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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 computationWed, 21 Dec 2016 13:21:44 +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/21/t14823229290kjynus58iwt1mp.htm/, Retrieved Mon, 06 May 2024 17:09:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302216, Retrieved Mon, 06 May 2024 17:09:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65

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] [n1308...] [2016-12-21 12:21:44] [b7f10b15eba379294ac5bdad7f2e1205] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5570
5755
6316.67
6318.33
6548.33
6661.67
6051.67
6191.67
7070
7220
7010
6671.67
6668.33
6921.67
7086.67
7636.67
7840
7340
6868.33
6138.33
5413.33
5686.67
5266.67
5448.33
5208.33
5155
5413.33
5571.67
5245
5488.33
5376.67
5200
5173.33
5098.33
4498.33
4791.67
5351.67
4846.67
4473.33
4855
4775
4678.33
4618.33
4763.33
4665
4626.67
4820
4753.33
4960
5410
5711.67
5626.67
5413.33
5028.33
5080
4921.67
4810
4681.67
4580
4523.33
4510
4311.67
4230

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=302216&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=302216&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302216&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)846144Range3610Trim Var.575301
V(Y[t],d=1,D=0)104851Range1608.33Trim Var.54781.8
V(Y[t],d=2,D=0)177778Range2063.34Trim Var.97198.1
V(Y[t],d=3,D=0)472723Range3165.02Trim Var.287663
V(Y[t],d=0,D=1)952029Range3913.34Trim Var.668040
V(Y[t],d=1,D=1)236445Range2558.33Trim Var.132515
V(Y[t],d=2,D=1)439352Range2978.34Trim Var.251048
V(Y[t],d=3,D=1)1208720Range4520.01Trim Var.851357
V(Y[t],d=0,D=2)2710810Range6065.01Trim Var.1977910
V(Y[t],d=1,D=2)757822Range3904.99Trim Var.508431
V(Y[t],d=2,D=2)1403460Range5333.34Trim Var.901326
V(Y[t],d=3,D=2)3786540Range6926.69Trim Var.2870710

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 846144 & Range & 3610 & Trim Var. & 575301 \tabularnewline
V(Y[t],d=1,D=0) & 104851 & Range & 1608.33 & Trim Var. & 54781.8 \tabularnewline
V(Y[t],d=2,D=0) & 177778 & Range & 2063.34 & Trim Var. & 97198.1 \tabularnewline
V(Y[t],d=3,D=0) & 472723 & Range & 3165.02 & Trim Var. & 287663 \tabularnewline
V(Y[t],d=0,D=1) & 952029 & Range & 3913.34 & Trim Var. & 668040 \tabularnewline
V(Y[t],d=1,D=1) & 236445 & Range & 2558.33 & Trim Var. & 132515 \tabularnewline
V(Y[t],d=2,D=1) & 439352 & Range & 2978.34 & Trim Var. & 251048 \tabularnewline
V(Y[t],d=3,D=1) & 1208720 & Range & 4520.01 & Trim Var. & 851357 \tabularnewline
V(Y[t],d=0,D=2) & 2710810 & Range & 6065.01 & Trim Var. & 1977910 \tabularnewline
V(Y[t],d=1,D=2) & 757822 & Range & 3904.99 & Trim Var. & 508431 \tabularnewline
V(Y[t],d=2,D=2) & 1403460 & Range & 5333.34 & Trim Var. & 901326 \tabularnewline
V(Y[t],d=3,D=2) & 3786540 & Range & 6926.69 & Trim Var. & 2870710 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302216&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]846144[/C][C]Range[/C][C]3610[/C][C]Trim Var.[/C][C]575301[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]104851[/C][C]Range[/C][C]1608.33[/C][C]Trim Var.[/C][C]54781.8[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]177778[/C][C]Range[/C][C]2063.34[/C][C]Trim Var.[/C][C]97198.1[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]472723[/C][C]Range[/C][C]3165.02[/C][C]Trim Var.[/C][C]287663[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]952029[/C][C]Range[/C][C]3913.34[/C][C]Trim Var.[/C][C]668040[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]236445[/C][C]Range[/C][C]2558.33[/C][C]Trim Var.[/C][C]132515[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]439352[/C][C]Range[/C][C]2978.34[/C][C]Trim Var.[/C][C]251048[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]1208720[/C][C]Range[/C][C]4520.01[/C][C]Trim Var.[/C][C]851357[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]2710810[/C][C]Range[/C][C]6065.01[/C][C]Trim Var.[/C][C]1977910[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]757822[/C][C]Range[/C][C]3904.99[/C][C]Trim Var.[/C][C]508431[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]1403460[/C][C]Range[/C][C]5333.34[/C][C]Trim Var.[/C][C]901326[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]3786540[/C][C]Range[/C][C]6926.69[/C][C]Trim Var.[/C][C]2870710[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302216&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302216&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)846144Range3610Trim Var.575301
V(Y[t],d=1,D=0)104851Range1608.33Trim Var.54781.8
V(Y[t],d=2,D=0)177778Range2063.34Trim Var.97198.1
V(Y[t],d=3,D=0)472723Range3165.02Trim Var.287663
V(Y[t],d=0,D=1)952029Range3913.34Trim Var.668040
V(Y[t],d=1,D=1)236445Range2558.33Trim Var.132515
V(Y[t],d=2,D=1)439352Range2978.34Trim Var.251048
V(Y[t],d=3,D=1)1208720Range4520.01Trim Var.851357
V(Y[t],d=0,D=2)2710810Range6065.01Trim Var.1977910
V(Y[t],d=1,D=2)757822Range3904.99Trim Var.508431
V(Y[t],d=2,D=2)1403460Range5333.34Trim Var.901326
V(Y[t],d=3,D=2)3786540Range6926.69Trim Var.2870710


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()