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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 computationMon, 08 Dec 2008 13:03:35 -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/08/t1228766679oaveyb0q65xaa05.htm/, Retrieved Thu, 16 May 2024 18:38:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30898, Retrieved Thu, 16 May 2024 18:38:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact167

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Spectral Analysis] [Aanvulling Q8] [2008-12-08 18:54:28] [b1bd16d1f47bfe13feacf1c27a0abba5]
-    D  [Spectral Analysis] [Aanvulling Q8(2)] [2008-12-08 19:19:21] [b1bd16d1f47bfe13feacf1c27a0abba5]
-   PD    [Spectral Analysis] [Aanvulling Q8 (3)] [2008-12-08 19:22:47] [b1bd16d1f47bfe13feacf1c27a0abba5]
F RMPD        [Variance Reduction Matrix] [eigen reeks step ...] [2008-12-08 20:03:35] [e7b1048c2c3a353441b9143db4404b91] [Current]
Feedback Forum
2008-12-14 16:01:39 [Sofie Mertens] [reply] 
Waarom is men juist op zoek naar de kleinste variantie? Een beetje uitleg hieromtrent zou mogen. Dit is namelijk omdat de variantie het risico, de volatiliteit in een tijdreeks voorstelt. Dit risico wil men zo klein mogelijk houden en dus zoekt men de combinatie van de gewone differentiatie en de seizoenale differentiatie die de kleinste variantie oplevert. Hoe kleiner de variantie, hoe meer men ook kan verklaren van de tijdreeks.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
97,8
107,4
117,5
105,6
97,4
99,5
98,0
104,3
100,6
101,1
103,9
96,9
95,5
108,4
117,0
103,8
100,8
110,6
104,0
112,6
107,3
98,9
109,8
104,9
102,2
123,9
124,9
112,7
121,9
100,6
104,3
120,4
107,5
102,9
125,6
107,5
108,8
128,4
121,1
119,5
128,7
108,7
105,5
119,8
111,3
110,6
120,1
97,5
107,7
127,3
117,2
119,8
116,2
111,0
112,4
130,6
109,1
118,8
123,9
101,6
112,8
128,0
129,6
125,8
119,5
115,7
113,6
129,7
112,0
116,8
127,0
112,1
114,2
121,1
131,6
125,0
120,4
117,7
117,5
120,6
127,5
112,3
124,5
115,2
105,4

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'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30898&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30898&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30898&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'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)95.2122633053221Range36.1Trim Var.71.1241513513514
V(Y[t],d=1,D=0)119.782799770511Range45.3Trim Var.75.7598241392077
V(Y[t],d=2,D=0)328.117140758155Range74.3Trim Var.220.810350076104
V(Y[t],d=3,D=0)1004.95738030714Range139Trim Var.648.207198748044
V(Y[t],d=0,D=1)40.1340943683409Range33.6Trim Var.21.2510336538462
V(Y[t],d=1,D=1)75.0755379499217Range55.7Trim Var.39.7155158730159
V(Y[t],d=2,D=1)226.253513078471Range86Trim Var.106.195151049667
V(Y[t],d=3,D=1)741.842113871635Range166.9Trim Var.355.179153886832
V(Y[t],d=0,D=2)92.817Range39.4Trim Var.56.6287590711176
V(Y[t],d=1,D=2)143.775864406780Range71.2Trim Var.80.9414116002795
V(Y[t],d=2,D=2)415.207627118644Range103.8Trim Var.234.084753265602
V(Y[t],d=3,D=2)1354.69443436177Range194.2Trim Var.818.819064856712

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 95.2122633053221 & Range & 36.1 & Trim Var. & 71.1241513513514 \tabularnewline
V(Y[t],d=1,D=0) & 119.782799770511 & Range & 45.3 & Trim Var. & 75.7598241392077 \tabularnewline
V(Y[t],d=2,D=0) & 328.117140758155 & Range & 74.3 & Trim Var. & 220.810350076104 \tabularnewline
V(Y[t],d=3,D=0) & 1004.95738030714 & Range & 139 & Trim Var. & 648.207198748044 \tabularnewline
V(Y[t],d=0,D=1) & 40.1340943683409 & Range & 33.6 & Trim Var. & 21.2510336538462 \tabularnewline
V(Y[t],d=1,D=1) & 75.0755379499217 & Range & 55.7 & Trim Var. & 39.7155158730159 \tabularnewline
V(Y[t],d=2,D=1) & 226.253513078471 & Range & 86 & Trim Var. & 106.195151049667 \tabularnewline
V(Y[t],d=3,D=1) & 741.842113871635 & Range & 166.9 & Trim Var. & 355.179153886832 \tabularnewline
V(Y[t],d=0,D=2) & 92.817 & Range & 39.4 & Trim Var. & 56.6287590711176 \tabularnewline
V(Y[t],d=1,D=2) & 143.775864406780 & Range & 71.2 & Trim Var. & 80.9414116002795 \tabularnewline
V(Y[t],d=2,D=2) & 415.207627118644 & Range & 103.8 & Trim Var. & 234.084753265602 \tabularnewline
V(Y[t],d=3,D=2) & 1354.69443436177 & Range & 194.2 & Trim Var. & 818.819064856712 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30898&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]95.2122633053221[/C][C]Range[/C][C]36.1[/C][C]Trim Var.[/C][C]71.1241513513514[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]119.782799770511[/C][C]Range[/C][C]45.3[/C][C]Trim Var.[/C][C]75.7598241392077[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]328.117140758155[/C][C]Range[/C][C]74.3[/C][C]Trim Var.[/C][C]220.810350076104[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]1004.95738030714[/C][C]Range[/C][C]139[/C][C]Trim Var.[/C][C]648.207198748044[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]40.1340943683409[/C][C]Range[/C][C]33.6[/C][C]Trim Var.[/C][C]21.2510336538462[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]75.0755379499217[/C][C]Range[/C][C]55.7[/C][C]Trim Var.[/C][C]39.7155158730159[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]226.253513078471[/C][C]Range[/C][C]86[/C][C]Trim Var.[/C][C]106.195151049667[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]741.842113871635[/C][C]Range[/C][C]166.9[/C][C]Trim Var.[/C][C]355.179153886832[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]92.817[/C][C]Range[/C][C]39.4[/C][C]Trim Var.[/C][C]56.6287590711176[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]143.775864406780[/C][C]Range[/C][C]71.2[/C][C]Trim Var.[/C][C]80.9414116002795[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]415.207627118644[/C][C]Range[/C][C]103.8[/C][C]Trim Var.[/C][C]234.084753265602[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]1354.69443436177[/C][C]Range[/C][C]194.2[/C][C]Trim Var.[/C][C]818.819064856712[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30898&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30898&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)95.2122633053221Range36.1Trim Var.71.1241513513514
V(Y[t],d=1,D=0)119.782799770511Range45.3Trim Var.75.7598241392077
V(Y[t],d=2,D=0)328.117140758155Range74.3Trim Var.220.810350076104
V(Y[t],d=3,D=0)1004.95738030714Range139Trim Var.648.207198748044
V(Y[t],d=0,D=1)40.1340943683409Range33.6Trim Var.21.2510336538462
V(Y[t],d=1,D=1)75.0755379499217Range55.7Trim Var.39.7155158730159
V(Y[t],d=2,D=1)226.253513078471Range86Trim Var.106.195151049667
V(Y[t],d=3,D=1)741.842113871635Range166.9Trim Var.355.179153886832
V(Y[t],d=0,D=2)92.817Range39.4Trim Var.56.6287590711176
V(Y[t],d=1,D=2)143.775864406780Range71.2Trim Var.80.9414116002795
V(Y[t],d=2,D=2)415.207627118644Range103.8Trim Var.234.084753265602
V(Y[t],d=3,D=2)1354.69443436177Range194.2Trim Var.818.819064856712


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')