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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 computationTue, 09 Dec 2008 06:00:44 -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/09/t1228827679o0va5oh5nm1psl6.htm/, Retrieved Sat, 18 May 2024 04:49:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31353, Retrieved Sat, 18 May 2024 04:49:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact194

Tree of Dependent Computations

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 RMPD  [Standard Deviation-Mean Plot] [Identification an...] [2008-12-09 12:57:00] [8ac58ef7b35dc5a117bc162cf16850e9]
F RM D      [Variance Reduction Matrix] [Identification an...] [2008-12-09 13:00:44] [acca1d0ee7cc95ffc080d0867a313954] [Current]
F RM          [(Partial) Autocorrelation Function] [Identification an...] [2008-12-09 13:03:20] [8ac58ef7b35dc5a117bc162cf16850e9]
F RM            [Spectral Analysis] [Identification an...] [2008-12-09 13:05:46] [8ac58ef7b35dc5a117bc162cf16850e9]
F RM              [(Partial) Autocorrelation Function] [Identification an...] [2008-12-09 13:10:48] [8ac58ef7b35dc5a117bc162cf16850e9]
- RMP               [ARIMA Backward Selection] [ARIMA workshop IP] [2008-12-09 16:55:50] [74be16979710d4c4e7c6647856088456]
F RMP               [ARIMA Backward Selection] [Identification an...] [2008-12-09 17:00:28] [74be16979710d4c4e7c6647856088456]
F                     [ARIMA Backward Selection] [step 5 ip] [2008-12-09 18:09:34] [74be16979710d4c4e7c6647856088456]
F   P               [(Partial) Autocorrelation Function] [step 4 ip] [2008-12-09 18:08:11] [74be16979710d4c4e7c6647856088456]
F   P             [Spectral Analysis] [step 2 cp ip] [2008-12-09 18:07:03] [74be16979710d4c4e7c6647856088456]
F   P           [(Partial) Autocorrelation Function] [step 2 acf1 ip] [2008-12-09 18:05:59] [74be16979710d4c4e7c6647856088456]
Feedback Forum
2008-12-15 15:34:45 [Jessica Alves Pires] [reply] 
Goede conclusie. Je hebt de juiste waarden voor d en D gevonden. Je had hier misschien ook iets kunnen zeggen over de getrimde variantie.
2008-12-15 21:53:20 [Jonas Janssens] [reply] 
Juiste berekeningen.
Je gebruikt deze methode om te identificeren welke differentiaties nodig zijn om de tijdreeks stationair te maken.
2008-12-16 16:39:50 [c00776cbed2786c9c4960950021bd861] [reply] 
Je moest inderdaad naar de laagste variantie zoeken, zo kan je de d en D vinden.
Je moet ook controleren of de getrimde variantie bij deze d en D ook het kleinste is. Want deze variantie is betrouwbaarder.
2008-12-16 19:39:49 [Kevin Vermeiren] [reply] 
De student geeft hier een zeer beperkt antwoord. Het klopt wel wat de student als conclusie weergeeft namelijk dat d=0 en D=1. Hier wordt niets over de methode zelf verteld. Er moet gezocht worden naar de variantie met de kleinste waarde, hoe kleiner deze waarde, hoe meer het model verklaart. Hier had nog vermeld kunnen worden waarom dit zo is. De reden hiervoor is dat de variantie het risico, de volatiliteit van de tijdreeks weergeeft. Ook had de student kunnen vermelden of al dan niet sprake is van outliers. Indien dit het geval zou zijn zou er gewerkt moeten worden met de getrimde waarden ten einde een betrouwbaarder beeld te bekomen.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
110.40
96.40
101.90
106.20
81.00
94.70
101.00
109.40
102.30
90.70
96.20
96.10
106.00
103.10
102.00
104.70
86.00
92.10
106.90
112.60
101.70
92.00
97.40
97.00
105.40
102.70
98.10
104.50
87.40
89.90
109.80
111.70
98.60
96.90
95.10
97.00
112.70
102.90
97.40
111.40
87.40
96.80
114.10
110.30
103.90
101.60
94.60
95.90
104.70
102.80
98.10
113.90
80.90
95.70
113.20
105.90
108.80
102.30
99.00
100.70
115.50

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31353&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31353&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31353&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'George Udny Yule' @ 72.249.76.132






Variance Reduction Matrix
V(Y[t],d=0,D=0)65.3014316939891Range34.6Trim Var.35.5192760180996
V(Y[t],d=1,D=0)124.666720338983Range52.9Trim Var.76.1226275331936
V(Y[t],d=2,D=0)317.433477498539Range96.6Trim Var.169.309760522496
V(Y[t],d=3,D=0)945.515680580762Range165.9Trim Var.479.238533182504
V(Y[t],d=0,D=1)14.6942517006803Range18.8Trim Var.8.77081949058693
V(Y[t],d=1,D=1)28.342695035461Range20.1Trim Var.21.0229558652729
V(Y[t],d=2,D=1)85.3747086031453Range33.8Trim Var.62.184512195122
V(Y[t],d=3,D=1)276.149067632850Range57.5000000000001Trim Var.205.121820512821
V(Y[t],d=0,D=2)35.1497297297297Range34.1Trim Var.16.5804734848485
V(Y[t],d=1,D=2)46.0717142857143Range29.2Trim Var.29.1047983870968
V(Y[t],d=2,D=2)123.685764705882Range47.3999999999999Trim Var.78.8750322580646
V(Y[t],d=3,D=2)394.048493761141Range83Trim Var.247.805068965518

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 65.3014316939891 & Range & 34.6 & Trim Var. & 35.5192760180996 \tabularnewline
V(Y[t],d=1,D=0) & 124.666720338983 & Range & 52.9 & Trim Var. & 76.1226275331936 \tabularnewline
V(Y[t],d=2,D=0) & 317.433477498539 & Range & 96.6 & Trim Var. & 169.309760522496 \tabularnewline
V(Y[t],d=3,D=0) & 945.515680580762 & Range & 165.9 & Trim Var. & 479.238533182504 \tabularnewline
V(Y[t],d=0,D=1) & 14.6942517006803 & Range & 18.8 & Trim Var. & 8.77081949058693 \tabularnewline
V(Y[t],d=1,D=1) & 28.342695035461 & Range & 20.1 & Trim Var. & 21.0229558652729 \tabularnewline
V(Y[t],d=2,D=1) & 85.3747086031453 & Range & 33.8 & Trim Var. & 62.184512195122 \tabularnewline
V(Y[t],d=3,D=1) & 276.149067632850 & Range & 57.5000000000001 & Trim Var. & 205.121820512821 \tabularnewline
V(Y[t],d=0,D=2) & 35.1497297297297 & Range & 34.1 & Trim Var. & 16.5804734848485 \tabularnewline
V(Y[t],d=1,D=2) & 46.0717142857143 & Range & 29.2 & Trim Var. & 29.1047983870968 \tabularnewline
V(Y[t],d=2,D=2) & 123.685764705882 & Range & 47.3999999999999 & Trim Var. & 78.8750322580646 \tabularnewline
V(Y[t],d=3,D=2) & 394.048493761141 & Range & 83 & Trim Var. & 247.805068965518 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31353&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]65.3014316939891[/C][C]Range[/C][C]34.6[/C][C]Trim Var.[/C][C]35.5192760180996[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]124.666720338983[/C][C]Range[/C][C]52.9[/C][C]Trim Var.[/C][C]76.1226275331936[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]317.433477498539[/C][C]Range[/C][C]96.6[/C][C]Trim Var.[/C][C]169.309760522496[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]945.515680580762[/C][C]Range[/C][C]165.9[/C][C]Trim Var.[/C][C]479.238533182504[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]14.6942517006803[/C][C]Range[/C][C]18.8[/C][C]Trim Var.[/C][C]8.77081949058693[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]28.342695035461[/C][C]Range[/C][C]20.1[/C][C]Trim Var.[/C][C]21.0229558652729[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]85.3747086031453[/C][C]Range[/C][C]33.8[/C][C]Trim Var.[/C][C]62.184512195122[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]276.149067632850[/C][C]Range[/C][C]57.5000000000001[/C][C]Trim Var.[/C][C]205.121820512821[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]35.1497297297297[/C][C]Range[/C][C]34.1[/C][C]Trim Var.[/C][C]16.5804734848485[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]46.0717142857143[/C][C]Range[/C][C]29.2[/C][C]Trim Var.[/C][C]29.1047983870968[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]123.685764705882[/C][C]Range[/C][C]47.3999999999999[/C][C]Trim Var.[/C][C]78.8750322580646[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]394.048493761141[/C][C]Range[/C][C]83[/C][C]Trim Var.[/C][C]247.805068965518[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31353&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31353&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)65.3014316939891Range34.6Trim Var.35.5192760180996
V(Y[t],d=1,D=0)124.666720338983Range52.9Trim Var.76.1226275331936
V(Y[t],d=2,D=0)317.433477498539Range96.6Trim Var.169.309760522496
V(Y[t],d=3,D=0)945.515680580762Range165.9Trim Var.479.238533182504
V(Y[t],d=0,D=1)14.6942517006803Range18.8Trim Var.8.77081949058693
V(Y[t],d=1,D=1)28.342695035461Range20.1Trim Var.21.0229558652729
V(Y[t],d=2,D=1)85.3747086031453Range33.8Trim Var.62.184512195122
V(Y[t],d=3,D=1)276.149067632850Range57.5000000000001Trim Var.205.121820512821
V(Y[t],d=0,D=2)35.1497297297297Range34.1Trim Var.16.5804734848485
V(Y[t],d=1,D=2)46.0717142857143Range29.2Trim Var.29.1047983870968
V(Y[t],d=2,D=2)123.685764705882Range47.3999999999999Trim Var.78.8750322580646
V(Y[t],d=3,D=2)394.048493761141Range83Trim Var.247.805068965518


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 0 ; par9 = 0 ;
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')