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R Software Module

rwasp_spectrum.wasp

Title produced by software

Spectral Analysis

Date of computation

Mon, 08 Dec 2008 11:56:38 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/08/t12287626518lzzu2z4c31lze2.htm/, Retrieved Thu, 16 May 2024 13:36:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30711, Retrieved Thu, 16 May 2024 13:36:02 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

206

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

-     [Spectral Analysis] [Unemployment - St...] [2008-12-08 17:28:52] [57850c80fd59ccfb28f882be994e814e]
F         [Spectral Analysis] [STEP 2 3] [2008-12-08 18:56:38] [e11d930c9e2984715c66c796cf63ef19] [Current]

Feedback Forum

2008-12-11 13:23:13 [72e979bcc364082694890d2eccc1a66f] [reply] 
Door d en D eenmaal te differentiëren zien we dat we nu te maken hebben met een stationaire trend. Het cumulatief periodogram valt volledig binnen het betrouwbaarheidsinterval. We kunnen dus geen trend of seizoenaliteit meer waarnemen.  
De student heeft dit correct uitgevoerd maar er wordt weinig uitleg gegeven.
2008-12-13 20:54:08 [Li Tang Hu] [reply] 
omdat je ook hier weer lambda gelijk gesteld hebt aan 1 kom je een ander resultaat uit. met d=1 en D=1 is de trend er duidlijk uit, maar in je grafieken kunnen we nog duidlijk seizoensinvloeden waarnemen. het trapjespatroon is helemaal niet weg, ik zou in dit geval dus nog eens seizoenaal differntieeren (D=2) en zien wat je dan uitkomt.  
wanneer je de lambdawaarde wel had ingesteld zou je maar 1keer seizoenaal en trendmatig moeten differentieren om de tijdreeks stationair proberen te maken.
2008-12-13 21:53:44 [Li Tang Hu] [reply] 
je moet hier dus controleren of na de differentiatie de tijdreeks stationair is. dit gaan we zowel op ACF als op de raw en cumulatieve periodogram kunnen zien. in jouw grafiek zijn er nog duidelijk seizoensinvloeden te zien, dus kunnen ze stellen dat de tijdreeks niet volledig stationair is...we gaan dus op zoek moeten gaan naar AR- en/of MA processen die onze tijdreeks beinvloeden.
2008-12-14 10:32:43 [Stéphanie Claes] [reply] 
Het dalende patroon is verdwenen en de pieken staan niet meer op regelmatige afstand van elkaar. De tijdreeks is stationair gemaakt.  
Uit het cumulatief periodogram kunnen we afleiden dat er inderdaad nog seizonaliteit aanwezig is. Dit zullen we moeten wegwerken met een AR of een MA proces.  
2008-12-14 10:47:56 [94a54c888ac7f7d6874c3108eb0e1808] [reply] 
De tijdreeks is stationair gemaakt. Het cumulatief periodogram valt volledig binnen het betrouwbaarheidsinterval van 95%. We kunnen dus geen trend of seizoenaliteit meer waarnemen.
2008-12-14 11:07:27 [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.

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30711&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30711&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30711&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Raw Periodogram
Parameter	Value
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)	100270846.729248
0.0417 (24)	101857150.885389
0.0625 (16)	56008655.679396
0.0833 (12)	7273636.644526
0.1042 (9.6)	115869850.325455
0.125 (8)	14302931.059639
0.1458 (6.8571)	51272468.651275
0.1667 (6)	10238280.063963
0.1875 (5.3333)	34185743.34003
0.2083 (4.8)	71841282.396453
0.2292 (4.3636)	27897329.669252
0.25 (4)	47841210.146026
0.2708 (3.6923)	157244992.48216
0.2917 (3.4286)	33256131.521845
0.3125 (3.2)	39271133.480745
0.3333 (3)	50421524.046216
0.3542 (2.8235)	113951268.970108
0.375 (2.6667)	50434628.01532
0.3958 (2.5263)	11824634.842019
0.4167 (2.4)	2478608.895135
0.4375 (2.2857)	121632123.089855
0.4583 (2.1818)	45267013.689176
0.4792 (2.087)	118338824.932604
0.5 (2)	6402399.534773

\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) & 100270846.729248 \tabularnewline
0.0417 (24) & 101857150.885389 \tabularnewline
0.0625 (16) & 56008655.679396 \tabularnewline
0.0833 (12) & 7273636.644526 \tabularnewline
0.1042 (9.6) & 115869850.325455 \tabularnewline
0.125 (8) & 14302931.059639 \tabularnewline
0.1458 (6.8571) & 51272468.651275 \tabularnewline
0.1667 (6) & 10238280.063963 \tabularnewline
0.1875 (5.3333) & 34185743.34003 \tabularnewline
0.2083 (4.8) & 71841282.396453 \tabularnewline
0.2292 (4.3636) & 27897329.669252 \tabularnewline
0.25 (4) & 47841210.146026 \tabularnewline
0.2708 (3.6923) & 157244992.48216 \tabularnewline
0.2917 (3.4286) & 33256131.521845 \tabularnewline
0.3125 (3.2) & 39271133.480745 \tabularnewline
0.3333 (3) & 50421524.046216 \tabularnewline
0.3542 (2.8235) & 113951268.970108 \tabularnewline
0.375 (2.6667) & 50434628.01532 \tabularnewline
0.3958 (2.5263) & 11824634.842019 \tabularnewline
0.4167 (2.4) & 2478608.895135 \tabularnewline
0.4375 (2.2857) & 121632123.089855 \tabularnewline
0.4583 (2.1818) & 45267013.689176 \tabularnewline
0.4792 (2.087) & 118338824.932604 \tabularnewline
0.5 (2) & 6402399.534773 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30711&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]100270846.729248[/C][/ROW]
[ROW][C]0.0417 (24)[/C][C]101857150.885389[/C][/ROW]
[ROW][C]0.0625 (16)[/C][C]56008655.679396[/C][/ROW]
[ROW][C]0.0833 (12)[/C][C]7273636.644526[/C][/ROW]
[ROW][C]0.1042 (9.6)[/C][C]115869850.325455[/C][/ROW]
[ROW][C]0.125 (8)[/C][C]14302931.059639[/C][/ROW]
[ROW][C]0.1458 (6.8571)[/C][C]51272468.651275[/C][/ROW]
[ROW][C]0.1667 (6)[/C][C]10238280.063963[/C][/ROW]
[ROW][C]0.1875 (5.3333)[/C][C]34185743.34003[/C][/ROW]
[ROW][C]0.2083 (4.8)[/C][C]71841282.396453[/C][/ROW]
[ROW][C]0.2292 (4.3636)[/C][C]27897329.669252[/C][/ROW]
[ROW][C]0.25 (4)[/C][C]47841210.146026[/C][/ROW]
[ROW][C]0.2708 (3.6923)[/C][C]157244992.48216[/C][/ROW]
[ROW][C]0.2917 (3.4286)[/C][C]33256131.521845[/C][/ROW]
[ROW][C]0.3125 (3.2)[/C][C]39271133.480745[/C][/ROW]
[ROW][C]0.3333 (3)[/C][C]50421524.046216[/C][/ROW]
[ROW][C]0.3542 (2.8235)[/C][C]113951268.970108[/C][/ROW]
[ROW][C]0.375 (2.6667)[/C][C]50434628.01532[/C][/ROW]
[ROW][C]0.3958 (2.5263)[/C][C]11824634.842019[/C][/ROW]
[ROW][C]0.4167 (2.4)[/C][C]2478608.895135[/C][/ROW]
[ROW][C]0.4375 (2.2857)[/C][C]121632123.089855[/C][/ROW]
[ROW][C]0.4583 (2.1818)[/C][C]45267013.689176[/C][/ROW]
[ROW][C]0.4792 (2.087)[/C][C]118338824.932604[/C][/ROW]
[ROW][C]0.5 (2)[/C][C]6402399.534773[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30711&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30711&T=1

As an alternative you can also use a QR Code:

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

Raw Periodogram
Parameter	Value
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)	100270846.729248
0.0417 (24)	101857150.885389
0.0625 (16)	56008655.679396
0.0833 (12)	7273636.644526
0.1042 (9.6)	115869850.325455
0.125 (8)	14302931.059639
0.1458 (6.8571)	51272468.651275
0.1667 (6)	10238280.063963
0.1875 (5.3333)	34185743.34003
0.2083 (4.8)	71841282.396453
0.2292 (4.3636)	27897329.669252
0.25 (4)	47841210.146026
0.2708 (3.6923)	157244992.48216
0.2917 (3.4286)	33256131.521845
0.3125 (3.2)	39271133.480745
0.3333 (3)	50421524.046216
0.3542 (2.8235)	113951268.970108
0.375 (2.6667)	50434628.01532
0.3958 (2.5263)	11824634.842019
0.4167 (2.4)	2478608.895135
0.4375 (2.2857)	121632123.089855
0.4583 (2.1818)	45267013.689176
0.4792 (2.087)	118338824.932604
0.5 (2)	6402399.534773

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 1 ; par3 = 1 ; par4 = 12 ;

Parameters (R input):

par1 = 1 ; par2 = 1 ; par3 = 1 ; par4 = 12 ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code