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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 computationMon, 08 Dec 2008 11:29:56 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/08/t122876104015lzpb6uk9hqklr.htm/, Retrieved Thu, 16 May 2024 13:41:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30653, Retrieved Thu, 16 May 2024 13:41:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact191

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Run sequence plot...] [2008-12-02 22:19:27] [ed2ba3b6182103c15c0ab511ae4e6284]
- RMPD  [Standard Deviation-Mean Plot] [SD mean plot] [2008-12-06 11:49:39] [ed2ba3b6182103c15c0ab511ae4e6284]
F RM      [Variance Reduction Matrix] [variance reduction] [2008-12-06 12:44:59] [ed2ba3b6182103c15c0ab511ae4e6284]
F    D        [Variance Reduction Matrix] [VRM Vlaanderen] [2008-12-08 18:29:56] [3817f5e632a8bfeb1be7b5e8c86bd450] [Current]
Feedback Forum
2008-12-15 08:22:12 [Glenn De Maeyer] [reply] 
Als we kijken naar de berekeningen en de gebruikte software loste ik step 2 goed op. Enkel de verklaringen zijn te beknopt. Daarom loste ik de taak hier opnieuw op maar dan met unemployment data.

Variance reduction matrix

http://www.freestatistics.org/blog/index.php?v=date/2008/Dec/15/t12293281189uokrv2hf06li3f.htm

We noteren de kleinste waarde 795.483036989776 waar d = 1 en D = 1, dit wil zeggen dat we één maal gewoon en één maal seizonaal moeten differentiëren om de datareeks stationair te maken.


Autocorrelation function

http://www.freestatistics.org/blog/index.php?v=date/2008/Dec/15/t1229328245riclpjxysffnhqp.htm

Wanneer we de grafiek analyseren merken we duidelijk een lange termijn trend op. Deze werken we weg door de parameters correct aan te passen.

We voeren dus nu in de software de correcte waarden in. (Lambda= 0,5, d=1, D=1 lags=60)

http://www.freestatistics.org/blog/index.php?v=date/2008/Dec/15/t1229328575r41j4a7qfnzz9pi.htm

Op deze grafiek is de trend verdwenen. We vermoeden trouwens een conjunctuur, we vermoeden dus een AR proces.

Cumulative periodogram

http://www.freestatistics.org/blog/index.php?v=date/2008/Dec/15/t12293289767j1xpvxsk8gnjgi.htm

We merken hier een afwijking op naar boven toe. Dit wijst er op dat er sprake is van een AR proces. AR is een goed proces wanneer we conjunctuur vermoeden.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12300.00
12092.80
12380.80
12196.90
9455.00
13168.00
13427.90
11980.50
11884.80
11691.70
12233.80
14341.40
13130.70
12421.10
14285.80
12864.60
11160.20
14316.20
14388.70
14013.90
13419.00
12769.60
13315.50
15332.90
14243.00
13824.40
14962.90
13202.90
12199.00
15508.90
14199.80
15169.60
14058.00
13786.20
14147.90
16541.70
13587.50
15582.40
15802.80
14130.50
12923.20
15612.20
16033.70
16036.60
14037.80
15330.60
15038.30
17401.80
14992.50
16043.70
16929.60
15921.30
14417.20
15961.00
17851.90
16483.90
14215.50
17429.70
17839.50
17629.20

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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=30653&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=30653&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30653&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132






Variance Reduction Matrix
V(Y[t],d=0,D=0)3266717.22620057Range8396.9Trim Var.2195746.37298393
V(Y[t],d=1,D=0)2609348.68158387Range6667.2Trim Var.1817456.76176343
V(Y[t],d=2,D=0)7245770.43095281Range11802.9Trim Var.4784037.57545626
V(Y[t],d=3,D=0)22394890.3811905Range20205.1Trim Var.15048042.4697490
V(Y[t],d=0,D=1)1783241.43201957Range6136.4Trim Var.1180150.45189716
V(Y[t],d=1,D=1)3642866.68785196Range7454.5Trim Var.2554885.56722479
V(Y[t],d=2,D=1)8681423.28342006Range14096.2Trim Var.5208368.97895652
V(Y[t],d=3,D=1)22470918.570149Range19951.2Trim Var.14939420.8402828
V(Y[t],d=0,D=2)6116828.39047872Range10262.7Trim Var.4282079.96149245
V(Y[t],d=1,D=2)12081013.019963Range13337.5Trim Var.8270536.06639024
V(Y[t],d=2,D=2)27959082.6296039Range23161.1Trim Var.17004690.5404103
V(Y[t],d=3,D=2)71098367.1397273Range33357.8Trim Var.46203418.8307827

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 3266717.22620057 & Range & 8396.9 & Trim Var. & 2195746.37298393 \tabularnewline
V(Y[t],d=1,D=0) & 2609348.68158387 & Range & 6667.2 & Trim Var. & 1817456.76176343 \tabularnewline
V(Y[t],d=2,D=0) & 7245770.43095281 & Range & 11802.9 & Trim Var. & 4784037.57545626 \tabularnewline
V(Y[t],d=3,D=0) & 22394890.3811905 & Range & 20205.1 & Trim Var. & 15048042.4697490 \tabularnewline
V(Y[t],d=0,D=1) & 1783241.43201957 & Range & 6136.4 & Trim Var. & 1180150.45189716 \tabularnewline
V(Y[t],d=1,D=1) & 3642866.68785196 & Range & 7454.5 & Trim Var. & 2554885.56722479 \tabularnewline
V(Y[t],d=2,D=1) & 8681423.28342006 & Range & 14096.2 & Trim Var. & 5208368.97895652 \tabularnewline
V(Y[t],d=3,D=1) & 22470918.570149 & Range & 19951.2 & Trim Var. & 14939420.8402828 \tabularnewline
V(Y[t],d=0,D=2) & 6116828.39047872 & Range & 10262.7 & Trim Var. & 4282079.96149245 \tabularnewline
V(Y[t],d=1,D=2) & 12081013.019963 & Range & 13337.5 & Trim Var. & 8270536.06639024 \tabularnewline
V(Y[t],d=2,D=2) & 27959082.6296039 & Range & 23161.1 & Trim Var. & 17004690.5404103 \tabularnewline
V(Y[t],d=3,D=2) & 71098367.1397273 & Range & 33357.8 & Trim Var. & 46203418.8307827 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30653&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]3266717.22620057[/C][C]Range[/C][C]8396.9[/C][C]Trim Var.[/C][C]2195746.37298393[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]2609348.68158387[/C][C]Range[/C][C]6667.2[/C][C]Trim Var.[/C][C]1817456.76176343[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]7245770.43095281[/C][C]Range[/C][C]11802.9[/C][C]Trim Var.[/C][C]4784037.57545626[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]22394890.3811905[/C][C]Range[/C][C]20205.1[/C][C]Trim Var.[/C][C]15048042.4697490[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]1783241.43201957[/C][C]Range[/C][C]6136.4[/C][C]Trim Var.[/C][C]1180150.45189716[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]3642866.68785196[/C][C]Range[/C][C]7454.5[/C][C]Trim Var.[/C][C]2554885.56722479[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]8681423.28342006[/C][C]Range[/C][C]14096.2[/C][C]Trim Var.[/C][C]5208368.97895652[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]22470918.570149[/C][C]Range[/C][C]19951.2[/C][C]Trim Var.[/C][C]14939420.8402828[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]6116828.39047872[/C][C]Range[/C][C]10262.7[/C][C]Trim Var.[/C][C]4282079.96149245[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]12081013.019963[/C][C]Range[/C][C]13337.5[/C][C]Trim Var.[/C][C]8270536.06639024[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]27959082.6296039[/C][C]Range[/C][C]23161.1[/C][C]Trim Var.[/C][C]17004690.5404103[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]71098367.1397273[/C][C]Range[/C][C]33357.8[/C][C]Trim Var.[/C][C]46203418.8307827[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30653&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30653&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
V(Y[t],d=0,D=0)3266717.22620057Range8396.9Trim Var.2195746.37298393
V(Y[t],d=1,D=0)2609348.68158387Range6667.2Trim Var.1817456.76176343
V(Y[t],d=2,D=0)7245770.43095281Range11802.9Trim Var.4784037.57545626
V(Y[t],d=3,D=0)22394890.3811905Range20205.1Trim Var.15048042.4697490
V(Y[t],d=0,D=1)1783241.43201957Range6136.4Trim Var.1180150.45189716
V(Y[t],d=1,D=1)3642866.68785196Range7454.5Trim Var.2554885.56722479
V(Y[t],d=2,D=1)8681423.28342006Range14096.2Trim Var.5208368.97895652
V(Y[t],d=3,D=1)22470918.570149Range19951.2Trim Var.14939420.8402828
V(Y[t],d=0,D=2)6116828.39047872Range10262.7Trim Var.4282079.96149245
V(Y[t],d=1,D=2)12081013.019963Range13337.5Trim Var.8270536.06639024
V(Y[t],d=2,D=2)27959082.6296039Range23161.1Trim Var.17004690.5404103
V(Y[t],d=3,D=2)71098367.1397273Range33357.8Trim Var.46203418.8307827


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 6 ;
Parameters (R input):
par1 = 6 ;
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')