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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, 14 Dec 2014 22:41:14 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/14/t1418596884j6n84jzfss3urs2.htm/, Retrieved Thu, 31 Oct 2024 22:55:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=267923, Retrieved Thu, 31 Oct 2024 22:55:42 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [Variance Reduction Matrix] [] [2011-12-06 19:45:50] [b98453cac15ba1066b407e146608df68]
- RMP       [Variance Reduction Matrix] [] [2014-12-14 22:41:14] [6870495cd5e22452491bd29e9b20b7c8] [Current]
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Dataseries X:
655362
873127
1107897
1555964
1671159
1493308
2957796
2638691
1305669
1280496
921900
867888
652586
913831
1108544
1555827
1699283
1509458
3268975
2425016
1312703
1365498
934453
775019
651142
843192
1146766
1652601
1465906
1652734
2922334
2702805
1458956
1410363
1019279
936574
708917
885295
1099663
1576220
1487870
1488635
2882530
2677026
1404398
1344370
936865
872705
628151
953712
1160384
1400618
1661511
1495347
2918786
2775677
1407026
1370199
964526
850851
683118
847224
1073256
1514326
1503734
1507712
2865698
2788128
1391596
1366378
946295
859626




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\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 & 0 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267923&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267923&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267923&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Variance Reduction Matrix
V(Y[t],d=0,D=0)4.6824e+11Range2640820Trim Var.3.28076e+11
V(Y[t],d=1,D=0)3.84287e+11Range3156050Trim Var.1.6883e+11
V(Y[t],d=2,D=0)7.80672e+11Range4552820Trim Var.4.57771e+11
V(Y[t],d=3,D=0)2.17712e+12Range7243090Trim Var.1.19508e+12
V(Y[t],d=0,D=1)12196100000Range657820Trim Var.5567910000
V(Y[t],d=1,D=1)32668200000Range1149280Trim Var.11856100000
V(Y[t],d=2,D=1)1.12467e+11Range1980920Trim Var.41537100000
V(Y[t],d=3,D=1)4.05657e+11Range3851230Trim Var.1.57976e+11
V(Y[t],d=0,D=2)38817800000Range1149280Trim Var.18797700000
V(Y[t],d=1,D=2)1.04471e+11Range1934230Trim Var.38546500000
V(Y[t],d=2,D=2)3.64771e+11Range3435760Trim Var.1.34362e+11
V(Y[t],d=3,D=2)1.33072e+12Range6543560Trim Var.4.96505e+11

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 4.6824e+11 & Range & 2640820 & Trim Var. & 3.28076e+11 \tabularnewline
V(Y[t],d=1,D=0) & 3.84287e+11 & Range & 3156050 & Trim Var. & 1.6883e+11 \tabularnewline
V(Y[t],d=2,D=0) & 7.80672e+11 & Range & 4552820 & Trim Var. & 4.57771e+11 \tabularnewline
V(Y[t],d=3,D=0) & 2.17712e+12 & Range & 7243090 & Trim Var. & 1.19508e+12 \tabularnewline
V(Y[t],d=0,D=1) & 12196100000 & Range & 657820 & Trim Var. & 5567910000 \tabularnewline
V(Y[t],d=1,D=1) & 32668200000 & Range & 1149280 & Trim Var. & 11856100000 \tabularnewline
V(Y[t],d=2,D=1) & 1.12467e+11 & Range & 1980920 & Trim Var. & 41537100000 \tabularnewline
V(Y[t],d=3,D=1) & 4.05657e+11 & Range & 3851230 & Trim Var. & 1.57976e+11 \tabularnewline
V(Y[t],d=0,D=2) & 38817800000 & Range & 1149280 & Trim Var. & 18797700000 \tabularnewline
V(Y[t],d=1,D=2) & 1.04471e+11 & Range & 1934230 & Trim Var. & 38546500000 \tabularnewline
V(Y[t],d=2,D=2) & 3.64771e+11 & Range & 3435760 & Trim Var. & 1.34362e+11 \tabularnewline
V(Y[t],d=3,D=2) & 1.33072e+12 & Range & 6543560 & Trim Var. & 4.96505e+11 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267923&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]4.6824e+11[/C][C]Range[/C][C]2640820[/C][C]Trim Var.[/C][C]3.28076e+11[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]3.84287e+11[/C][C]Range[/C][C]3156050[/C][C]Trim Var.[/C][C]1.6883e+11[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]7.80672e+11[/C][C]Range[/C][C]4552820[/C][C]Trim Var.[/C][C]4.57771e+11[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]2.17712e+12[/C][C]Range[/C][C]7243090[/C][C]Trim Var.[/C][C]1.19508e+12[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12196100000[/C][C]Range[/C][C]657820[/C][C]Trim Var.[/C][C]5567910000[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]32668200000[/C][C]Range[/C][C]1149280[/C][C]Trim Var.[/C][C]11856100000[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]1.12467e+11[/C][C]Range[/C][C]1980920[/C][C]Trim Var.[/C][C]41537100000[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]4.05657e+11[/C][C]Range[/C][C]3851230[/C][C]Trim Var.[/C][C]1.57976e+11[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]38817800000[/C][C]Range[/C][C]1149280[/C][C]Trim Var.[/C][C]18797700000[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]1.04471e+11[/C][C]Range[/C][C]1934230[/C][C]Trim Var.[/C][C]38546500000[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]3.64771e+11[/C][C]Range[/C][C]3435760[/C][C]Trim Var.[/C][C]1.34362e+11[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]1.33072e+12[/C][C]Range[/C][C]6543560[/C][C]Trim Var.[/C][C]4.96505e+11[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267923&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267923&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)4.6824e+11Range2640820Trim Var.3.28076e+11
V(Y[t],d=1,D=0)3.84287e+11Range3156050Trim Var.1.6883e+11
V(Y[t],d=2,D=0)7.80672e+11Range4552820Trim Var.4.57771e+11
V(Y[t],d=3,D=0)2.17712e+12Range7243090Trim Var.1.19508e+12
V(Y[t],d=0,D=1)12196100000Range657820Trim Var.5567910000
V(Y[t],d=1,D=1)32668200000Range1149280Trim Var.11856100000
V(Y[t],d=2,D=1)1.12467e+11Range1980920Trim Var.41537100000
V(Y[t],d=3,D=1)4.05657e+11Range3851230Trim Var.1.57976e+11
V(Y[t],d=0,D=2)38817800000Range1149280Trim Var.18797700000
V(Y[t],d=1,D=2)1.04471e+11Range1934230Trim Var.38546500000
V(Y[t],d=2,D=2)3.64771e+11Range3435760Trim Var.1.34362e+11
V(Y[t],d=3,D=2)1.33072e+12Range6543560Trim Var.4.96505e+11



Parameters (Session):
par1 = 6 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 12 ;
R code (references can be found in the software module):
par1 <- '12'
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(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()