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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_variancereduction.wasp
Title produced by softwareVariance Reduction Matrix
Date of computationWed, 03 Dec 2008 07:36:31 -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/03/t1228315032uc5yrbguq6d01ld.htm/, Retrieved Fri, 17 May 2024 01:23:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28712, Retrieved Fri, 17 May 2024 01:23:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact223

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [(Partial) Autocorrelation Function] [paper bel20 autoc...] [2008-12-03 13:05:59] [f58cc3b532da25682c394745f1a82535]
-   PD  [(Partial) Autocorrelation Function] [paper variance re...] [2008-12-03 14:08:24] [f58cc3b532da25682c394745f1a82535]
F RM        [Variance Reduction Matrix] [paper variance re...] [2008-12-03 14:36:31] [b09437381d488816ab9f5cf07e347c02] [Current]
Feedback Forum
2008-12-13 14:15:01 [Ken Wright] [reply] 
correct,.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.
2008-12-14 19:23:21 [Vincent Vanden Poel] [reply] 
Correct. De Variance Reduction Matrix geeft de waarden weer nadat er gedifferentieerd is. Het werkt volgens volgende formule: Nablad * NablaDS * Yt = et waarbij d = # keer gewoon gedifferentieerd en D = # keer seizoenaal gedifferentieerd. Deze laatste waarde wordt gebruikt om seizoenaliteit te verwijderen.
De 2e kolom geeft de bijhorende varianties weer. Dit is het risico/ de volatiliteit dat in de tijdreeksen zit. Deze waarde moet zo klein mogelijk zijn opdat men veel zou kunnen verklaren. We moeten ons dus de vraag stellen welke differentiatie nodig is om zoveel mogelijk van de tijdreeks te verklaren.
Indien er veel outliers zijn is het interessanter om te kijken naar de getrimde variantiewaarden. Hier bekomt men de laagste variantie bij één maal niet seizoenaal te differencieren. Dit is ook zo bij de getrimde variantie.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2659.81
2638.53
2720.25
2745.88
2735.7
2811.7
2799.43
2555.28
2304.98
2214.95
2065.81
1940.49
2042
1995.37
1946.81
1765.9
1635.25
1833.42
1910.43
1959.67
1969.6
2061.41
2093.48
2120.88
2174.56
2196.72
2350.44
2440.25
2408.64
2472.81
2407.6
2454.62
2448.05
2497.84
2645.64
2756.76
2849.27
2921.44
2981.85
3080.58
3106.22
3119.31
3061.26
3097.31
3161.69
3257.16
3277.01
3295.32
3363.99
3494.17
3667.03
3813.06
3917.96
3895.51
3801.06
3570.12
3701.61
3862.27
3970.1
4138.52
4199.75
4290.89
4443.91
4502.64
4356.98
4591.27
4696.96
4621.4
4562.84
4202.52
4296.49
4435.23
4105.18
4116.68
3844.49
3720.98
3674.4
3857.62
3801.06
3504.37
3032.6
3047.03

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'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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28712&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28712&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28712&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Variance Reduction Matrix
V(Y[t],d=0,D=0)730089.612795438Range3061.71Trim Var.558610.003844112
V(Y[t],d=1,D=0)18799.7211922531Range706.060000000001Trim Var.9677.33499565392
V(Y[t],d=2,D=0)26516.4514715032Range954.99Trim Var.13037.0991281495
V(Y[t],d=3,D=0)68225.2344829277Range1435.58000000000Trim Var.31160.7523170222
V(Y[t],d=0,D=1)440568.588512961Range2581.52Trim Var.325150.014788154
V(Y[t],d=1,D=1)29419.4624747229Range895.73Trim Var.14351.9942560656
V(Y[t],d=2,D=1)39068.9326508341Range1149.56000000000Trim Var.15116.2722484463
V(Y[t],d=3,D=1)88191.671401176Range1637.25Trim Var.35468.1324147282
V(Y[t],d=0,D=2)764301.338006897Range4265.31Trim Var.412823.553420211
V(Y[t],d=1,D=2)67191.8602966792Range1481.9Trim Var.36962.4172958432
V(Y[t],d=2,D=2)83559.0698573702Range1798.42Trim Var.32865.8322367755
V(Y[t],d=3,D=2)160818.574090438Range2067.57000000001Trim Var.82356.3577046769

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 730089.612795438 & Range & 3061.71 & Trim Var. & 558610.003844112 \tabularnewline
V(Y[t],d=1,D=0) & 18799.7211922531 & Range & 706.060000000001 & Trim Var. & 9677.33499565392 \tabularnewline
V(Y[t],d=2,D=0) & 26516.4514715032 & Range & 954.99 & Trim Var. & 13037.0991281495 \tabularnewline
V(Y[t],d=3,D=0) & 68225.2344829277 & Range & 1435.58000000000 & Trim Var. & 31160.7523170222 \tabularnewline
V(Y[t],d=0,D=1) & 440568.588512961 & Range & 2581.52 & Trim Var. & 325150.014788154 \tabularnewline
V(Y[t],d=1,D=1) & 29419.4624747229 & Range & 895.73 & Trim Var. & 14351.9942560656 \tabularnewline
V(Y[t],d=2,D=1) & 39068.9326508341 & Range & 1149.56000000000 & Trim Var. & 15116.2722484463 \tabularnewline
V(Y[t],d=3,D=1) & 88191.671401176 & Range & 1637.25 & Trim Var. & 35468.1324147282 \tabularnewline
V(Y[t],d=0,D=2) & 764301.338006897 & Range & 4265.31 & Trim Var. & 412823.553420211 \tabularnewline
V(Y[t],d=1,D=2) & 67191.8602966792 & Range & 1481.9 & Trim Var. & 36962.4172958432 \tabularnewline
V(Y[t],d=2,D=2) & 83559.0698573702 & Range & 1798.42 & Trim Var. & 32865.8322367755 \tabularnewline
V(Y[t],d=3,D=2) & 160818.574090438 & Range & 2067.57000000001 & Trim Var. & 82356.3577046769 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28712&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]730089.612795438[/C][C]Range[/C][C]3061.71[/C][C]Trim Var.[/C][C]558610.003844112[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]18799.7211922531[/C][C]Range[/C][C]706.060000000001[/C][C]Trim Var.[/C][C]9677.33499565392[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]26516.4514715032[/C][C]Range[/C][C]954.99[/C][C]Trim Var.[/C][C]13037.0991281495[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]68225.2344829277[/C][C]Range[/C][C]1435.58000000000[/C][C]Trim Var.[/C][C]31160.7523170222[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]440568.588512961[/C][C]Range[/C][C]2581.52[/C][C]Trim Var.[/C][C]325150.014788154[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]29419.4624747229[/C][C]Range[/C][C]895.73[/C][C]Trim Var.[/C][C]14351.9942560656[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]39068.9326508341[/C][C]Range[/C][C]1149.56000000000[/C][C]Trim Var.[/C][C]15116.2722484463[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]88191.671401176[/C][C]Range[/C][C]1637.25[/C][C]Trim Var.[/C][C]35468.1324147282[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]764301.338006897[/C][C]Range[/C][C]4265.31[/C][C]Trim Var.[/C][C]412823.553420211[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]67191.8602966792[/C][C]Range[/C][C]1481.9[/C][C]Trim Var.[/C][C]36962.4172958432[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]83559.0698573702[/C][C]Range[/C][C]1798.42[/C][C]Trim Var.[/C][C]32865.8322367755[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]160818.574090438[/C][C]Range[/C][C]2067.57000000001[/C][C]Trim Var.[/C][C]82356.3577046769[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28712&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28712&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)730089.612795438Range3061.71Trim Var.558610.003844112
V(Y[t],d=1,D=0)18799.7211922531Range706.060000000001Trim Var.9677.33499565392
V(Y[t],d=2,D=0)26516.4514715032Range954.99Trim Var.13037.0991281495
V(Y[t],d=3,D=0)68225.2344829277Range1435.58000000000Trim Var.31160.7523170222
V(Y[t],d=0,D=1)440568.588512961Range2581.52Trim Var.325150.014788154
V(Y[t],d=1,D=1)29419.4624747229Range895.73Trim Var.14351.9942560656
V(Y[t],d=2,D=1)39068.9326508341Range1149.56000000000Trim Var.15116.2722484463
V(Y[t],d=3,D=1)88191.671401176Range1637.25Trim Var.35468.1324147282
V(Y[t],d=0,D=2)764301.338006897Range4265.31Trim Var.412823.553420211
V(Y[t],d=1,D=2)67191.8602966792Range1481.9Trim Var.36962.4172958432
V(Y[t],d=2,D=2)83559.0698573702Range1798.42Trim Var.32865.8322367755
V(Y[t],d=3,D=2)160818.574090438Range2067.57000000001Trim Var.82356.3577046769


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 0 ; par3 = 1 ; par4 = 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')