2732,1
2621,7
2483,7
2479,3
2684,6
2834,7
2566,1
2251,2
2350
2299,8
2542,8
2530,2
2508,1
2616,8
2534,1
2181,8
2578,9
2841,9
2529,9
2103,2
2326,2
2452,6
2782,1
2727,3
2648,2
2760,7
2613
2225,4
2713,9
2923,3
2707
2473,9
2521
2531,8
3068,8
2826,9
2674,2
2966,6
2798,8
2629,6
3124,6
3115,7
3083
2863,9
2728,7
2789,4
3225,7
3148,2
2836,5
3153,5
2656,9
2834,7
3172,5
2998,8
3103,1
2735,6
2818,1
2874,4
3438,5
2949,1
3306,8
3530
3003,8
3206,4
3514,6
3522,6
3525,5
2996,2
3231,1
3030
3541,7
3113,2
3390,8
3424,2
3079,8
3123,4
3317,1
3579,9
3317,9
2668,1
3609,2
3535,2
3644,7
3925,7
3663,2
3905,3
3990
3695,8

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'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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29830&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29830&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29830&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'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)181255.745039417Range1886.8Trim Var.119722.013021680
V(Y[t],d=1,D=0)87203.0984249084Range1590.9Trim Var.54874.2394012346
V(Y[t],d=2,D=0)235038.182133583Range2644.4Trim Var.144442.456651899
V(Y[t],d=3,D=0)732996.426777324Range4584.7Trim Var.437466.439792275
V(Y[t],d=0,D=1)64023.8890363924Range1409.7Trim Var.36579.7411091549
V(Y[t],d=1,D=1)54092.2649107433Range1249.6Trim Var.26432.2319839034
V(Y[t],d=2,D=1)160531.966921412Range2361.3Trim Var.81719.5243146998
V(Y[t],d=3,D=1)518333.287747779Range4359.7Trim Var.245283.194680307
V(Y[t],d=0,D=2)122030.685924056Range1464.2Trim Var.81753.9521920904
V(Y[t],d=1,D=2)84586.9324513795Range1577.9Trim Var.45228.1175394506
V(Y[t],d=2,D=2)241964.816608392Range2627Trim Var.128419.287371446
V(Y[t],d=3,D=2)817364.854774039Range4561Trim Var.398988.623258146

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 181255.745039417 & Range & 1886.8 & Trim Var. & 119722.013021680 \tabularnewline
V(Y[t],d=1,D=0) & 87203.0984249084 & Range & 1590.9 & Trim Var. & 54874.2394012346 \tabularnewline
V(Y[t],d=2,D=0) & 235038.182133583 & Range & 2644.4 & Trim Var. & 144442.456651899 \tabularnewline
V(Y[t],d=3,D=0) & 732996.426777324 & Range & 4584.7 & Trim Var. & 437466.439792275 \tabularnewline
V(Y[t],d=0,D=1) & 64023.8890363924 & Range & 1409.7 & Trim Var. & 36579.7411091549 \tabularnewline
V(Y[t],d=1,D=1) & 54092.2649107433 & Range & 1249.6 & Trim Var. & 26432.2319839034 \tabularnewline
V(Y[t],d=2,D=1) & 160531.966921412 & Range & 2361.3 & Trim Var. & 81719.5243146998 \tabularnewline
V(Y[t],d=3,D=1) & 518333.287747779 & Range & 4359.7 & Trim Var. & 245283.194680307 \tabularnewline
V(Y[t],d=0,D=2) & 122030.685924056 & Range & 1464.2 & Trim Var. & 81753.9521920904 \tabularnewline
V(Y[t],d=1,D=2) & 84586.9324513795 & Range & 1577.9 & Trim Var. & 45228.1175394506 \tabularnewline
V(Y[t],d=2,D=2) & 241964.816608392 & Range & 2627 & Trim Var. & 128419.287371446 \tabularnewline
V(Y[t],d=3,D=2) & 817364.854774039 & Range & 4561 & Trim Var. & 398988.623258146 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29830&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]181255.745039417[/C][C]Range[/C][C]1886.8[/C][C]Trim Var.[/C][C]119722.013021680[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]87203.0984249084[/C][C]Range[/C][C]1590.9[/C][C]Trim Var.[/C][C]54874.2394012346[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]235038.182133583[/C][C]Range[/C][C]2644.4[/C][C]Trim Var.[/C][C]144442.456651899[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]732996.426777324[/C][C]Range[/C][C]4584.7[/C][C]Trim Var.[/C][C]437466.439792275[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]64023.8890363924[/C][C]Range[/C][C]1409.7[/C][C]Trim Var.[/C][C]36579.7411091549[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]54092.2649107433[/C][C]Range[/C][C]1249.6[/C][C]Trim Var.[/C][C]26432.2319839034[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]160531.966921412[/C][C]Range[/C][C]2361.3[/C][C]Trim Var.[/C][C]81719.5243146998[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]518333.287747779[/C][C]Range[/C][C]4359.7[/C][C]Trim Var.[/C][C]245283.194680307[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]122030.685924056[/C][C]Range[/C][C]1464.2[/C][C]Trim Var.[/C][C]81753.9521920904[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]84586.9324513795[/C][C]Range[/C][C]1577.9[/C][C]Trim Var.[/C][C]45228.1175394506[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]241964.816608392[/C][C]Range[/C][C]2627[/C][C]Trim Var.[/C][C]128419.287371446[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]817364.854774039[/C][C]Range[/C][C]4561[/C][C]Trim Var.[/C][C]398988.623258146[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29830&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29830&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)181255.745039417Range1886.8Trim Var.119722.013021680
V(Y[t],d=1,D=0)87203.0984249084Range1590.9Trim Var.54874.2394012346
V(Y[t],d=2,D=0)235038.182133583Range2644.4Trim Var.144442.456651899
V(Y[t],d=3,D=0)732996.426777324Range4584.7Trim Var.437466.439792275
V(Y[t],d=0,D=1)64023.8890363924Range1409.7Trim Var.36579.7411091549
V(Y[t],d=1,D=1)54092.2649107433Range1249.6Trim Var.26432.2319839034
V(Y[t],d=2,D=1)160531.966921412Range2361.3Trim Var.81719.5243146998
V(Y[t],d=3,D=1)518333.287747779Range4359.7Trim Var.245283.194680307
V(Y[t],d=0,D=2)122030.685924056Range1464.2Trim Var.81753.9521920904
V(Y[t],d=1,D=2)84586.9324513795Range1577.9Trim Var.45228.1175394506
V(Y[t],d=2,D=2)241964.816608392Range2627Trim Var.128419.287371446
V(Y[t],d=3,D=2)817364.854774039Range4561Trim Var.398988.623258146


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
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')