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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 computationSat, 10 Dec 2016 14:09:37 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/10/t1481375551eib1zx5tlnmg2da.htm/, Retrieved Mon, 06 May 2024 07:13:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298678, Retrieved Mon, 06 May 2024 07:13:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67

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] [Variantie Reducti...] [2016-12-10 13:09:37] [6fe662842930c5949e61d44eeb8a265b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4419
4336
4214
4294
4650
4608
4650
4625
4739
5010
4808
4474
4527
4652
4677
4904
4851
4956
4819
4940
5217
5305
5265
5256
5671
5617
5811
5728
5629
5490
5605
4944
5555
5956
5872
5795
6033
6337
6396
6244
6200
6082
5866
5917
6134
6428
6187
6228
6269
6586
6223
6724
6294
6445
6163
6207
6816
6850
6439
6401
6913
6969
7064
6987
6882
6683
6530
6748
6773
7375
7208
6676
7167
7146
7193
7162
7145
6819
6702
6702
6782
7307
6818
6966
7012
7754
7462
7183
7165
7299
7103
6950
7506
7708
7693
7495
7955
8316
9230
8654
8307
7940
7509
7752
8310
8616
8358
8150
8664
8817
8927
8537
8497
8270
7658
8049
8365
8971
8854
8540
8878
9184
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time0 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298678&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]0 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298678&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298678&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R ServerBig Analytics Cloud Computing Center






Variance Reduction Matrix
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.
V(Y[t],d=0,D=0)1680860Range5016Trim Var.1214290
V(Y[t],d=1,D=0)91026.9Range1575Trim Var.54385.3
V(Y[t],d=2,D=0)195717Range2762Trim Var.107166
V(Y[t],d=3,D=0)571468Range4091Trim Var.304299
V(Y[t],d=0,D=1)117814Range2158Trim Var.58729
V(Y[t],d=1,D=1)112333Range2010Trim Var.61937.1
V(Y[t],d=2,D=1)331025Range3090Trim Var.194838
V(Y[t],d=3,D=1)1143030Range5472Trim Var.676023
V(Y[t],d=0,D=2)334857Range3570Trim Var.165464
V(Y[t],d=1,D=2)353369Range3555Trim Var.204096
V(Y[t],d=2,D=2)1068680Range4911Trim Var.646534
V(Y[t],d=3,D=2)3718140Range8991Trim Var.2296320

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
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. \tabularnewline
V(Y[t],d=0,D=0) & 1680860 & Range & 5016 & Trim Var. & 1214290 \tabularnewline
V(Y[t],d=1,D=0) & 91026.9 & Range & 1575 & Trim Var. & 54385.3 \tabularnewline
V(Y[t],d=2,D=0) & 195717 & Range & 2762 & Trim Var. & 107166 \tabularnewline
V(Y[t],d=3,D=0) & 571468 & Range & 4091 & Trim Var. & 304299 \tabularnewline
V(Y[t],d=0,D=1) & 117814 & Range & 2158 & Trim Var. & 58729 \tabularnewline
V(Y[t],d=1,D=1) & 112333 & Range & 2010 & Trim Var. & 61937.1 \tabularnewline
V(Y[t],d=2,D=1) & 331025 & Range & 3090 & Trim Var. & 194838 \tabularnewline
V(Y[t],d=3,D=1) & 1143030 & Range & 5472 & Trim Var. & 676023 \tabularnewline
V(Y[t],d=0,D=2) & 334857 & Range & 3570 & Trim Var. & 165464 \tabularnewline
V(Y[t],d=1,D=2) & 353369 & Range & 3555 & Trim Var. & 204096 \tabularnewline
V(Y[t],d=2,D=2) & 1068680 & Range & 4911 & Trim Var. & 646534 \tabularnewline
V(Y[t],d=3,D=2) & 3718140 & Range & 8991 & Trim Var. & 2296320 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298678&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]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.[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]1680860[/C][C]Range[/C][C]5016[/C][C]Trim Var.[/C][C]1214290[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]91026.9[/C][C]Range[/C][C]1575[/C][C]Trim Var.[/C][C]54385.3[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]195717[/C][C]Range[/C][C]2762[/C][C]Trim Var.[/C][C]107166[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]571468[/C][C]Range[/C][C]4091[/C][C]Trim Var.[/C][C]304299[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]117814[/C][C]Range[/C][C]2158[/C][C]Trim Var.[/C][C]58729[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]112333[/C][C]Range[/C][C]2010[/C][C]Trim Var.[/C][C]61937.1[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]331025[/C][C]Range[/C][C]3090[/C][C]Trim Var.[/C][C]194838[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]1143030[/C][C]Range[/C][C]5472[/C][C]Trim Var.[/C][C]676023[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]334857[/C][C]Range[/C][C]3570[/C][C]Trim Var.[/C][C]165464[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]353369[/C][C]Range[/C][C]3555[/C][C]Trim Var.[/C][C]204096[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]1068680[/C][C]Range[/C][C]4911[/C][C]Trim Var.[/C][C]646534[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]3718140[/C][C]Range[/C][C]8991[/C][C]Trim Var.[/C][C]2296320[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298678&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298678&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
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.
V(Y[t],d=0,D=0)1680860Range5016Trim Var.1214290
V(Y[t],d=1,D=0)91026.9Range1575Trim Var.54385.3
V(Y[t],d=2,D=0)195717Range2762Trim Var.107166
V(Y[t],d=3,D=0)571468Range4091Trim Var.304299
V(Y[t],d=0,D=1)117814Range2158Trim Var.58729
V(Y[t],d=1,D=1)112333Range2010Trim Var.61937.1
V(Y[t],d=2,D=1)331025Range3090Trim Var.194838
V(Y[t],d=3,D=1)1143030Range5472Trim Var.676023
V(Y[t],d=0,D=2)334857Range3570Trim Var.165464
V(Y[t],d=1,D=2)353369Range3555Trim Var.204096
V(Y[t],d=2,D=2)1068680Range4911Trim Var.646534
V(Y[t],d=3,D=2)3718140Range8991Trim Var.2296320


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()