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Author

*The author of this computation has been verified*

R Software Module

rwasp_variancereduction.wasp

Title produced by software

Variance Reduction Matrix

Date of computation

Tue, 29 Nov 2016 21:55:29 +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/2016/Nov/29/t1480453213x68pyu4d2jc9w7u.htm/, Retrieved Tue, 07 May 2024 06:48:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297291, Retrieved Tue, 07 May 2024 06:48:06 +0000

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Estimated Impact

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] [VRM times series ...] [2016-11-29 20:55:29] [fd005a509166a1985dac46f39e8d81c5] [Current]

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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	1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297291&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=297291&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297291&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	1 seconds
R Server	Big Analytics Cloud Computing Center

Variance Reduction Matrix
V(Y[t],d=0,D=0)	329967	Range	2012	Trim Var.	257497
V(Y[t],d=1,D=0)	23947	Range	474	Trim Var.	21161.6
V(Y[t],d=2,D=0)	47185.9	Range	726	Trim Var.	38037.9
V(Y[t],d=3,D=0)	96494.8	Range	1032	Trim Var.	82802.7
V(Y[t],d=0,D=1)	8417.95	Range	366	Trim Var.	5284.78
V(Y[t],d=1,D=1)	1935.97	Range	256	Trim Var.	449.457
V(Y[t],d=2,D=1)	4369.38	Range	452	Trim Var.	788.657
V(Y[t],d=3,D=1)	11461	Range	750	Trim Var.	2027.64
V(Y[t],d=0,D=2)	7369.03	Range	310	Trim Var.	5345.5
V(Y[t],d=1,D=2)	3699.72	Range	296	Trim Var.	1360.41
V(Y[t],d=2,D=2)	7519.66	Range	482	Trim Var.	2175.78
V(Y[t],d=3,D=2)	18961.9	Range	760	Trim Var.	6211.91

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 329967 & Range & 2012 & Trim Var. & 257497 \tabularnewline
V(Y[t],d=1,D=0) & 23947 & Range & 474 & Trim Var. & 21161.6 \tabularnewline
V(Y[t],d=2,D=0) & 47185.9 & Range & 726 & Trim Var. & 38037.9 \tabularnewline
V(Y[t],d=3,D=0) & 96494.8 & Range & 1032 & Trim Var. & 82802.7 \tabularnewline
V(Y[t],d=0,D=1) & 8417.95 & Range & 366 & Trim Var. & 5284.78 \tabularnewline
V(Y[t],d=1,D=1) & 1935.97 & Range & 256 & Trim Var. & 449.457 \tabularnewline
V(Y[t],d=2,D=1) & 4369.38 & Range & 452 & Trim Var. & 788.657 \tabularnewline
V(Y[t],d=3,D=1) & 11461 & Range & 750 & Trim Var. & 2027.64 \tabularnewline
V(Y[t],d=0,D=2) & 7369.03 & Range & 310 & Trim Var. & 5345.5 \tabularnewline
V(Y[t],d=1,D=2) & 3699.72 & Range & 296 & Trim Var. & 1360.41 \tabularnewline
V(Y[t],d=2,D=2) & 7519.66 & Range & 482 & Trim Var. & 2175.78 \tabularnewline
V(Y[t],d=3,D=2) & 18961.9 & Range & 760 & Trim Var. & 6211.91 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297291&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]329967[/C][C]Range[/C][C]2012[/C][C]Trim Var.[/C][C]257497[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]23947[/C][C]Range[/C][C]474[/C][C]Trim Var.[/C][C]21161.6[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]47185.9[/C][C]Range[/C][C]726[/C][C]Trim Var.[/C][C]38037.9[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]96494.8[/C][C]Range[/C][C]1032[/C][C]Trim Var.[/C][C]82802.7[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]8417.95[/C][C]Range[/C][C]366[/C][C]Trim Var.[/C][C]5284.78[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1935.97[/C][C]Range[/C][C]256[/C][C]Trim Var.[/C][C]449.457[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]4369.38[/C][C]Range[/C][C]452[/C][C]Trim Var.[/C][C]788.657[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11461[/C][C]Range[/C][C]750[/C][C]Trim Var.[/C][C]2027.64[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]7369.03[/C][C]Range[/C][C]310[/C][C]Trim Var.[/C][C]5345.5[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]3699.72[/C][C]Range[/C][C]296[/C][C]Trim Var.[/C][C]1360.41[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]7519.66[/C][C]Range[/C][C]482[/C][C]Trim Var.[/C][C]2175.78[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]18961.9[/C][C]Range[/C][C]760[/C][C]Trim Var.[/C][C]6211.91[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297291&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297291&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)	329967	Range	2012	Trim Var.	257497
V(Y[t],d=1,D=0)	23947	Range	474	Trim Var.	21161.6
V(Y[t],d=2,D=0)	47185.9	Range	726	Trim Var.	38037.9
V(Y[t],d=3,D=0)	96494.8	Range	1032	Trim Var.	82802.7
V(Y[t],d=0,D=1)	8417.95	Range	366	Trim Var.	5284.78
V(Y[t],d=1,D=1)	1935.97	Range	256	Trim Var.	449.457
V(Y[t],d=2,D=1)	4369.38	Range	452	Trim Var.	788.657
V(Y[t],d=3,D=1)	11461	Range	750	Trim Var.	2027.64
V(Y[t],d=0,D=2)	7369.03	Range	310	Trim Var.	5345.5
V(Y[t],d=1,D=2)	3699.72	Range	296	Trim Var.	1360.41
V(Y[t],d=2,D=2)	7519.66	Range	482	Trim Var.	2175.78
V(Y[t],d=3,D=2)	18961.9	Range	760	Trim Var.	6211.91

Figure 1

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Parameters (Session):

par1 = additive ; par2 = 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()

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Input Parameters & R Code