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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

Sun, 18 Dec 2016 13:57:56 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/18/t1482065999ywpds6jv6jjfd4q.htm/, Retrieved Fri, 21 Feb 2025 18:23:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301051, Retrieved Fri, 21 Feb 2025 18:23:57 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

123

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

-     [Exponential Smoothing] [] [2016-12-18 12:31:12] [683f400e1b95307fc738e729f07c4fce]
- RM D    [Variance Reduction Matrix] [] [2016-12-18 12:57:56] [404ac5ee4f7301873f6a96ef36861981] [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	0 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 time0 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301051&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]

0 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301051&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301051&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	0 seconds
R Server	Big Analytics Cloud Computing Center

Variance Reduction Matrix
V(Y[t],d=0,D=0)	237116	Range	1700	Trim Var.	184224
V(Y[t],d=1,D=0)	2350.98	Range	295	Trim Var.	1339.13
V(Y[t],d=2,D=0)	3006.51	Range	295	Trim Var.	1446.23
V(Y[t],d=3,D=0)	7992.63	Range	490	Trim Var.	4170.06
V(Y[t],d=0,D=1)	93596	Range	1190	Trim Var.	64049.1
V(Y[t],d=1,D=1)	4190.09	Range	305	Trim Var.	2398.3
V(Y[t],d=2,D=1)	6957.45	Range	425	Trim Var.	3838.64
V(Y[t],d=3,D=1)	17895.2	Range	590	Trim Var.	11028.5
V(Y[t],d=0,D=2)	40518.5	Range	1010	Trim Var.	27315.1
V(Y[t],d=1,D=2)	13902	Range	575	Trim Var.	8914.54
V(Y[t],d=2,D=2)	23263.2	Range	735	Trim Var.	14284.8
V(Y[t],d=3,D=2)	59616.3	Range	1005	Trim Var.	40405.3

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 237116 & Range & 1700 & Trim Var. & 184224 \tabularnewline
V(Y[t],d=1,D=0) & 2350.98 & Range & 295 & Trim Var. & 1339.13 \tabularnewline
V(Y[t],d=2,D=0) & 3006.51 & Range & 295 & Trim Var. & 1446.23 \tabularnewline
V(Y[t],d=3,D=0) & 7992.63 & Range & 490 & Trim Var. & 4170.06 \tabularnewline
V(Y[t],d=0,D=1) & 93596 & Range & 1190 & Trim Var. & 64049.1 \tabularnewline
V(Y[t],d=1,D=1) & 4190.09 & Range & 305 & Trim Var. & 2398.3 \tabularnewline
V(Y[t],d=2,D=1) & 6957.45 & Range & 425 & Trim Var. & 3838.64 \tabularnewline
V(Y[t],d=3,D=1) & 17895.2 & Range & 590 & Trim Var. & 11028.5 \tabularnewline
V(Y[t],d=0,D=2) & 40518.5 & Range & 1010 & Trim Var. & 27315.1 \tabularnewline
V(Y[t],d=1,D=2) & 13902 & Range & 575 & Trim Var. & 8914.54 \tabularnewline
V(Y[t],d=2,D=2) & 23263.2 & Range & 735 & Trim Var. & 14284.8 \tabularnewline
V(Y[t],d=3,D=2) & 59616.3 & Range & 1005 & Trim Var. & 40405.3 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301051&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]237116[/C][C]Range[/C][C]1700[/C][C]Trim Var.[/C][C]184224[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]2350.98[/C][C]Range[/C][C]295[/C][C]Trim Var.[/C][C]1339.13[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]3006.51[/C][C]Range[/C][C]295[/C][C]Trim Var.[/C][C]1446.23[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]7992.63[/C][C]Range[/C][C]490[/C][C]Trim Var.[/C][C]4170.06[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]93596[/C][C]Range[/C][C]1190[/C][C]Trim Var.[/C][C]64049.1[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]4190.09[/C][C]Range[/C][C]305[/C][C]Trim Var.[/C][C]2398.3[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]6957.45[/C][C]Range[/C][C]425[/C][C]Trim Var.[/C][C]3838.64[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]17895.2[/C][C]Range[/C][C]590[/C][C]Trim Var.[/C][C]11028.5[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]40518.5[/C][C]Range[/C][C]1010[/C][C]Trim Var.[/C][C]27315.1[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]13902[/C][C]Range[/C][C]575[/C][C]Trim Var.[/C][C]8914.54[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]23263.2[/C][C]Range[/C][C]735[/C][C]Trim Var.[/C][C]14284.8[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]59616.3[/C][C]Range[/C][C]1005[/C][C]Trim Var.[/C][C]40405.3[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301051&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301051&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)	237116	Range	1700	Trim Var.	184224
V(Y[t],d=1,D=0)	2350.98	Range	295	Trim Var.	1339.13
V(Y[t],d=2,D=0)	3006.51	Range	295	Trim Var.	1446.23
V(Y[t],d=3,D=0)	7992.63	Range	490	Trim Var.	4170.06
V(Y[t],d=0,D=1)	93596	Range	1190	Trim Var.	64049.1
V(Y[t],d=1,D=1)	4190.09	Range	305	Trim Var.	2398.3
V(Y[t],d=2,D=1)	6957.45	Range	425	Trim Var.	3838.64
V(Y[t],d=3,D=1)	17895.2	Range	590	Trim Var.	11028.5
V(Y[t],d=0,D=2)	40518.5	Range	1010	Trim Var.	27315.1
V(Y[t],d=1,D=2)	13902	Range	575	Trim Var.	8914.54
V(Y[t],d=2,D=2)	23263.2	Range	735	Trim Var.	14284.8
V(Y[t],d=3,D=2)	59616.3	Range	1005	Trim Var.	40405.3

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 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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