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Author's title

Author

*Unverified author*

R Software Module

rwasp_variancereduction.wasp

Title produced by software

Variance Reduction Matrix

Date of computation

Sun, 11 Feb 2018 05:39:46 +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/2018/Feb/11/t15183242557h7g2aksgr3owop.htm/, Retrieved Sun, 05 May 2024 16:16:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=314974, Retrieved Sun, 05 May 2024 16:16:20 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

131

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

-       [Variance Reduction Matrix] [wet comp fluctuat...] [2018-02-11 04:39:46] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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5.895469777
5.997666788
6.652787366
6.53629601
6.21971819
6.207510457
6.113605242
6.203989225
6.139667938
5.638265769
5.651774878
5.28598516
5.036362309
4.707204707
4.478278918
4.706594164
5.029827125
5.515461434
5.433237248
5.514600705
5.105197564
5.2923896
5.485631688
5.155105654
5.141067044
5.220602822
5.491259251
5.706626246
5.90059945
6.236021202
6.419699145
6.654331316
6.744032889
6.937454365
7.197700078
7.346288153
7.274908898
7.178979231
7.515291542
7.573211164
7.823759145
8.035666152
8.155118125
8.157872116
8.084436184
8.137069196
8.245613656
8.105688213
7.404773835
7.219714315
7.263525579
7.310073102
7.335847069
7.59287662
7.624829882
7.695153038
7.118308928
6.85031897
7.010709132
7.105654335
6.881475322
7.026132816
7.217004911
7.146186359
7.193631514
7.346460563
7.309030765
7.207683183
7.645844738
8.077163139
8.690196221
8.689169289
8.427231822
8.189968778
7.59590134
6.785433323
7.574348356
7.717538901
7.560839301
6.412039548
6.275627377
6.379274092
6.45844535
6.764022863
7.106365981
7.410545161
7.616164936
7.77827833
8.602322938
8.758083511
8.513460399
8.475588226
8.455316261
8.458517177
8.787520149
8.688826744
8.826226206
8.847910072
8.526987021
8.023091225
6.791731388
6.415837851
6.583586097
6.415542616
6.794993585
6.986537916
7.434223705
7.714065726
7.918804599
8.121458262
8.295803292
8.358190521
8.325710505
8.343724316
8.009434218
8.073583005
8.080102462
8.122438717
8.199115608
8.272326384
8.231846657
7.765215993
7.114714951
6.955567014
6.346092029
5.827750603
6.503422534
6.692910307
6.828707532
7.096290653
7.771786566
8.03452597
7.89081166
8.292218411
7.917709696

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 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 time5 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=314974&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]

5 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=314974&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=314974&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	5 seconds
R Server	Big Analytics Cloud Computing Center

Variance Reduction Matrix
V(Y[t],d=0,D=0)	12.9423	Range	13.9146	Trim Var.	10.5583
V(Y[t],d=1,D=0)	0.298601	Range	14.45	Trim Var.	0.0823765
V(Y[t],d=2,D=0)	0.534344	Range	13.9981	Trim Var.	0.155133
V(Y[t],d=3,D=0)	1.56795	Range	26.3966	Trim Var.	0.453789
V(Y[t],d=0,D=1)	3.29944	Range	21.986	Trim Var.	1.27899
V(Y[t],d=1,D=1)	0.651133	Range	22.0427	Trim Var.	0.227402
V(Y[t],d=2,D=1)	1.0593	Range	24.5008	Trim Var.	0.396293
V(Y[t],d=3,D=1)	3.09025	Range	40.7313	Trim Var.	1.16323
V(Y[t],d=0,D=2)	10.7057	Range	39.0881	Trim Var.	4.2347
V(Y[t],d=1,D=2)	2.06211	Range	42.2149	Trim Var.	0.750305
V(Y[t],d=2,D=2)	3.18755	Range	37.2623	Trim Var.	1.22694
V(Y[t],d=3,D=2)	9.29128	Range	66.8137	Trim Var.	3.60433

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 12.9423 & Range & 13.9146 & Trim Var. & 10.5583 \tabularnewline
V(Y[t],d=1,D=0) & 0.298601 & Range & 14.45 & Trim Var. & 0.0823765 \tabularnewline
V(Y[t],d=2,D=0) & 0.534344 & Range & 13.9981 & Trim Var. & 0.155133 \tabularnewline
V(Y[t],d=3,D=0) & 1.56795 & Range & 26.3966 & Trim Var. & 0.453789 \tabularnewline
V(Y[t],d=0,D=1) & 3.29944 & Range & 21.986 & Trim Var. & 1.27899 \tabularnewline
V(Y[t],d=1,D=1) & 0.651133 & Range & 22.0427 & Trim Var. & 0.227402 \tabularnewline
V(Y[t],d=2,D=1) & 1.0593 & Range & 24.5008 & Trim Var. & 0.396293 \tabularnewline
V(Y[t],d=3,D=1) & 3.09025 & Range & 40.7313 & Trim Var. & 1.16323 \tabularnewline
V(Y[t],d=0,D=2) & 10.7057 & Range & 39.0881 & Trim Var. & 4.2347 \tabularnewline
V(Y[t],d=1,D=2) & 2.06211 & Range & 42.2149 & Trim Var. & 0.750305 \tabularnewline
V(Y[t],d=2,D=2) & 3.18755 & Range & 37.2623 & Trim Var. & 1.22694 \tabularnewline
V(Y[t],d=3,D=2) & 9.29128 & Range & 66.8137 & Trim Var. & 3.60433 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=314974&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]12.9423[/C][C]Range[/C][C]13.9146[/C][C]Trim Var.[/C][C]10.5583[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.298601[/C][C]Range[/C][C]14.45[/C][C]Trim Var.[/C][C]0.0823765[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.534344[/C][C]Range[/C][C]13.9981[/C][C]Trim Var.[/C][C]0.155133[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]1.56795[/C][C]Range[/C][C]26.3966[/C][C]Trim Var.[/C][C]0.453789[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]3.29944[/C][C]Range[/C][C]21.986[/C][C]Trim Var.[/C][C]1.27899[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.651133[/C][C]Range[/C][C]22.0427[/C][C]Trim Var.[/C][C]0.227402[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]1.0593[/C][C]Range[/C][C]24.5008[/C][C]Trim Var.[/C][C]0.396293[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]3.09025[/C][C]Range[/C][C]40.7313[/C][C]Trim Var.[/C][C]1.16323[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]10.7057[/C][C]Range[/C][C]39.0881[/C][C]Trim Var.[/C][C]4.2347[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]2.06211[/C][C]Range[/C][C]42.2149[/C][C]Trim Var.[/C][C]0.750305[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]3.18755[/C][C]Range[/C][C]37.2623[/C][C]Trim Var.[/C][C]1.22694[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]9.29128[/C][C]Range[/C][C]66.8137[/C][C]Trim Var.[/C][C]3.60433[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=314974&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=314974&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)	12.9423	Range	13.9146	Trim Var.	10.5583
V(Y[t],d=1,D=0)	0.298601	Range	14.45	Trim Var.	0.0823765
V(Y[t],d=2,D=0)	0.534344	Range	13.9981	Trim Var.	0.155133
V(Y[t],d=3,D=0)	1.56795	Range	26.3966	Trim Var.	0.453789
V(Y[t],d=0,D=1)	3.29944	Range	21.986	Trim Var.	1.27899
V(Y[t],d=1,D=1)	0.651133	Range	22.0427	Trim Var.	0.227402
V(Y[t],d=2,D=1)	1.0593	Range	24.5008	Trim Var.	0.396293
V(Y[t],d=3,D=1)	3.09025	Range	40.7313	Trim Var.	1.16323
V(Y[t],d=0,D=2)	10.7057	Range	39.0881	Trim Var.	4.2347
V(Y[t],d=1,D=2)	2.06211	Range	42.2149	Trim Var.	0.750305
V(Y[t],d=2,D=2)	3.18755	Range	37.2623	Trim Var.	1.22694
V(Y[t],d=3,D=2)	9.29128	Range	66.8137	Trim Var.	3.60433

Figure 1

PNG link

Postscript link

PDF link

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()

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code