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R Software Module

rwasp_variancereduction.wasp

Title produced by software

Variance Reduction Matrix

Date of computation

Wed, 24 Jan 2018 10:32:07 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2018/Jan/24/t1516786341okg2zpzfoukd5or.htm/, Retrieved Mon, 06 May 2024 10:18:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=312276, Retrieved Mon, 06 May 2024 10:18:40 +0000

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Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Variance Reduction Matrix] [variance reductio...] [2018-01-24 09:32:07] [1f2811b4b3eab344c60f6986921522b4] [Current]

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1.72923686058208
0.122433126801145
0.523768788982079
-0.50175942601324
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0.0717422351702872
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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	Big 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=312276&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]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=312276&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=312276&T=0

As an alternative you can also use a 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 Output	view raw output of R engine
Computing time	2 seconds
R Server	Big Analytics Cloud Computing Center

Variance Reduction Matrix
V(Y[t],d=0,D=0)	1.67896	Range	7.8743	Trim Var.	0.98386
V(Y[t],d=1,D=0)	3.50592	Range	9.78514	Trim Var.	2.18297
V(Y[t],d=2,D=0)	10.59	Range	18.3475	Trim Var.	6.4921
V(Y[t],d=3,D=0)	35.404	Range	33.1235	Trim Var.	21.9711
V(Y[t],d=0,D=1)	3.10523	Range	9.19837	Trim Var.	1.80129
V(Y[t],d=1,D=1)	6.42812	Range	14.4613	Trim Var.	4.18954
V(Y[t],d=2,D=1)	19.5682	Range	22.4996	Trim Var.	13.2642
V(Y[t],d=3,D=1)	65.8704	Range	37.6432	Trim Var.	44.8441
V(Y[t],d=0,D=2)	9.02429	Range	16.1259	Trim Var.	5.35095
V(Y[t],d=1,D=2)	18.8789	Range	23.8394	Trim Var.	12.242
V(Y[t],d=2,D=2)	56.8189	Range	42.6814	Trim Var.	39.0947
V(Y[t],d=3,D=2)	188.932	Range	69.4048	Trim Var.	130.032

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 1.67896 & Range & 7.8743 & Trim Var. & 0.98386 \tabularnewline
V(Y[t],d=1,D=0) & 3.50592 & Range & 9.78514 & Trim Var. & 2.18297 \tabularnewline
V(Y[t],d=2,D=0) & 10.59 & Range & 18.3475 & Trim Var. & 6.4921 \tabularnewline
V(Y[t],d=3,D=0) & 35.404 & Range & 33.1235 & Trim Var. & 21.9711 \tabularnewline
V(Y[t],d=0,D=1) & 3.10523 & Range & 9.19837 & Trim Var. & 1.80129 \tabularnewline
V(Y[t],d=1,D=1) & 6.42812 & Range & 14.4613 & Trim Var. & 4.18954 \tabularnewline
V(Y[t],d=2,D=1) & 19.5682 & Range & 22.4996 & Trim Var. & 13.2642 \tabularnewline
V(Y[t],d=3,D=1) & 65.8704 & Range & 37.6432 & Trim Var. & 44.8441 \tabularnewline
V(Y[t],d=0,D=2) & 9.02429 & Range & 16.1259 & Trim Var. & 5.35095 \tabularnewline
V(Y[t],d=1,D=2) & 18.8789 & Range & 23.8394 & Trim Var. & 12.242 \tabularnewline
V(Y[t],d=2,D=2) & 56.8189 & Range & 42.6814 & Trim Var. & 39.0947 \tabularnewline
V(Y[t],d=3,D=2) & 188.932 & Range & 69.4048 & Trim Var. & 130.032 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=312276&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]1.67896[/C][C]Range[/C][C]7.8743[/C][C]Trim Var.[/C][C]0.98386[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]3.50592[/C][C]Range[/C][C]9.78514[/C][C]Trim Var.[/C][C]2.18297[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]10.59[/C][C]Range[/C][C]18.3475[/C][C]Trim Var.[/C][C]6.4921[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]35.404[/C][C]Range[/C][C]33.1235[/C][C]Trim Var.[/C][C]21.9711[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]3.10523[/C][C]Range[/C][C]9.19837[/C][C]Trim Var.[/C][C]1.80129[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]6.42812[/C][C]Range[/C][C]14.4613[/C][C]Trim Var.[/C][C]4.18954[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]19.5682[/C][C]Range[/C][C]22.4996[/C][C]Trim Var.[/C][C]13.2642[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]65.8704[/C][C]Range[/C][C]37.6432[/C][C]Trim Var.[/C][C]44.8441[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]9.02429[/C][C]Range[/C][C]16.1259[/C][C]Trim Var.[/C][C]5.35095[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]18.8789[/C][C]Range[/C][C]23.8394[/C][C]Trim Var.[/C][C]12.242[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]56.8189[/C][C]Range[/C][C]42.6814[/C][C]Trim Var.[/C][C]39.0947[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]188.932[/C][C]Range[/C][C]69.4048[/C][C]Trim Var.[/C][C]130.032[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=312276&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=312276&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Variance Reduction Matrix
V(Y[t],d=0,D=0)	1.67896	Range	7.8743	Trim Var.	0.98386
V(Y[t],d=1,D=0)	3.50592	Range	9.78514	Trim Var.	2.18297
V(Y[t],d=2,D=0)	10.59	Range	18.3475	Trim Var.	6.4921
V(Y[t],d=3,D=0)	35.404	Range	33.1235	Trim Var.	21.9711
V(Y[t],d=0,D=1)	3.10523	Range	9.19837	Trim Var.	1.80129
V(Y[t],d=1,D=1)	6.42812	Range	14.4613	Trim Var.	4.18954
V(Y[t],d=2,D=1)	19.5682	Range	22.4996	Trim Var.	13.2642
V(Y[t],d=3,D=1)	65.8704	Range	37.6432	Trim Var.	44.8441
V(Y[t],d=0,D=2)	9.02429	Range	16.1259	Trim Var.	5.35095
V(Y[t],d=1,D=2)	18.8789	Range	23.8394	Trim Var.	12.242
V(Y[t],d=2,D=2)	56.8189	Range	42.6814	Trim Var.	39.0947
V(Y[t],d=3,D=2)	188.932	Range	69.4048	Trim Var.	130.032

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

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()

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code