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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_variancereduction.wasp
Title produced by softwareVariance Reduction Matrix
Date of computationSun, 18 Dec 2016 16:50:26 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/18/t14820762656txkjku99viek43.htm/, Retrieved Wed, 08 May 2024 22:55:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301151, Retrieved Wed, 08 May 2024 22:55:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Variance Reduction Matrix] [variantie reducti...] [2016-12-18 15:50:26] [33f2a624cfeb2efbc43d2c77b7c0dad6] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4870
4240
3800
3990
3290
4710
4210
4440
5040
5070
4900
4790
3890
3450
4080
3280
3130
3310
3860
4570
5110
4820
4250
4210
3610
3710
2760
2710
2710
3290
2670
3620
4440
3910
4610
3760
3460
3020
3360
2610
2670
2480
2610
3320
2800
3030
3740
3060
3040
2620
3190
2750
2630
3290
2430
2730
3690
2980
2590
3360
2370
2200
2330
2370
2200
2430
2400
2840
2870
3320
3090
2680
2420
2550
2420
2430
2330
2520
2630
2570
2800
2680
2430
2790
2420
2750
2350
2330
2290
2330
2490
2480
2760
2590
2950
2570
2960
2540
2400
2470
2390
2310
2470
2490
2510
2690
3060
2690
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R ServerBig 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=301151&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=301151&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301151&T=0

As an alternative you can also use a QR Code:  
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 Outputview raw output of R engine
Computing time0 seconds
R ServerBig Analytics Cloud Computing Center






Variance Reduction Matrix
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.
V(Y[t],d=0,D=0)619102Range2910Trim Var.429921
V(Y[t],d=1,D=0)217785Range2410Trim Var.125597
V(Y[t],d=2,D=0)564177Range4040Trim Var.328664
V(Y[t],d=3,D=0)1851790Range7050Trim Var.1073880
V(Y[t],d=0,D=1)233661Range2530Trim Var.137632
V(Y[t],d=1,D=1)405328Range3060Trim Var.245195
V(Y[t],d=2,D=1)1241880Range4970Trim Var.780269
V(Y[t],d=3,D=1)4171170Range9420Trim Var.2788890
V(Y[t],d=0,D=2)631152Range4240Trim Var.330128
V(Y[t],d=1,D=2)1367760Range5520Trim Var.782839
V(Y[t],d=2,D=2)4194580Range9030Trim Var.2475710
V(Y[t],d=3,D=2)13821900Range16490Trim Var.8905940

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
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. \tabularnewline
V(Y[t],d=0,D=0) & 619102 & Range & 2910 & Trim Var. & 429921 \tabularnewline
V(Y[t],d=1,D=0) & 217785 & Range & 2410 & Trim Var. & 125597 \tabularnewline
V(Y[t],d=2,D=0) & 564177 & Range & 4040 & Trim Var. & 328664 \tabularnewline
V(Y[t],d=3,D=0) & 1851790 & Range & 7050 & Trim Var. & 1073880 \tabularnewline
V(Y[t],d=0,D=1) & 233661 & Range & 2530 & Trim Var. & 137632 \tabularnewline
V(Y[t],d=1,D=1) & 405328 & Range & 3060 & Trim Var. & 245195 \tabularnewline
V(Y[t],d=2,D=1) & 1241880 & Range & 4970 & Trim Var. & 780269 \tabularnewline
V(Y[t],d=3,D=1) & 4171170 & Range & 9420 & Trim Var. & 2788890 \tabularnewline
V(Y[t],d=0,D=2) & 631152 & Range & 4240 & Trim Var. & 330128 \tabularnewline
V(Y[t],d=1,D=2) & 1367760 & Range & 5520 & Trim Var. & 782839 \tabularnewline
V(Y[t],d=2,D=2) & 4194580 & Range & 9030 & Trim Var. & 2475710 \tabularnewline
V(Y[t],d=3,D=2) & 13821900 & Range & 16490 & Trim Var. & 8905940 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301151&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]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.[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]619102[/C][C]Range[/C][C]2910[/C][C]Trim Var.[/C][C]429921[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]217785[/C][C]Range[/C][C]2410[/C][C]Trim Var.[/C][C]125597[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]564177[/C][C]Range[/C][C]4040[/C][C]Trim Var.[/C][C]328664[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]1851790[/C][C]Range[/C][C]7050[/C][C]Trim Var.[/C][C]1073880[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]233661[/C][C]Range[/C][C]2530[/C][C]Trim Var.[/C][C]137632[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]405328[/C][C]Range[/C][C]3060[/C][C]Trim Var.[/C][C]245195[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]1241880[/C][C]Range[/C][C]4970[/C][C]Trim Var.[/C][C]780269[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]4171170[/C][C]Range[/C][C]9420[/C][C]Trim Var.[/C][C]2788890[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]631152[/C][C]Range[/C][C]4240[/C][C]Trim Var.[/C][C]330128[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]1367760[/C][C]Range[/C][C]5520[/C][C]Trim Var.[/C][C]782839[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]4194580[/C][C]Range[/C][C]9030[/C][C]Trim Var.[/C][C]2475710[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]13821900[/C][C]Range[/C][C]16490[/C][C]Trim Var.[/C][C]8905940[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301151&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301151&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Variance Reduction Matrix
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.
V(Y[t],d=0,D=0)619102Range2910Trim Var.429921
V(Y[t],d=1,D=0)217785Range2410Trim Var.125597
V(Y[t],d=2,D=0)564177Range4040Trim Var.328664
V(Y[t],d=3,D=0)1851790Range7050Trim Var.1073880
V(Y[t],d=0,D=1)233661Range2530Trim Var.137632
V(Y[t],d=1,D=1)405328Range3060Trim Var.245195
V(Y[t],d=2,D=1)1241880Range4970Trim Var.780269
V(Y[t],d=3,D=1)4171170Range9420Trim Var.2788890
V(Y[t],d=0,D=2)631152Range4240Trim Var.330128
V(Y[t],d=1,D=2)1367760Range5520Trim Var.782839
V(Y[t],d=2,D=2)4194580Range9030Trim Var.2475710
V(Y[t],d=3,D=2)13821900Range16490Trim Var.8905940


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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()