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Author

*The author of this computation has been verified*

R Software Module

rwasp_variancereduction.wasp

Title produced by software

Variance Reduction Matrix

Date of computation

Sat, 06 Dec 2008 02:12:19 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/06/t12285547957e5ow3uexij2qp1.htm/, Retrieved Sat, 25 May 2024 21:55:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29427, Retrieved Sat, 25 May 2024 21:55:41 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

225

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
F RMP     [Variance Reduction Matrix] [step 2] [2008-12-06 09:12:19] [a9e6d7cd6e144e8b311d9f96a24c5a25] [Current]
- RMP       [Spectral Analysis] [step 2] [2008-12-06 18:00:08] [9f5bfe3b95f9ec3d2ed4c0a560a9648a] 
F RMPD      [Spectral Analysis] [step 2] [2008-12-06 18:04:18] [9f5bfe3b95f9ec3d2ed4c0a560a9648a] 
F RMPD      [Spectral Analysis] [step 2] [2008-12-06 18:06:54] [9f5bfe3b95f9ec3d2ed4c0a560a9648a] 
F RMPD      [Spectral Analysis] [step 2] [2008-12-06 18:09:24] [9f5bfe3b95f9ec3d2ed4c0a560a9648a] 
F   P         [Spectral Analysis] [step 3] [2008-12-06 18:24:41] [9f5bfe3b95f9ec3d2ed4c0a560a9648a] 
F RMPD      [(Partial) Autocorrelation Function] [step 2] [2008-12-06 18:12:25] [9f5bfe3b95f9ec3d2ed4c0a560a9648a] 
F RMPD      [(Partial) Autocorrelation Function] [step 2] [2008-12-06 18:14:47] [9f5bfe3b95f9ec3d2ed4c0a560a9648a] 
F RMPD      [(Partial) Autocorrelation Function] [step 2] [2008-12-06 18:17:03] [9f5bfe3b95f9ec3d2ed4c0a560a9648a] 
F   P         [(Partial) Autocorrelation Function] [step 3] [2008-12-06 18:22:51] [9f5bfe3b95f9ec3d2ed4c0a560a9648a] 

Feedback Forum

2008-12-13 10:14:11 [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’. Nog steeds geeft de differentiatie d=1 en D=0 de beste oplossing. 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.
2008-12-13 10:40:33 [Sam De Cuyper] [reply] 
Juist maar je zegt niets over de getrimde variantie. De getrimde variantie is de variantie met weglating van de grootste en de kleinste waarnemingen (extrema) in de tijdreeks. Ook de getrimde var is voor bijde d's (1) het kleinst. Met deze calculator kan je enkel berekenen welke differentiatie je moet toepassen om de tijdreeks stationair te maken.
2008-12-16 18:56:21 [Kevin Vermeiren] [reply] 
De student vermeldt hier goed dat hoe kleiner de variantie hoe minder het risico, de volatiliteit van de tijdreeks en hoe meer het model kan verklaren. Er moet dus inderdaad naar de variantie met de kleinste waarde gezocht worden.  Het klopt dat d=1 en D=1. Hier had nog bijgevoegd mogen worden dat indien er sprake zou zijn van outliers, er gekeken dient te worden naar de kolom met de getrimde variantie. De 5% hoogste en laagste waarden worden dan weggelaten. De invloed van outliers op de variantie wordt dus gereduceerd en een betrouwbaarder beeld wordt bekomen. 

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29427&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29427&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29427&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Variance Reduction Matrix
V(Y[t],d=0,D=0)	24040.7319917109	Range	708.9	Trim Var.	14891.1423067379
V(Y[t],d=1,D=0)	1855.27831616522	Range	306.2	Trim Var.	1019.21726473461
V(Y[t],d=2,D=0)	3601.51571083278	Range	388.2	Trim Var.	1764.07169175190
V(Y[t],d=3,D=0)	10155.4683153647	Range	595.5	Trim Var.	5250.86267655406
V(Y[t],d=0,D=1)	10061.5318845559	Range	585.7	Trim Var.	5798.12009737033
V(Y[t],d=1,D=1)	795.483036989776	Range	221.9	Trim Var.	451.063415764475
V(Y[t],d=2,D=1)	1251.20020977106	Range	223.4	Trim Var.	751.938251968809
V(Y[t],d=3,D=1)	3933.17493248985	Range	389.7	Trim Var.	2351.74535475078
V(Y[t],d=0,D=2)	23022.65043915	Range	819	Trim Var.	13637.4877562041
V(Y[t],d=1,D=2)	2352.87163598807	Range	333.6	Trim Var.	1332.90434353283
V(Y[t],d=2,D=2)	3506.43060400436	Range	407	Trim Var.	2059.39114521349
V(Y[t],d=3,D=2)	10920.6579647792	Range	659.1	Trim Var.	6490.07402051023

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 24040.7319917109 & Range & 708.9 & Trim Var. & 14891.1423067379 \tabularnewline
V(Y[t],d=1,D=0) & 1855.27831616522 & Range & 306.2 & Trim Var. & 1019.21726473461 \tabularnewline
V(Y[t],d=2,D=0) & 3601.51571083278 & Range & 388.2 & Trim Var. & 1764.07169175190 \tabularnewline
V(Y[t],d=3,D=0) & 10155.4683153647 & Range & 595.5 & Trim Var. & 5250.86267655406 \tabularnewline
V(Y[t],d=0,D=1) & 10061.5318845559 & Range & 585.7 & Trim Var. & 5798.12009737033 \tabularnewline
V(Y[t],d=1,D=1) & 795.483036989776 & Range & 221.9 & Trim Var. & 451.063415764475 \tabularnewline
V(Y[t],d=2,D=1) & 1251.20020977106 & Range & 223.4 & Trim Var. & 751.938251968809 \tabularnewline
V(Y[t],d=3,D=1) & 3933.17493248985 & Range & 389.7 & Trim Var. & 2351.74535475078 \tabularnewline
V(Y[t],d=0,D=2) & 23022.65043915 & Range & 819 & Trim Var. & 13637.4877562041 \tabularnewline
V(Y[t],d=1,D=2) & 2352.87163598807 & Range & 333.6 & Trim Var. & 1332.90434353283 \tabularnewline
V(Y[t],d=2,D=2) & 3506.43060400436 & Range & 407 & Trim Var. & 2059.39114521349 \tabularnewline
V(Y[t],d=3,D=2) & 10920.6579647792 & Range & 659.1 & Trim Var. & 6490.07402051023 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29427&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]24040.7319917109[/C][C]Range[/C][C]708.9[/C][C]Trim Var.[/C][C]14891.1423067379[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1855.27831616522[/C][C]Range[/C][C]306.2[/C][C]Trim Var.[/C][C]1019.21726473461[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]3601.51571083278[/C][C]Range[/C][C]388.2[/C][C]Trim Var.[/C][C]1764.07169175190[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]10155.4683153647[/C][C]Range[/C][C]595.5[/C][C]Trim Var.[/C][C]5250.86267655406[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]10061.5318845559[/C][C]Range[/C][C]585.7[/C][C]Trim Var.[/C][C]5798.12009737033[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]795.483036989776[/C][C]Range[/C][C]221.9[/C][C]Trim Var.[/C][C]451.063415764475[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]1251.20020977106[/C][C]Range[/C][C]223.4[/C][C]Trim Var.[/C][C]751.938251968809[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]3933.17493248985[/C][C]Range[/C][C]389.7[/C][C]Trim Var.[/C][C]2351.74535475078[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]23022.65043915[/C][C]Range[/C][C]819[/C][C]Trim Var.[/C][C]13637.4877562041[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]2352.87163598807[/C][C]Range[/C][C]333.6[/C][C]Trim Var.[/C][C]1332.90434353283[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]3506.43060400436[/C][C]Range[/C][C]407[/C][C]Trim Var.[/C][C]2059.39114521349[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]10920.6579647792[/C][C]Range[/C][C]659.1[/C][C]Trim Var.[/C][C]6490.07402051023[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29427&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29427&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Variance Reduction Matrix
V(Y[t],d=0,D=0)	24040.7319917109	Range	708.9	Trim Var.	14891.1423067379
V(Y[t],d=1,D=0)	1855.27831616522	Range	306.2	Trim Var.	1019.21726473461
V(Y[t],d=2,D=0)	3601.51571083278	Range	388.2	Trim Var.	1764.07169175190
V(Y[t],d=3,D=0)	10155.4683153647	Range	595.5	Trim Var.	5250.86267655406
V(Y[t],d=0,D=1)	10061.5318845559	Range	585.7	Trim Var.	5798.12009737033
V(Y[t],d=1,D=1)	795.483036989776	Range	221.9	Trim Var.	451.063415764475
V(Y[t],d=2,D=1)	1251.20020977106	Range	223.4	Trim Var.	751.938251968809
V(Y[t],d=3,D=1)	3933.17493248985	Range	389.7	Trim Var.	2351.74535475078
V(Y[t],d=0,D=2)	23022.65043915	Range	819	Trim Var.	13637.4877562041
V(Y[t],d=1,D=2)	2352.87163598807	Range	333.6	Trim Var.	1332.90434353283
V(Y[t],d=2,D=2)	3506.43060400436	Range	407	Trim Var.	2059.39114521349
V(Y[t],d=3,D=2)	10920.6579647792	Range	659.1	Trim Var.	6490.07402051023

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code