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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 14:09:55 +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/t14813754868bxpzkl6lsebtfy.htm/, Retrieved Mon, 06 May 2024 06:34:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298677, Retrieved Mon, 06 May 2024 06:34:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74

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] [N2440 Variance re...] [2016-12-10 13:09:55] [1eb03b74c4069f30e782d39ada1a3213] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3744.5
4098.5
4094
4083
4081.5
4227.5
4246.5
4468
4418.5
4508.5
4836.5
4797
4798.5
4933
4793.5
5020
4987
4738
4784.5
4721.5
4756.5
4666
4535.5
4347
4272
4152
4096.5
4193.5
4244.5
4415.5
4365
4280
4288.5
4289
4166
4179.5
4389.5
4577.5
4322.5
4075.5
3785
3740.5
3755
3795.5
3698
3678.5
3760.5
3892
3844
3831
3957.5
3995
4150
4388
4416
4533.5
4789.5
5160.5
5041
5151.5
5334
5631.5
5620.5
5690
5713
5715.5
5881
6028.5
6018.5
6343
6347
6450.5
6337
6354
6246.5
6520.5
6618.5
6593.5
6481.5
6357
6274
5939
5825.5
5755.5
5764
5668
5760
5801
5814
5726
5668
5489.5
5498
5619.5
5630
5496.5
5318.5
5142.5
5097.5
5021
4989
5008.5
5011.5
5026.5
5080
4979
5133
5143.5
5062.5
5190.5
5116.5
5129
5057.5
5085
5140
5251.5

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=298677&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=298677&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298677&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)632593Range2940Trim Var.478800
V(Y[t],d=1,D=0)18420.9Range706Trim Var.10273.3
V(Y[t],d=2,D=0)27684.8Range872Trim Var.16099.6
V(Y[t],d=3,D=0)78571.5Range1375.5Trim Var.47968.4
V(Y[t],d=0,D=1)589044Range2668Trim Var.454433
V(Y[t],d=1,D=1)43291.2Range1116Trim Var.25396
V(Y[t],d=2,D=1)61379.9Range1174.5Trim Var.37771
V(Y[t],d=3,D=1)163389Range1981.5Trim Var.104736
V(Y[t],d=0,D=2)1106230Range4541Trim Var.761263
V(Y[t],d=1,D=2)134239Range1795Trim Var.85946.6
V(Y[t],d=2,D=2)192161Range2120.5Trim Var.116584
V(Y[t],d=3,D=2)488181Range3157Trim Var.323182

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 632593 & Range & 2940 & Trim Var. & 478800 \tabularnewline
V(Y[t],d=1,D=0) & 18420.9 & Range & 706 & Trim Var. & 10273.3 \tabularnewline
V(Y[t],d=2,D=0) & 27684.8 & Range & 872 & Trim Var. & 16099.6 \tabularnewline
V(Y[t],d=3,D=0) & 78571.5 & Range & 1375.5 & Trim Var. & 47968.4 \tabularnewline
V(Y[t],d=0,D=1) & 589044 & Range & 2668 & Trim Var. & 454433 \tabularnewline
V(Y[t],d=1,D=1) & 43291.2 & Range & 1116 & Trim Var. & 25396 \tabularnewline
V(Y[t],d=2,D=1) & 61379.9 & Range & 1174.5 & Trim Var. & 37771 \tabularnewline
V(Y[t],d=3,D=1) & 163389 & Range & 1981.5 & Trim Var. & 104736 \tabularnewline
V(Y[t],d=0,D=2) & 1106230 & Range & 4541 & Trim Var. & 761263 \tabularnewline
V(Y[t],d=1,D=2) & 134239 & Range & 1795 & Trim Var. & 85946.6 \tabularnewline
V(Y[t],d=2,D=2) & 192161 & Range & 2120.5 & Trim Var. & 116584 \tabularnewline
V(Y[t],d=3,D=2) & 488181 & Range & 3157 & Trim Var. & 323182 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298677&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]632593[/C][C]Range[/C][C]2940[/C][C]Trim Var.[/C][C]478800[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]18420.9[/C][C]Range[/C][C]706[/C][C]Trim Var.[/C][C]10273.3[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]27684.8[/C][C]Range[/C][C]872[/C][C]Trim Var.[/C][C]16099.6[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]78571.5[/C][C]Range[/C][C]1375.5[/C][C]Trim Var.[/C][C]47968.4[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]589044[/C][C]Range[/C][C]2668[/C][C]Trim Var.[/C][C]454433[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]43291.2[/C][C]Range[/C][C]1116[/C][C]Trim Var.[/C][C]25396[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]61379.9[/C][C]Range[/C][C]1174.5[/C][C]Trim Var.[/C][C]37771[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]163389[/C][C]Range[/C][C]1981.5[/C][C]Trim Var.[/C][C]104736[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]1106230[/C][C]Range[/C][C]4541[/C][C]Trim Var.[/C][C]761263[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]134239[/C][C]Range[/C][C]1795[/C][C]Trim Var.[/C][C]85946.6[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]192161[/C][C]Range[/C][C]2120.5[/C][C]Trim Var.[/C][C]116584[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]488181[/C][C]Range[/C][C]3157[/C][C]Trim Var.[/C][C]323182[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298677&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298677&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)632593Range2940Trim Var.478800
V(Y[t],d=1,D=0)18420.9Range706Trim Var.10273.3
V(Y[t],d=2,D=0)27684.8Range872Trim Var.16099.6
V(Y[t],d=3,D=0)78571.5Range1375.5Trim Var.47968.4
V(Y[t],d=0,D=1)589044Range2668Trim Var.454433
V(Y[t],d=1,D=1)43291.2Range1116Trim Var.25396
V(Y[t],d=2,D=1)61379.9Range1174.5Trim Var.37771
V(Y[t],d=3,D=1)163389Range1981.5Trim Var.104736
V(Y[t],d=0,D=2)1106230Range4541Trim Var.761263
V(Y[t],d=1,D=2)134239Range1795Trim Var.85946.6
V(Y[t],d=2,D=2)192161Range2120.5Trim Var.116584
V(Y[t],d=3,D=2)488181Range3157Trim Var.323182


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()