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R Software Module

rwasp_variancereduction.wasp

Title produced by software

Variance Reduction Matrix

Date of computation

Wed, 03 Dec 2008 09:42:26 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/03/t1228322592kg75zneq1xnznfg.htm/, Retrieved Sun, 19 May 2024 05:54:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28782, Retrieved Sun, 19 May 2024 05:54:40 +0000

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Estimated Impact

218

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

F       [Variance Reduction Matrix] [VRM] [2008-12-03 16:42:26] [21d7d81e7693ad6dde5aadefb1046611] [Current]

Feedback Forum

2008-12-14 21:15:31 [Bob Leysen] [reply] 
We zoeken in de tabel van VRM naar de laagste waarde omdat hoe kleiner de variantie, hoe beter. De variantie is het kleinst bij d=1 en D=1 
 
V(Y[t],d=1,D=1) 27829417.8485348 Range 33755 Trim Var. 13651830.8361384 
2008-12-15 18:01:39 [Davy De Nef] [reply] 
2008-12-15 18:01:53 [Davy De Nef] [reply] 
In stap 2 wordt er onder andere aan de hand van de Variance Reduction Matrix gezocht naar het aantal keer dat er seizoenaal (D) en niet-seizoenaal (d) gedifferentieerd zal moeten worden om de tijdreeks stationair te maken. 
 
Concreet komt het erop neer dat we in de tabel die geproduceerd wordt door de software op zoek gaan naar de laagste waarde. Bij de berekening wordt de seizoenale periode ingesteld op 12 omdat we hier werken met maandcijfers. 
 
In dit geval is dat bij: d=1 en D=1 
V(Y[t],d=1,D=1) 27829417.8485348 Range 33755 Trim Var. 13651830.8361384  
 
Er zal dus 1x seizoenaal gedifferentieerd en 1x niet-seizoenaal gedifferentieerd moeten worden. 

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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	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28782&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28782&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28782&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	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Variance Reduction Matrix
V(Y[t],d=0,D=0)	776710454.13045	Range	115276	Trim Var.	565305841.408895
V(Y[t],d=1,D=0)	163212794.48939	Range	65564	Trim Var.	77795594.8062271
V(Y[t],d=2,D=0)	250294472.854273	Range	81499	Trim Var.	132495461.586258
V(Y[t],d=3,D=0)	575321862.471701	Range	125171	Trim Var.	286098920.703408
V(Y[t],d=0,D=1)	448479775.739084	Range	75835	Trim Var.	350142230.077442
V(Y[t],d=1,D=1)	27829417.8485348	Range	33755	Trim Var.	13651830.8361384
V(Y[t],d=2,D=1)	64059176.1747573	Range	44005	Trim Var.	30812499.8732680
V(Y[t],d=3,D=1)	210532546.624595	Range	76554	Trim Var.	107602141.210989
V(Y[t],d=0,D=2)	442096472.251773	Range	78685	Trim Var.	336962853.554073
V(Y[t],d=1,D=2)	77620935.2204301	Range	55325	Trim Var.	36983570.8374963
V(Y[t],d=2,D=2)	188580722.391782	Range	80924	Trim Var.	106515398.327160
V(Y[t],d=3,D=2)	604809504.585348	Range	137469	Trim Var.	326922116.05

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 776710454.13045 & Range & 115276 & Trim Var. & 565305841.408895 \tabularnewline
V(Y[t],d=1,D=0) & 163212794.48939 & Range & 65564 & Trim Var. & 77795594.8062271 \tabularnewline
V(Y[t],d=2,D=0) & 250294472.854273 & Range & 81499 & Trim Var. & 132495461.586258 \tabularnewline
V(Y[t],d=3,D=0) & 575321862.471701 & Range & 125171 & Trim Var. & 286098920.703408 \tabularnewline
V(Y[t],d=0,D=1) & 448479775.739084 & Range & 75835 & Trim Var. & 350142230.077442 \tabularnewline
V(Y[t],d=1,D=1) & 27829417.8485348 & Range & 33755 & Trim Var. & 13651830.8361384 \tabularnewline
V(Y[t],d=2,D=1) & 64059176.1747573 & Range & 44005 & Trim Var. & 30812499.8732680 \tabularnewline
V(Y[t],d=3,D=1) & 210532546.624595 & Range & 76554 & Trim Var. & 107602141.210989 \tabularnewline
V(Y[t],d=0,D=2) & 442096472.251773 & Range & 78685 & Trim Var. & 336962853.554073 \tabularnewline
V(Y[t],d=1,D=2) & 77620935.2204301 & Range & 55325 & Trim Var. & 36983570.8374963 \tabularnewline
V(Y[t],d=2,D=2) & 188580722.391782 & Range & 80924 & Trim Var. & 106515398.327160 \tabularnewline
V(Y[t],d=3,D=2) & 604809504.585348 & Range & 137469 & Trim Var. & 326922116.05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28782&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]776710454.13045[/C][C]Range[/C][C]115276[/C][C]Trim Var.[/C][C]565305841.408895[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]163212794.48939[/C][C]Range[/C][C]65564[/C][C]Trim Var.[/C][C]77795594.8062271[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]250294472.854273[/C][C]Range[/C][C]81499[/C][C]Trim Var.[/C][C]132495461.586258[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]575321862.471701[/C][C]Range[/C][C]125171[/C][C]Trim Var.[/C][C]286098920.703408[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]448479775.739084[/C][C]Range[/C][C]75835[/C][C]Trim Var.[/C][C]350142230.077442[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]27829417.8485348[/C][C]Range[/C][C]33755[/C][C]Trim Var.[/C][C]13651830.8361384[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]64059176.1747573[/C][C]Range[/C][C]44005[/C][C]Trim Var.[/C][C]30812499.8732680[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]210532546.624595[/C][C]Range[/C][C]76554[/C][C]Trim Var.[/C][C]107602141.210989[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]442096472.251773[/C][C]Range[/C][C]78685[/C][C]Trim Var.[/C][C]336962853.554073[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]77620935.2204301[/C][C]Range[/C][C]55325[/C][C]Trim Var.[/C][C]36983570.8374963[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]188580722.391782[/C][C]Range[/C][C]80924[/C][C]Trim Var.[/C][C]106515398.327160[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]604809504.585348[/C][C]Range[/C][C]137469[/C][C]Trim Var.[/C][C]326922116.05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28782&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28782&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)	776710454.13045	Range	115276	Trim Var.	565305841.408895
V(Y[t],d=1,D=0)	163212794.48939	Range	65564	Trim Var.	77795594.8062271
V(Y[t],d=2,D=0)	250294472.854273	Range	81499	Trim Var.	132495461.586258
V(Y[t],d=3,D=0)	575321862.471701	Range	125171	Trim Var.	286098920.703408
V(Y[t],d=0,D=1)	448479775.739084	Range	75835	Trim Var.	350142230.077442
V(Y[t],d=1,D=1)	27829417.8485348	Range	33755	Trim Var.	13651830.8361384
V(Y[t],d=2,D=1)	64059176.1747573	Range	44005	Trim Var.	30812499.8732680
V(Y[t],d=3,D=1)	210532546.624595	Range	76554	Trim Var.	107602141.210989
V(Y[t],d=0,D=2)	442096472.251773	Range	78685	Trim Var.	336962853.554073
V(Y[t],d=1,D=2)	77620935.2204301	Range	55325	Trim Var.	36983570.8374963
V(Y[t],d=2,D=2)	188580722.391782	Range	80924	Trim Var.	106515398.327160
V(Y[t],d=3,D=2)	604809504.585348	Range	137469	Trim Var.	326922116.05

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')

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