Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

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, 02 Dec 2008 13:44:40 -0700

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/2008/Dec/02/t1228250725lg6sznp3xc0wkcw.htm/, Retrieved Sun, 19 May 2024 10:50:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28423, Retrieved Sun, 19 May 2024 10:50:04 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

non stationary time series VRM

Estimated Impact

204

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

F     [Law of Averages] [Random Walk Simul...] [2008-11-25 18:31:28] [b98453cac15ba1066b407e146608df68]
F RM D  [(Partial) Autocorrelation Function] [non stationary ti...] [2008-12-02 20:37:52] [47f64d63202c1921bd27f3073f07a153]
F    D    [(Partial) Autocorrelation Function] [non stationary ti...] [2008-12-02 20:40:11] [47f64d63202c1921bd27f3073f07a153]
-           [(Partial) Autocorrelation Function] [non stationary ti...] [2008-12-02 20:41:59] [47f64d63202c1921bd27f3073f07a153]
F RM            [Variance Reduction Matrix] [non stationary ti...] [2008-12-02 20:44:40] [74c7506a1ea162af3aa8be25bcd05d28] [Current]
F RM              [Spectral Analysis] [non stationary ti...] [2008-12-02 20:47:05] [47f64d63202c1921bd27f3073f07a153] 
F                   [Spectral Analysis] [non stationary ti...] [2008-12-02 20:48:32] [47f64d63202c1921bd27f3073f07a153] 
-                     [Spectral Analysis] [non stationary ti...] [2008-12-02 20:50:22] [47f64d63202c1921bd27f3073f07a153] 
-   P                   [Spectral Analysis] [non stat time ser...] [2008-12-03 12:45:11] [c96f3dce3a823a83b6ede18389e1cfd4] 
F   P                     [Spectral Analysis] [non stat time ser...] [2008-12-03 13:14:38] [c96f3dce3a823a83b6ede18389e1cfd4] 
F   P                       [Spectral Analysis] [non stat time ser...] [2008-12-03 13:17:56] [c96f3dce3a823a83b6ede18389e1cfd4] 
F                             [Spectral Analysis] [ARMA processing Q...] [2008-12-09 09:14:41] [c96f3dce3a823a83b6ede18389e1cfd4] 
F   P                           [Spectral Analysis] [ARMA processing Q...] [2008-12-09 16:01:38] [c96f3dce3a823a83b6ede18389e1cfd4] 
F RMP                           [ARIMA Backward Selection] [ARMA processing Q...] [2008-12-09 16:04:21] [c96f3dce3a823a83b6ede18389e1cfd4] 
F   P                   [Spectral Analysis] [non stationary ti...] [2008-12-03 13:15:10] [47f64d63202c1921bd27f3073f07a153] 
F   P                     [Spectral Analysis] [non stationary ti...] [2008-12-03 13:18:22] [47f64d63202c1921bd27f3073f07a153] 
-   P                       [Spectral Analysis] [ARMA proces WS5 Q...] [2008-12-08 20:37:02] [47f64d63202c1921bd27f3073f07a153] 
F   P                         [Spectral Analysis] [arma processen WS...] [2008-12-09 16:12:33] [47f64d63202c1921bd27f3073f07a153] 
F   P                 [Spectral Analysis] [non stat time ser...] [2008-12-03 12:43:05] [c96f3dce3a823a83b6ede18389e1cfd4] 
-   P               [Spectral Analysis] [non stat time ser...] [2008-12-03 12:41:24] [c96f3dce3a823a83b6ede18389e1cfd4] 
F   P             [Variance Reduction Matrix] [non stat time ser...] [2008-12-03 12:39:20] [c96f3dce3a823a83b6ede18389e1cfd4] 
F   P             [Variance Reduction Matrix] [ARMA proces WS5 Q...] [2008-12-08 20:31:01] [47f64d63202c1921bd27f3073f07a153] 
F RMP               [(Partial) Autocorrelation Function] [arma processen WS...] [2008-12-09 15:55:54] [47f64d63202c1921bd27f3073f07a153] 
F RMP                 [Spectral Analysis] [arma processen WS...] [2008-12-09 16:01:45] [47f64d63202c1921bd27f3073f07a153] 
F   P                 [(Partial) Autocorrelation Function] [arma processen WS...] [2008-12-09 16:10:15] [47f64d63202c1921bd27f3073f07a153] 

Feedback Forum

2008-12-08 17:42:10 [6066575aa30c0611e452e930b1dff53d] [reply] 
Men had eventueel kunnen vermelden dat als men een tijdreeks wil voorspellen, dat de variantie dan het risico voorstelt dat in de tijdreeks zit. We trachten dus de variantie zo klein mogelijk te maken. De kleinste variantie is  0.0757909343200741(bij d=2 en D=1). Dit is dus bij 2 keer differentiëren en 1 keer seizoenaal differentiëren. We vinden dus hetzelfde resultaat als bij de autocorrelatie. 

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

8.4
8.4
8.4
8.6
8.9
8.8
8.3
7.5
7.2
7.5
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.6
8.2
8.1
8
8.6
8.7
8.8
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8.1
8.2
8.1
8.1
7.9
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.6
6.2
6.2
6.8
6.9
6.8

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	'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28423&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28423&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28423&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	'George Udny Yule' @ 72.249.76.132

Variance Reduction Matrix
V(Y[t],d=0,D=0)	0.55675956284153	Range	3.1	Trim Var.	0.304753401360544
V(Y[t],d=1,D=0)	0.101649717514124	Range	2.1	Trim Var.	0.0363197586726998
V(Y[t],d=2,D=0)	0.12947983635301	Range	1.8	Trim Var.	0.072564705882353
V(Y[t],d=3,D=0)	0.270163339382940	Range	2.8	Trim Var.	0.134328808446456
V(Y[t],d=0,D=1)	0.308333333333333	Range	2.4	Trim Var.	0.179623477297896
V(Y[t],d=1,D=1)	0.0775487588652483	Range	1.2	Trim Var.	0.0382307692307692
V(Y[t],d=2,D=1)	0.0757909343200741	Range	1.2	Trim Var.	0.0438397435897437
V(Y[t],d=3,D=1)	0.160425120772947	Range	1.5	Trim Var.	0.0981987179487183
V(Y[t],d=0,D=2)	0.248693693693694	Range	2.3	Trim Var.	0.155587121212121
V(Y[t],d=1,D=2)	0.129230158730159	Range	1.50000000000000	Trim Var.	0.0761290322580644
V(Y[t],d=2,D=2)	0.151042016806723	Range	1.70000000000000	Trim Var.	0.0849462365591397
V(Y[t],d=3,D=2)	0.411203208556149	Range	2.59999999999999	Trim Var.	0.235402298850575

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.55675956284153 & Range & 3.1 & Trim Var. & 0.304753401360544 \tabularnewline
V(Y[t],d=1,D=0) & 0.101649717514124 & Range & 2.1 & Trim Var. & 0.0363197586726998 \tabularnewline
V(Y[t],d=2,D=0) & 0.12947983635301 & Range & 1.8 & Trim Var. & 0.072564705882353 \tabularnewline
V(Y[t],d=3,D=0) & 0.270163339382940 & Range & 2.8 & Trim Var. & 0.134328808446456 \tabularnewline
V(Y[t],d=0,D=1) & 0.308333333333333 & Range & 2.4 & Trim Var. & 0.179623477297896 \tabularnewline
V(Y[t],d=1,D=1) & 0.0775487588652483 & Range & 1.2 & Trim Var. & 0.0382307692307692 \tabularnewline
V(Y[t],d=2,D=1) & 0.0757909343200741 & Range & 1.2 & Trim Var. & 0.0438397435897437 \tabularnewline
V(Y[t],d=3,D=1) & 0.160425120772947 & Range & 1.5 & Trim Var. & 0.0981987179487183 \tabularnewline
V(Y[t],d=0,D=2) & 0.248693693693694 & Range & 2.3 & Trim Var. & 0.155587121212121 \tabularnewline
V(Y[t],d=1,D=2) & 0.129230158730159 & Range & 1.50000000000000 & Trim Var. & 0.0761290322580644 \tabularnewline
V(Y[t],d=2,D=2) & 0.151042016806723 & Range & 1.70000000000000 & Trim Var. & 0.0849462365591397 \tabularnewline
V(Y[t],d=3,D=2) & 0.411203208556149 & Range & 2.59999999999999 & Trim Var. & 0.235402298850575 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28423&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.55675956284153[/C][C]Range[/C][C]3.1[/C][C]Trim Var.[/C][C]0.304753401360544[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.101649717514124[/C][C]Range[/C][C]2.1[/C][C]Trim Var.[/C][C]0.0363197586726998[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.12947983635301[/C][C]Range[/C][C]1.8[/C][C]Trim Var.[/C][C]0.072564705882353[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.270163339382940[/C][C]Range[/C][C]2.8[/C][C]Trim Var.[/C][C]0.134328808446456[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.308333333333333[/C][C]Range[/C][C]2.4[/C][C]Trim Var.[/C][C]0.179623477297896[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.0775487588652483[/C][C]Range[/C][C]1.2[/C][C]Trim Var.[/C][C]0.0382307692307692[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.0757909343200741[/C][C]Range[/C][C]1.2[/C][C]Trim Var.[/C][C]0.0438397435897437[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]0.160425120772947[/C][C]Range[/C][C]1.5[/C][C]Trim Var.[/C][C]0.0981987179487183[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]0.248693693693694[/C][C]Range[/C][C]2.3[/C][C]Trim Var.[/C][C]0.155587121212121[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.129230158730159[/C][C]Range[/C][C]1.50000000000000[/C][C]Trim Var.[/C][C]0.0761290322580644[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.151042016806723[/C][C]Range[/C][C]1.70000000000000[/C][C]Trim Var.[/C][C]0.0849462365591397[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]0.411203208556149[/C][C]Range[/C][C]2.59999999999999[/C][C]Trim Var.[/C][C]0.235402298850575[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28423&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28423&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)	0.55675956284153	Range	3.1	Trim Var.	0.304753401360544
V(Y[t],d=1,D=0)	0.101649717514124	Range	2.1	Trim Var.	0.0363197586726998
V(Y[t],d=2,D=0)	0.12947983635301	Range	1.8	Trim Var.	0.072564705882353
V(Y[t],d=3,D=0)	0.270163339382940	Range	2.8	Trim Var.	0.134328808446456
V(Y[t],d=0,D=1)	0.308333333333333	Range	2.4	Trim Var.	0.179623477297896
V(Y[t],d=1,D=1)	0.0775487588652483	Range	1.2	Trim Var.	0.0382307692307692
V(Y[t],d=2,D=1)	0.0757909343200741	Range	1.2	Trim Var.	0.0438397435897437
V(Y[t],d=3,D=1)	0.160425120772947	Range	1.5	Trim Var.	0.0981987179487183
V(Y[t],d=0,D=2)	0.248693693693694	Range	2.3	Trim Var.	0.155587121212121
V(Y[t],d=1,D=2)	0.129230158730159	Range	1.50000000000000	Trim Var.	0.0761290322580644
V(Y[t],d=2,D=2)	0.151042016806723	Range	1.70000000000000	Trim Var.	0.0849462365591397
V(Y[t],d=3,D=2)	0.411203208556149	Range	2.59999999999999	Trim Var.	0.235402298850575

Parameters (Session):

par1 = 500 ; par2 = 0.5 ;

Parameters (R input):

par1 = 12 ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
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)
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(x,lag=1,differences=smalld)
if (bigd > 0) myx <- diff(myx,lag=par1,differences=bigd)
a<-table.element(a,var(myx))
a<-table.element(a,'Range',header=TRUE)
a<-table.element(a,max(myx)-min(myx))
a<-table.element(a,'Trim Var.',header=TRUE)
smyx <- sort(myx)
sn <- length(smyx)
a<-table.element(a,var(smyx[smyx>quantile(smyx,0.05) & smyxa<-table.row.end(a)
}
}
a<-table.end(a)
table.save(a,file='mytable.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code