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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 13:55:56 +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/t1481374603uw9owy7641h1slx.htm/, Retrieved Mon, 06 May 2024 08:52:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298672, Retrieved Mon, 06 May 2024 08:52:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD    [Variance Reduction Matrix] [N2380 Variance re...] [2016-12-10 12:55:56] [1eb03b74c4069f30e782d39ada1a3213] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6353
6425
6428
6465
6447
6439
6498
6491
6485
6564
6577
6628
6571
6585
6657
6717
6799
6876
6916
6987
7029
7032
7030
7042
7084
7133
7164
7160
7139
7260
7262
7132
7171
6971
7069
7043
6975
6969
6979
6987
7005
7039
7039
7187
6998
6969
7086
7095
7285
7083
7151
7116
7149
7144
7128
7183
7140
7121
7154
7155
7166
7162
7145
7181
7300
7218
7289
7319
7406
7468
7450
7493
7542
7584
7647
7707
7819
7775
7871
7815
7843
7843
7814
7779
7745
7730
7740
7783
7743
7803
7823
7863
7962
8085
8091
8180
8214
8219
8143
8117
8048
8020
7972
7956
7879
7844
7915
7939
7850
7877
7835
7821
7838
7863
7841
7905

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298672&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298672&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298672&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 time1 seconds
R ServerBig Analytics Cloud Computing Center






Variance Reduction Matrix
V(Y[t],d=0,D=0)246575Range1866Trim Var.187316
V(Y[t],d=1,D=0)4048.45Range392Trim Var.1893.19
V(Y[t],d=2,D=0)9654.3Range690Trim Var.4021.29
V(Y[t],d=3,D=0)32290.1Range1235Trim Var.12070.1
V(Y[t],d=0,D=1)59591.4Range946Trim Var.43565.8
V(Y[t],d=1,D=1)8794.57Range506Trim Var.4571.44
V(Y[t],d=2,D=1)20335.4Range905Trim Var.9084.73
V(Y[t],d=3,D=1)68363.3Range1691Trim Var.27469
V(Y[t],d=0,D=2)137002Range1341Trim Var.106390
V(Y[t],d=1,D=2)26802.5Range916Trim Var.13248.8
V(Y[t],d=2,D=2)61860.1Range1535Trim Var.26175.2
V(Y[t],d=3,D=2)209890Range2671Trim Var.80852.1

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 246575 & Range & 1866 & Trim Var. & 187316 \tabularnewline
V(Y[t],d=1,D=0) & 4048.45 & Range & 392 & Trim Var. & 1893.19 \tabularnewline
V(Y[t],d=2,D=0) & 9654.3 & Range & 690 & Trim Var. & 4021.29 \tabularnewline
V(Y[t],d=3,D=0) & 32290.1 & Range & 1235 & Trim Var. & 12070.1 \tabularnewline
V(Y[t],d=0,D=1) & 59591.4 & Range & 946 & Trim Var. & 43565.8 \tabularnewline
V(Y[t],d=1,D=1) & 8794.57 & Range & 506 & Trim Var. & 4571.44 \tabularnewline
V(Y[t],d=2,D=1) & 20335.4 & Range & 905 & Trim Var. & 9084.73 \tabularnewline
V(Y[t],d=3,D=1) & 68363.3 & Range & 1691 & Trim Var. & 27469 \tabularnewline
V(Y[t],d=0,D=2) & 137002 & Range & 1341 & Trim Var. & 106390 \tabularnewline
V(Y[t],d=1,D=2) & 26802.5 & Range & 916 & Trim Var. & 13248.8 \tabularnewline
V(Y[t],d=2,D=2) & 61860.1 & Range & 1535 & Trim Var. & 26175.2 \tabularnewline
V(Y[t],d=3,D=2) & 209890 & Range & 2671 & Trim Var. & 80852.1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298672&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]246575[/C][C]Range[/C][C]1866[/C][C]Trim Var.[/C][C]187316[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]4048.45[/C][C]Range[/C][C]392[/C][C]Trim Var.[/C][C]1893.19[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]9654.3[/C][C]Range[/C][C]690[/C][C]Trim Var.[/C][C]4021.29[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]32290.1[/C][C]Range[/C][C]1235[/C][C]Trim Var.[/C][C]12070.1[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]59591.4[/C][C]Range[/C][C]946[/C][C]Trim Var.[/C][C]43565.8[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]8794.57[/C][C]Range[/C][C]506[/C][C]Trim Var.[/C][C]4571.44[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]20335.4[/C][C]Range[/C][C]905[/C][C]Trim Var.[/C][C]9084.73[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]68363.3[/C][C]Range[/C][C]1691[/C][C]Trim Var.[/C][C]27469[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]137002[/C][C]Range[/C][C]1341[/C][C]Trim Var.[/C][C]106390[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]26802.5[/C][C]Range[/C][C]916[/C][C]Trim Var.[/C][C]13248.8[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]61860.1[/C][C]Range[/C][C]1535[/C][C]Trim Var.[/C][C]26175.2[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]209890[/C][C]Range[/C][C]2671[/C][C]Trim Var.[/C][C]80852.1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298672&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298672&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)246575Range1866Trim Var.187316
V(Y[t],d=1,D=0)4048.45Range392Trim Var.1893.19
V(Y[t],d=2,D=0)9654.3Range690Trim Var.4021.29
V(Y[t],d=3,D=0)32290.1Range1235Trim Var.12070.1
V(Y[t],d=0,D=1)59591.4Range946Trim Var.43565.8
V(Y[t],d=1,D=1)8794.57Range506Trim Var.4571.44
V(Y[t],d=2,D=1)20335.4Range905Trim Var.9084.73
V(Y[t],d=3,D=1)68363.3Range1691Trim Var.27469
V(Y[t],d=0,D=2)137002Range1341Trim Var.106390
V(Y[t],d=1,D=2)26802.5Range916Trim Var.13248.8
V(Y[t],d=2,D=2)61860.1Range1535Trim Var.26175.2
V(Y[t],d=3,D=2)209890Range2671Trim Var.80852.1


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()