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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 computationSun, 30 Nov 2008 12:49:42 -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/Nov/30/t1228074841h4y3a2j6m9ftzfn.htm/, Retrieved Sun, 19 May 2024 08:55:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26711, Retrieved Sun, 19 May 2024 08:55:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact150

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Law of Averages] [Random Walk Simul...] [2008-11-25 18:31:28] [b98453cac15ba1066b407e146608df68]
F RMPD    [Variance Reduction Matrix] [Q3] [2008-11-30 19:49:42] [6d5cd2fe15d123a10639b4bf141c23b5] [Current]
Feedback Forum
2008-12-05 10:08:38 [Ine Coremans] [reply] 
De student heeft de berekening zelf uitgevoerd en de seizoensperiode aangepast, dit was echter niet nodig, hij had gewoon op de link moeten klikken in de vraag en op reproduce moeten klikken en dan de tabel moeten analyseren. Dan had hij moeten kijken in de tabel naar de waarde met de kleinste variantie, en hieruit de d en D kunnen afleiden.
2008-12-07 17:27:38 [Elias Van Deun] [reply] 
De Variance Reduction Matrix is een techniek die de verschillende differentie waarden test. Daarbij wordt ook de variantie getoond. De reeks met de kleinste variantie is het meest stationair. In dit voorbeeld is het d=1 en D=0.

Om tot deze conclusie te komen had de student de seizoensperiode niet moeten aanpassen.
2008-12-08 19:02:20 [Jeroen Michel] [reply] 
De test die hier wordt gebruikt (VRM test), wordt gebruikt om de verschillende waarden die een reeks bevat te onderzoeken. Voorts wordt in een tabel weergegeven wat de varianties zijn bij de waarden d en D.

d = het aantal keer dat de reeks niet-seizoenaal gedifferentieerd is.
D = het aantal keer dat de reeks seizoenaal gedifferentieerd is.

Wanneer we de bijbehorende tabel bekijken bij deze output zien we dat de kleinste variantie bestaat bij d:1 en D:0.

Er moet dus een niet-seizoenale randam-walk getrokken worden om deze tijdreeks stationair te maken. Dit verklaart bovenstaand resultaat en de conclusie van de student.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
112
118
132
129
121
135
148
148
136
119
104
118
115
126
141
135
125
149
170
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158
133
114
140
145
150
178
163
172
178
199
199
184
162
146
166
171
180
193
181
183
218
230
242
209
191
172
194
196
196
236
235
229
243
264
272
237
211
180
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204
188
235
227
234
264
302
293
259
229
203
229
242
233
267
269
270
315
364
347
312
274
237
278
284
277
317
313
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374
413
405
355
306
271
306
315
301
356
348
355
422
465
467
404
347
305
336
340
318
362
348
363
435
491
505
404
359
310
337
360
342
406
396
420
472
548
559
463
407
362
405
417
391
419
461
472
535
622
606
508
461
390
432

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=26711&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=26711&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26711&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)14391.9172008547Range518Trim Var.9847.79429133858
V(Y[t],d=1,D=0)1139.35152171772Range188Trim Var.612.29533808274
V(Y[t],d=2,D=0)1588.47427829388Range228Trim Var.876.603936507937
V(Y[t],d=3,D=0)3719.00577507599Range327Trim Var.2090.46334906897
V(Y[t],d=0,D=1)1139.35152171772Range188Trim Var.612.29533808274
V(Y[t],d=1,D=1)1588.47427829388Range228Trim Var.876.603936507937
V(Y[t],d=2,D=1)3719.00577507599Range327Trim Var.2090.46334906897
V(Y[t],d=3,D=1)10948.9103802672Range543Trim Var.6705.59085714286
V(Y[t],d=0,D=2)1588.47427829388Range228Trim Var.876.603936507937
V(Y[t],d=1,D=2)3719.00577507599Range327Trim Var.2090.46334906897
V(Y[t],d=2,D=2)10948.9103802672Range543Trim Var.6705.59085714286
V(Y[t],d=3,D=2)35462.4106975289Range1018Trim Var.21524.7421935484

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 14391.9172008547 & Range & 518 & Trim Var. & 9847.79429133858 \tabularnewline
V(Y[t],d=1,D=0) & 1139.35152171772 & Range & 188 & Trim Var. & 612.29533808274 \tabularnewline
V(Y[t],d=2,D=0) & 1588.47427829388 & Range & 228 & Trim Var. & 876.603936507937 \tabularnewline
V(Y[t],d=3,D=0) & 3719.00577507599 & Range & 327 & Trim Var. & 2090.46334906897 \tabularnewline
V(Y[t],d=0,D=1) & 1139.35152171772 & Range & 188 & Trim Var. & 612.29533808274 \tabularnewline
V(Y[t],d=1,D=1) & 1588.47427829388 & Range & 228 & Trim Var. & 876.603936507937 \tabularnewline
V(Y[t],d=2,D=1) & 3719.00577507599 & Range & 327 & Trim Var. & 2090.46334906897 \tabularnewline
V(Y[t],d=3,D=1) & 10948.9103802672 & Range & 543 & Trim Var. & 6705.59085714286 \tabularnewline
V(Y[t],d=0,D=2) & 1588.47427829388 & Range & 228 & Trim Var. & 876.603936507937 \tabularnewline
V(Y[t],d=1,D=2) & 3719.00577507599 & Range & 327 & Trim Var. & 2090.46334906897 \tabularnewline
V(Y[t],d=2,D=2) & 10948.9103802672 & Range & 543 & Trim Var. & 6705.59085714286 \tabularnewline
V(Y[t],d=3,D=2) & 35462.4106975289 & Range & 1018 & Trim Var. & 21524.7421935484 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26711&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]14391.9172008547[/C][C]Range[/C][C]518[/C][C]Trim Var.[/C][C]9847.79429133858[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1139.35152171772[/C][C]Range[/C][C]188[/C][C]Trim Var.[/C][C]612.29533808274[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1588.47427829388[/C][C]Range[/C][C]228[/C][C]Trim Var.[/C][C]876.603936507937[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]3719.00577507599[/C][C]Range[/C][C]327[/C][C]Trim Var.[/C][C]2090.46334906897[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]1139.35152171772[/C][C]Range[/C][C]188[/C][C]Trim Var.[/C][C]612.29533808274[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1588.47427829388[/C][C]Range[/C][C]228[/C][C]Trim Var.[/C][C]876.603936507937[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]3719.00577507599[/C][C]Range[/C][C]327[/C][C]Trim Var.[/C][C]2090.46334906897[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]10948.9103802672[/C][C]Range[/C][C]543[/C][C]Trim Var.[/C][C]6705.59085714286[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]1588.47427829388[/C][C]Range[/C][C]228[/C][C]Trim Var.[/C][C]876.603936507937[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]3719.00577507599[/C][C]Range[/C][C]327[/C][C]Trim Var.[/C][C]2090.46334906897[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]10948.9103802672[/C][C]Range[/C][C]543[/C][C]Trim Var.[/C][C]6705.59085714286[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]35462.4106975289[/C][C]Range[/C][C]1018[/C][C]Trim Var.[/C][C]21524.7421935484[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26711&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26711&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)14391.9172008547Range518Trim Var.9847.79429133858
V(Y[t],d=1,D=0)1139.35152171772Range188Trim Var.612.29533808274
V(Y[t],d=2,D=0)1588.47427829388Range228Trim Var.876.603936507937
V(Y[t],d=3,D=0)3719.00577507599Range327Trim Var.2090.46334906897
V(Y[t],d=0,D=1)1139.35152171772Range188Trim Var.612.29533808274
V(Y[t],d=1,D=1)1588.47427829388Range228Trim Var.876.603936507937
V(Y[t],d=2,D=1)3719.00577507599Range327Trim Var.2090.46334906897
V(Y[t],d=3,D=1)10948.9103802672Range543Trim Var.6705.59085714286
V(Y[t],d=0,D=2)1588.47427829388Range228Trim Var.876.603936507937
V(Y[t],d=1,D=2)3719.00577507599Range327Trim Var.2090.46334906897
V(Y[t],d=2,D=2)10948.9103802672Range543Trim Var.6705.59085714286
V(Y[t],d=3,D=2)35462.4106975289Range1018Trim Var.21524.7421935484


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ;
Parameters (R input):
par1 = 1 ;
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')