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Description of Statistical Computation

Author's title

Taak 10 Stap 2 Cumulatief Periodogram Aantal Inschrijvingen Nieuwe Wages me...

Author*The author of this computation has been verified*
R Software Modulerwasp_spectrum.wasp
Title produced by softwareSpectral Analysis
Date of computationThu, 04 Dec 2008 11:35:58 -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/04/t12284158131c161hackjv4ogt.htm/, Retrieved Sun, 19 May 2024 07:15:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29010, Retrieved Sun, 19 May 2024 07:15:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact227

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] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
F RMP   [Spectral Analysis] [] [2008-12-03 15:35:57] [819b576fab25b35cfda70f80599828ec]
F   P     [Spectral Analysis] [Taak 10 Stap 2 Cu...] [2008-12-03 15:43:09] [819b576fab25b35cfda70f80599828ec]
F   P       [Spectral Analysis] [Taak 10 stap 2 Cu...] [2008-12-03 15:48:19] [819b576fab25b35cfda70f80599828ec]
F   PD          [Spectral Analysis] [Taak 10 Stap 2 Cu...] [2008-12-04 18:35:58] [e08fee3874f3333d6b7a377a061b860d] [Current]
-   P             [Spectral Analysis] [Identification an...] [2008-12-08 19:28:10] [79c17183721a40a589db5f9f561947d8]
Feedback Forum
2008-12-14 12:01:37 [Jeroen Michel] [reply] 
Zoals de student stelt is er met voorgaande grafiek/berekening wel een gelijkaardig patroon op te tekenen, maar de LT-trend en seizoenaliteit zijn eruit gefilterd waardoor we kleinere treden opmerken op de grafiek.
2008-12-14 13:22:35 [Matthieu Blondeau] [reply] 
Ook hier heeft de student eerst berekent met d=0 en D=0 om daarna deze parameters aan te passen. Er is dan een trend te zien en in de Cumulative Periodogram valt de lijn buiten de betrouwbaarheidsinterval. Wanneer de student de waarden aanpast kan men in de Raw een geleidelijker verloop aflezen en in de Cumulative valt de lijn binnen de betrouwbaarheidsinterval maar er is nog altijd een trappend verloop.
2008-12-14 13:25:21 [Kevin Neelen] [reply] 
Uiteindelijk heeft de student de volgende gegevens ingevoerd: d = 1, D = 1 en Seasonal period = 12

We zien in principe weinig verschil met het cumulatief periodogram uit het model waarbij d = 1 en D = 0. De huidige grafiek ligt volledig binnen de stippellijnen, maar vertoont kleinere treden in zijn verloop dan de grafiek in het vorige model. Bij de Variance Reduction Matrix werd reeds tot de conclusie gekomen dat het model waarbij d = 1 en D = 1 het beste is.
2008-12-14 17:03:10 [Mehmet Yilmaz] [reply] 
De berekening en conclusies zijn correct.
2008-12-15 21:26:39 [Nilay Erdogdu] [reply] 
ok
2008-12-15 21:35:20 [Michael Van Spaandonck] [reply] 
In het model waarbij d = 0 en D = 0
http://www.freestatistics.org/blog/index.php?v=date/2008/Dec/04/t1228415508x9kon8guft3hlrd.htm
zien we dat de grafiek niet direct spectaculair omhoog schiet, maar iets verderop wel. We vermoeden dus toch een LT-trend die ongeveer 45% verklaart.
Ook vertoont de grafiek een trapsgewijs verloop, wat duidt op seizoensinvloeden.

In het model waarbij d = 1 en D = 0
http://www.freestatistics.org/blog/index.php?v=date/2008/Dec/04/t1228415672g7wpx7ngnqydbgz.htm
zien we dat het verloop nu volledig binnen de stippellijnen ligt, maar nog wel een trapsgewijs verloop (grote treden) vertoont, wat duidt op seizoensinvloeden.

We zien bij het huidige model in principe weinig verschil met het cumulatief periodogram uit het model waarbij d = 1 en D = 0. De huidige grafiek ligt volledig binnen de stippellijnen, maar vertoont kleinere treden in zijn verloop dan de grafiek in het vorige model.

Normaal gesproken zouden we door D te laten variëren moeten nagaan of de seizoensdifferentiatie nog verder doorgedreven moet worden, maar om de resterende autocorrelatie weg te werken kunnen ook de ARMA-modellen gebruikt worden. (Zie stap 4)
2008-12-15 21:38:40 [Michael Van Spaandonck] [reply] 
Algemene conclusie
De ideale differentiatie voor d is 1, net als voor D.
De vergelijking tot dusver: ▼▼12 Yt

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
58.972
59.249
63.955
53.785
52.760
44.795
37.348
32.370
32.717
40.974
33.591
21.124
58.608
46.865
51.378
46.235
47.206
45.382
41.227
33.795
31.295
42.625
33.625
21.538
56.421
53.152
53.536
52.408
41.454
38.271
35.306
26.414
31.917
38.030
27.534
18.387
50.556
43.901
48.572
43.899
37.532
40.357
35.489
29.027
34.485
42.598
30.306
26.451
47.460
50.104
61.465
53.726
39.477
43.895
31.481
29.896
33.842
39.120
33.702
25.094

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29010&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29010&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29010&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Raw Periodogram
ParameterValue
Box-Cox transformation parameter (lambda)1
Degree of non-seasonal differencing (d)1
Degree of seasonal differencing (D)1
Seasonal Period (s)12
Frequency (Period)Spectrum
0.0208 (48)0.323247
0.0417 (24)26.175666
0.0625 (16)2.881063
0.0833 (12)0.380139
0.1042 (9.6)2.505318
0.125 (8)57.285338
0.1458 (6.8571)6.92519
0.1667 (6)9.745845
0.1875 (5.3333)0.436757
0.2083 (4.8)67.290794
0.2292 (4.3636)1.245244
0.25 (4)18.59385
0.2708 (3.6923)6.420492
0.2917 (3.4286)6.951566
0.3125 (3.2)17.223419
0.3333 (3)53.257786
0.3542 (2.8235)90.67007
0.375 (2.6667)0.87525
0.3958 (2.5263)52.042462
0.4167 (2.4)9.340107
0.4375 (2.2857)7.909001
0.4583 (2.1818)98.7883
0.4792 (2.087)10.012686
0.5 (2)99.581888

\begin{tabular}{lllllllll}
\hline
Raw Periodogram \tabularnewline
Parameter & Value \tabularnewline
Box-Cox transformation parameter (lambda) & 1 \tabularnewline
Degree of non-seasonal differencing (d) & 1 \tabularnewline
Degree of seasonal differencing (D) & 1 \tabularnewline
Seasonal Period (s) & 12 \tabularnewline
Frequency (Period) & Spectrum \tabularnewline
0.0208 (48) & 0.323247 \tabularnewline
0.0417 (24) & 26.175666 \tabularnewline
0.0625 (16) & 2.881063 \tabularnewline
0.0833 (12) & 0.380139 \tabularnewline
0.1042 (9.6) & 2.505318 \tabularnewline
0.125 (8) & 57.285338 \tabularnewline
0.1458 (6.8571) & 6.92519 \tabularnewline
0.1667 (6) & 9.745845 \tabularnewline
0.1875 (5.3333) & 0.436757 \tabularnewline
0.2083 (4.8) & 67.290794 \tabularnewline
0.2292 (4.3636) & 1.245244 \tabularnewline
0.25 (4) & 18.59385 \tabularnewline
0.2708 (3.6923) & 6.420492 \tabularnewline
0.2917 (3.4286) & 6.951566 \tabularnewline
0.3125 (3.2) & 17.223419 \tabularnewline
0.3333 (3) & 53.257786 \tabularnewline
0.3542 (2.8235) & 90.67007 \tabularnewline
0.375 (2.6667) & 0.87525 \tabularnewline
0.3958 (2.5263) & 52.042462 \tabularnewline
0.4167 (2.4) & 9.340107 \tabularnewline
0.4375 (2.2857) & 7.909001 \tabularnewline
0.4583 (2.1818) & 98.7883 \tabularnewline
0.4792 (2.087) & 10.012686 \tabularnewline
0.5 (2) & 99.581888 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29010&T=1

[TABLE]
[ROW][C]Raw Periodogram[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]Box-Cox transformation parameter (lambda)[/C][C]1[/C][/ROW]
[ROW][C]Degree of non-seasonal differencing (d)[/C][C]1[/C][/ROW]
[ROW][C]Degree of seasonal differencing (D)[/C][C]1[/C][/ROW]
[ROW][C]Seasonal Period (s)[/C][C]12[/C][/ROW]
[ROW][C]Frequency (Period)[/C][C]Spectrum[/C][/ROW]
[ROW][C]0.0208 (48)[/C][C]0.323247[/C][/ROW]
[ROW][C]0.0417 (24)[/C][C]26.175666[/C][/ROW]
[ROW][C]0.0625 (16)[/C][C]2.881063[/C][/ROW]
[ROW][C]0.0833 (12)[/C][C]0.380139[/C][/ROW]
[ROW][C]0.1042 (9.6)[/C][C]2.505318[/C][/ROW]
[ROW][C]0.125 (8)[/C][C]57.285338[/C][/ROW]
[ROW][C]0.1458 (6.8571)[/C][C]6.92519[/C][/ROW]
[ROW][C]0.1667 (6)[/C][C]9.745845[/C][/ROW]
[ROW][C]0.1875 (5.3333)[/C][C]0.436757[/C][/ROW]
[ROW][C]0.2083 (4.8)[/C][C]67.290794[/C][/ROW]
[ROW][C]0.2292 (4.3636)[/C][C]1.245244[/C][/ROW]
[ROW][C]0.25 (4)[/C][C]18.59385[/C][/ROW]
[ROW][C]0.2708 (3.6923)[/C][C]6.420492[/C][/ROW]
[ROW][C]0.2917 (3.4286)[/C][C]6.951566[/C][/ROW]
[ROW][C]0.3125 (3.2)[/C][C]17.223419[/C][/ROW]
[ROW][C]0.3333 (3)[/C][C]53.257786[/C][/ROW]
[ROW][C]0.3542 (2.8235)[/C][C]90.67007[/C][/ROW]
[ROW][C]0.375 (2.6667)[/C][C]0.87525[/C][/ROW]
[ROW][C]0.3958 (2.5263)[/C][C]52.042462[/C][/ROW]
[ROW][C]0.4167 (2.4)[/C][C]9.340107[/C][/ROW]
[ROW][C]0.4375 (2.2857)[/C][C]7.909001[/C][/ROW]
[ROW][C]0.4583 (2.1818)[/C][C]98.7883[/C][/ROW]
[ROW][C]0.4792 (2.087)[/C][C]10.012686[/C][/ROW]
[ROW][C]0.5 (2)[/C][C]99.581888[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29010&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29010&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:

Raw Periodogram
ParameterValue
Box-Cox transformation parameter (lambda)1
Degree of non-seasonal differencing (d)1
Degree of seasonal differencing (D)1
Seasonal Period (s)12
Frequency (Period)Spectrum
0.0208 (48)0.323247
0.0417 (24)26.175666
0.0625 (16)2.881063
0.0833 (12)0.380139
0.1042 (9.6)2.505318
0.125 (8)57.285338
0.1458 (6.8571)6.92519
0.1667 (6)9.745845
0.1875 (5.3333)0.436757
0.2083 (4.8)67.290794
0.2292 (4.3636)1.245244
0.25 (4)18.59385
0.2708 (3.6923)6.420492
0.2917 (3.4286)6.951566
0.3125 (3.2)17.223419
0.3333 (3)53.257786
0.3542 (2.8235)90.67007
0.375 (2.6667)0.87525
0.3958 (2.5263)52.042462
0.4167 (2.4)9.340107
0.4375 (2.2857)7.909001
0.4583 (2.1818)98.7883
0.4792 (2.087)10.012686
0.5 (2)99.581888


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 12 ;
Parameters (R input):
par1 = 1 ; par2 = 1 ; par3 = 1 ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
if (par1 == 0) {
x <- log(x)
} else {
x <- (x ^ par1 - 1) / par1
}
if (par2 > 0) x <- diff(x,lag=1,difference=par2)
if (par3 > 0) x <- diff(x,lag=par4,difference=par3)
bitmap(file='test1.png')
r <- spectrum(x,main='Raw Periodogram')
dev.off()
bitmap(file='test2.png')
cpgram(x,main='Cumulative Periodogram')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Raw Periodogram',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Box-Cox transformation parameter (lambda)',header=TRUE)
a<-table.element(a,par1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Degree of non-seasonal differencing (d)',header=TRUE)
a<-table.element(a,par2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Degree of seasonal differencing (D)',header=TRUE)
a<-table.element(a,par3)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Seasonal Period (s)',header=TRUE)
a<-table.element(a,par4)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Frequency (Period)',header=TRUE)
a<-table.element(a,'Spectrum',header=TRUE)
a<-table.row.end(a)
for (i in 1:length(r$freq)) {
a<-table.row.start(a)
mylab <- round(r$freq[i],4)
mylab <- paste(mylab,' (',sep='')
mylab <- paste(mylab,round(1/r$freq[i],4),sep='')
mylab <- paste(mylab,')',sep='')
a<-table.element(a,mylab,header=TRUE)
a<-table.element(a,round(r$spec[i],6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')