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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 computationFri, 11 Dec 2015 10:14:40 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Dec/11/t1449828887vgxbg3lpeg5s4j4.htm/, Retrieved Thu, 16 May 2024 10:44:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285870, Retrieved Thu, 16 May 2024 10:44:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact111

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Variance Reduction Matrix] [] [2015-12-04 10:51:29] [0067001be1237c3bcd1f41c2117a7af9]
-    D    [Variance Reduction Matrix] [] [2015-12-11 10:14:40] [d108c84c57c191267df4a6d3f43a776a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
529
567
747
719
707
728
758
746
725
725
555
526
612
570
597
666
677
651
736
757
708
601
569
526
538
525
668
692
762
693
775
843
578
708
434
489
528
505
576
805
895
707
803
834
645
745
637
588
429
552
598
735
831
720
691
670
649
586
559
374
442
396
555
707
616
473
289
183
204
183
140
201
203
201
290
256
169
174
192
170
169
170
124
152
163
114
208
176
191
230
258
356
375
339
291
150
187
163
162
206
168
138
183
128
148
133
103
122
123
140
157
149
171
139
169
172
162
138
124
140
128
112
154
159
176
245
168
242
246
138
199
232
198
219
243
218
203
211
267
233
223
211
267
248
244
265
268
242
244
276
371

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285870&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285870&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285870&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 time0 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Variance Reduction Matrix
V(Y[t],d=0,D=0)56401.5Range792Trim Var.47490.5
V(Y[t],d=1,D=0)5966.74Range503Trim Var.2600.01
V(Y[t],d=2,D=0)13154.5Range799Trim Var.5401.26
V(Y[t],d=3,D=0)41155.7Range1532Trim Var.17323
V(Y[t],d=0,D=1)17778.4Range693Trim Var.8151.61
V(Y[t],d=1,D=1)8357.49Range488Trim Var.4609.86
V(Y[t],d=2,D=1)22414.1Range932Trim Var.11960.9
V(Y[t],d=3,D=1)74353.8Range1751Trim Var.37884.7
V(Y[t],d=0,D=2)36076.8Range923Trim Var.19936.5
V(Y[t],d=1,D=2)23979.7Range805Trim Var.12823.2
V(Y[t],d=2,D=2)66161.7Range1415Trim Var.34242
V(Y[t],d=3,D=2)220835Range2519Trim Var.104794

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 56401.5 & Range & 792 & Trim Var. & 47490.5 \tabularnewline
V(Y[t],d=1,D=0) & 5966.74 & Range & 503 & Trim Var. & 2600.01 \tabularnewline
V(Y[t],d=2,D=0) & 13154.5 & Range & 799 & Trim Var. & 5401.26 \tabularnewline
V(Y[t],d=3,D=0) & 41155.7 & Range & 1532 & Trim Var. & 17323 \tabularnewline
V(Y[t],d=0,D=1) & 17778.4 & Range & 693 & Trim Var. & 8151.61 \tabularnewline
V(Y[t],d=1,D=1) & 8357.49 & Range & 488 & Trim Var. & 4609.86 \tabularnewline
V(Y[t],d=2,D=1) & 22414.1 & Range & 932 & Trim Var. & 11960.9 \tabularnewline
V(Y[t],d=3,D=1) & 74353.8 & Range & 1751 & Trim Var. & 37884.7 \tabularnewline
V(Y[t],d=0,D=2) & 36076.8 & Range & 923 & Trim Var. & 19936.5 \tabularnewline
V(Y[t],d=1,D=2) & 23979.7 & Range & 805 & Trim Var. & 12823.2 \tabularnewline
V(Y[t],d=2,D=2) & 66161.7 & Range & 1415 & Trim Var. & 34242 \tabularnewline
V(Y[t],d=3,D=2) & 220835 & Range & 2519 & Trim Var. & 104794 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285870&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]56401.5[/C][C]Range[/C][C]792[/C][C]Trim Var.[/C][C]47490.5[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]5966.74[/C][C]Range[/C][C]503[/C][C]Trim Var.[/C][C]2600.01[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]13154.5[/C][C]Range[/C][C]799[/C][C]Trim Var.[/C][C]5401.26[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]41155.7[/C][C]Range[/C][C]1532[/C][C]Trim Var.[/C][C]17323[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]17778.4[/C][C]Range[/C][C]693[/C][C]Trim Var.[/C][C]8151.61[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]8357.49[/C][C]Range[/C][C]488[/C][C]Trim Var.[/C][C]4609.86[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]22414.1[/C][C]Range[/C][C]932[/C][C]Trim Var.[/C][C]11960.9[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]74353.8[/C][C]Range[/C][C]1751[/C][C]Trim Var.[/C][C]37884.7[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]36076.8[/C][C]Range[/C][C]923[/C][C]Trim Var.[/C][C]19936.5[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]23979.7[/C][C]Range[/C][C]805[/C][C]Trim Var.[/C][C]12823.2[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]66161.7[/C][C]Range[/C][C]1415[/C][C]Trim Var.[/C][C]34242[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]220835[/C][C]Range[/C][C]2519[/C][C]Trim Var.[/C][C]104794[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285870&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285870&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)56401.5Range792Trim Var.47490.5
V(Y[t],d=1,D=0)5966.74Range503Trim Var.2600.01
V(Y[t],d=2,D=0)13154.5Range799Trim Var.5401.26
V(Y[t],d=3,D=0)41155.7Range1532Trim Var.17323
V(Y[t],d=0,D=1)17778.4Range693Trim Var.8151.61
V(Y[t],d=1,D=1)8357.49Range488Trim Var.4609.86
V(Y[t],d=2,D=1)22414.1Range932Trim Var.11960.9
V(Y[t],d=3,D=1)74353.8Range1751Trim Var.37884.7
V(Y[t],d=0,D=2)36076.8Range923Trim Var.19936.5
V(Y[t],d=1,D=2)23979.7Range805Trim Var.12823.2
V(Y[t],d=2,D=2)66161.7Range1415Trim Var.34242
V(Y[t],d=3,D=2)220835Range2519Trim Var.104794


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.orig <- length(x)
x <- na.omit(x)
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)
if(n.orig!=n) {
a<-table.row.start(a)
a<-table.element(a,'Warning: NAs were removed from the time series! The results shown below will only be correct if the NAs are all located at the start and/or end of the time series.',6,F)
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(myx,lag=1,differences=smalld)
if (bigd > 0) myx <- diff(myx,lag=par1,differences=bigd)
a<-table.element(a,signif(var(myx), digits=6))
a<-table.element(a,'Range',header=TRUE)
a<-table.element(a,signif(max(myx)-min(myx), digits=6))
a<-table.element(a,'Trim Var.',header=TRUE)
smyx <- sort(myx)
sn <- length(smyx)
a<-table.element(a,signif(var(smyx[smyx>quantile(smyx,0.05) & smyxa<-table.row.end(a)
}
}
a<-table.end(a)
table.save(a,file='mytable.tab')
bitmap(file='pic0.png')
op <- par(mfrow=c(2,2))
plot(x,type='l',xlab='time',ylab='value',main='d=0, D=0')
plot(diff(x,lag=1,differences=1),type='l',xlab='time',ylab='value',main='d=1, D=0')
plot(diff(x,lag=par1,differences=1),type='l',xlab='time',ylab='value',main='d=0, D=1')
plot(diff(diff(x,lag=1,differences=1),lag=par1,differences=1),type='l',xlab='time',ylab='value',main='d=1, D=1')
par(op)
dev.off()