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Author's title

Author

*Unverified author*

R Software Module

rwasp_spectrum.wasp

Title produced by software

Spectral Analysis

Date of computation

Tue, 09 Dec 2008 12:52:29 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/09/t1228852396vnhv0mbidcg4l1q.htm/, Retrieved Fri, 17 May 2024 04:09:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31751, Retrieved Fri, 17 May 2024 04:09:35 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

k_vanderheggen

Estimated Impact

233

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

F       [Spectral Analysis] [eigen tijdreeks p...] [2008-12-09 19:52:29] [2731fa16c50d4727d0297daf34574cde] [Current]
-   P     [Spectral Analysis] [] [2008-12-16 14:06:20] [74be16979710d4c4e7c6647856088456] 
-   P     [Spectral Analysis] [Paper periodogram] [2008-12-18 15:18:25] [1640119c345fbfa2091dc1243f79f7a6] 

Feedback Forum

2008-12-14 13:55:35 [Jasmine Hendrikx] [reply] 
Evaluatie stap 2 Spectral Analysis: 
De berekening is goed uitgevoerd en de bespreking is goed. Het is inderdaad zo dat 58% verklaard kan worden door de langetermijntrend (een steil stijgende lijn aan de linkerkant). Er lijkt ook sprake te zijn van een lichte seizoenaliteit door de trapvorm, maar deze is niet zo duidelijk. 
2008-12-16 14:09:31 [Peter Van Doninck] [reply] 
Studente heeft terecht opgemerkt dat er een lange termijntrend aanwezig is. Dit zien we aangezien er een vrij lage frequentie is links in het periodogram. Wanneer we niet seizoenaal differentiëren krijgen we de volgende oplossing: http://www.freestatistics.org/blog/index.php?v=date/2008/Dec/16/t1229436443xlv6m8mlwbk04b6.htm 
 
Wanneer we nu naar het periodogram kijken, valt het op dat we binnen het 95% betrouwbaarheidsinterval zitten voor de meeste gevallen. Seizoenaal differentiëren is hier NIET nodig! We zullen ook te maken hebben met een AR-proces (afwijking naar boven)

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Dataseries X:

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Histogram

Boxplots

5.5
5.3
5.2
5.3
5.3
5
4.8
4.9
5.3
6
6.2
6.4
6.4
6.4
6.2
6.1
6
5.9
6.2
6.2
6.4
6.8
6.9
7
7
6.9
6.7
6.6
6.5
6.4
6.5
6.5
6.6
6.7
6.8
7.2
7.6
7.6
7.3
6.4
6.1
6.3
7.1
7.5
7.4
7.1
6.8
6.9
7.2
7.4
7.3
6.9
6.9
6.8
7.1
7.2
7.1
7
6.9
7
7.4
7.5
7.5
7.4
7.3
7
6.7
6.5
6.5
6.5
6.6
6.8
6.9
6.9
6.8
6.8
6.5
6.1
6
5.9
5.8
5.9
5.9
6.2
6.3
6.2
6
5.8
5.5
5.5
5.7
5.8

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	'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=31751&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=31751&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31751&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	'George Udny Yule' @ 72.249.76.132

Raw Periodogram
Parameter	Value
Box-Cox transformation parameter (lambda)	1
Degree of non-seasonal differencing (d)	0
Degree of seasonal differencing (D)	0
Seasonal Period (s)	12
Frequency (Period)	Spectrum
0.0104 (96)	8.141179
0.0208 (48)	0.118558
0.0312 (32)	0.836753
0.0417 (24)	0.817624
0.0521 (19.2)	0.324226
0.0625 (16)	0.280321
0.0729 (13.7143)	0.327721
0.0833 (12)	1.910449
0.0938 (10.6667)	0.579633
0.1042 (9.6)	0.17249
0.1146 (8.7273)	0.345452
0.125 (8)	0.256207
0.1354 (7.3846)	0.013111
0.1458 (6.8571)	0.409241
0.1562 (6.4)	0.408242
0.1667 (6)	0.220707
0.1771 (5.6471)	0.249688
0.1875 (5.3333)	0.082225
0.1979 (5.0526)	0.022774
0.2083 (4.8)	0.024909
0.2187 (4.5714)	0.011834
0.2292 (4.3636)	0.001919
0.2396 (4.1739)	0.013885
0.25 (4)	0.003316
0.2604 (3.84)	0.005768
0.2708 (3.6923)	0.010046
0.2812 (3.5556)	0.001903
0.2917 (3.4286)	0.000453
0.3021 (3.3103)	0.004497
0.3125 (3.2)	9.4e-05
0.3229 (3.0968)	0.001596
0.3333 (3)	0.014791
0.3438 (2.9091)	0.001029
0.3542 (2.8235)	0.007696
0.3646 (2.7429)	0.0023
0.375 (2.6667)	0.00305
0.3854 (2.5946)	0.003109
0.3958 (2.5263)	0.001706
0.4062 (2.4615)	0.005138
0.4167 (2.4)	0.018998
0.4271 (2.3415)	0.000492
0.4375 (2.2857)	0.002281
0.4479 (2.2326)	0.004674
0.4583 (2.1818)	0.001044
0.4688 (2.1333)	0.000882
0.4792 (2.087)	0.000736
0.4896 (2.0426)	0.009085
0.5 (2)	0.001276

\begin{tabular}{lllllllll}
\hline
Raw Periodogram \tabularnewline
Parameter & Value \tabularnewline
Box-Cox transformation parameter (lambda) & 1 \tabularnewline
Degree of non-seasonal differencing (d) & 0 \tabularnewline
Degree of seasonal differencing (D) & 0 \tabularnewline
Seasonal Period (s) & 12 \tabularnewline
Frequency (Period) & Spectrum \tabularnewline
0.0104 (96) & 8.141179 \tabularnewline
0.0208 (48) & 0.118558 \tabularnewline
0.0312 (32) & 0.836753 \tabularnewline
0.0417 (24) & 0.817624 \tabularnewline
0.0521 (19.2) & 0.324226 \tabularnewline
0.0625 (16) & 0.280321 \tabularnewline
0.0729 (13.7143) & 0.327721 \tabularnewline
0.0833 (12) & 1.910449 \tabularnewline
0.0938 (10.6667) & 0.579633 \tabularnewline
0.1042 (9.6) & 0.17249 \tabularnewline
0.1146 (8.7273) & 0.345452 \tabularnewline
0.125 (8) & 0.256207 \tabularnewline
0.1354 (7.3846) & 0.013111 \tabularnewline
0.1458 (6.8571) & 0.409241 \tabularnewline
0.1562 (6.4) & 0.408242 \tabularnewline
0.1667 (6) & 0.220707 \tabularnewline
0.1771 (5.6471) & 0.249688 \tabularnewline
0.1875 (5.3333) & 0.082225 \tabularnewline
0.1979 (5.0526) & 0.022774 \tabularnewline
0.2083 (4.8) & 0.024909 \tabularnewline
0.2187 (4.5714) & 0.011834 \tabularnewline
0.2292 (4.3636) & 0.001919 \tabularnewline
0.2396 (4.1739) & 0.013885 \tabularnewline
0.25 (4) & 0.003316 \tabularnewline
0.2604 (3.84) & 0.005768 \tabularnewline
0.2708 (3.6923) & 0.010046 \tabularnewline
0.2812 (3.5556) & 0.001903 \tabularnewline
0.2917 (3.4286) & 0.000453 \tabularnewline
0.3021 (3.3103) & 0.004497 \tabularnewline
0.3125 (3.2) & 9.4e-05 \tabularnewline
0.3229 (3.0968) & 0.001596 \tabularnewline
0.3333 (3) & 0.014791 \tabularnewline
0.3438 (2.9091) & 0.001029 \tabularnewline
0.3542 (2.8235) & 0.007696 \tabularnewline
0.3646 (2.7429) & 0.0023 \tabularnewline
0.375 (2.6667) & 0.00305 \tabularnewline
0.3854 (2.5946) & 0.003109 \tabularnewline
0.3958 (2.5263) & 0.001706 \tabularnewline
0.4062 (2.4615) & 0.005138 \tabularnewline
0.4167 (2.4) & 0.018998 \tabularnewline
0.4271 (2.3415) & 0.000492 \tabularnewline
0.4375 (2.2857) & 0.002281 \tabularnewline
0.4479 (2.2326) & 0.004674 \tabularnewline
0.4583 (2.1818) & 0.001044 \tabularnewline
0.4688 (2.1333) & 0.000882 \tabularnewline
0.4792 (2.087) & 0.000736 \tabularnewline
0.4896 (2.0426) & 0.009085 \tabularnewline
0.5 (2) & 0.001276 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31751&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]0[/C][/ROW]
[ROW][C]Degree of seasonal differencing (D)[/C][C]0[/C][/ROW]
[ROW][C]Seasonal Period (s)[/C][C]12[/C][/ROW]
[ROW][C]Frequency (Period)[/C][C]Spectrum[/C][/ROW]
[ROW][C]0.0104 (96)[/C][C]8.141179[/C][/ROW]
[ROW][C]0.0208 (48)[/C][C]0.118558[/C][/ROW]
[ROW][C]0.0312 (32)[/C][C]0.836753[/C][/ROW]
[ROW][C]0.0417 (24)[/C][C]0.817624[/C][/ROW]
[ROW][C]0.0521 (19.2)[/C][C]0.324226[/C][/ROW]
[ROW][C]0.0625 (16)[/C][C]0.280321[/C][/ROW]
[ROW][C]0.0729 (13.7143)[/C][C]0.327721[/C][/ROW]
[ROW][C]0.0833 (12)[/C][C]1.910449[/C][/ROW]
[ROW][C]0.0938 (10.6667)[/C][C]0.579633[/C][/ROW]
[ROW][C]0.1042 (9.6)[/C][C]0.17249[/C][/ROW]
[ROW][C]0.1146 (8.7273)[/C][C]0.345452[/C][/ROW]
[ROW][C]0.125 (8)[/C][C]0.256207[/C][/ROW]
[ROW][C]0.1354 (7.3846)[/C][C]0.013111[/C][/ROW]
[ROW][C]0.1458 (6.8571)[/C][C]0.409241[/C][/ROW]
[ROW][C]0.1562 (6.4)[/C][C]0.408242[/C][/ROW]
[ROW][C]0.1667 (6)[/C][C]0.220707[/C][/ROW]
[ROW][C]0.1771 (5.6471)[/C][C]0.249688[/C][/ROW]
[ROW][C]0.1875 (5.3333)[/C][C]0.082225[/C][/ROW]
[ROW][C]0.1979 (5.0526)[/C][C]0.022774[/C][/ROW]
[ROW][C]0.2083 (4.8)[/C][C]0.024909[/C][/ROW]
[ROW][C]0.2187 (4.5714)[/C][C]0.011834[/C][/ROW]
[ROW][C]0.2292 (4.3636)[/C][C]0.001919[/C][/ROW]
[ROW][C]0.2396 (4.1739)[/C][C]0.013885[/C][/ROW]
[ROW][C]0.25 (4)[/C][C]0.003316[/C][/ROW]
[ROW][C]0.2604 (3.84)[/C][C]0.005768[/C][/ROW]
[ROW][C]0.2708 (3.6923)[/C][C]0.010046[/C][/ROW]
[ROW][C]0.2812 (3.5556)[/C][C]0.001903[/C][/ROW]
[ROW][C]0.2917 (3.4286)[/C][C]0.000453[/C][/ROW]
[ROW][C]0.3021 (3.3103)[/C][C]0.004497[/C][/ROW]
[ROW][C]0.3125 (3.2)[/C][C]9.4e-05[/C][/ROW]
[ROW][C]0.3229 (3.0968)[/C][C]0.001596[/C][/ROW]
[ROW][C]0.3333 (3)[/C][C]0.014791[/C][/ROW]
[ROW][C]0.3438 (2.9091)[/C][C]0.001029[/C][/ROW]
[ROW][C]0.3542 (2.8235)[/C][C]0.007696[/C][/ROW]
[ROW][C]0.3646 (2.7429)[/C][C]0.0023[/C][/ROW]
[ROW][C]0.375 (2.6667)[/C][C]0.00305[/C][/ROW]
[ROW][C]0.3854 (2.5946)[/C][C]0.003109[/C][/ROW]
[ROW][C]0.3958 (2.5263)[/C][C]0.001706[/C][/ROW]
[ROW][C]0.4062 (2.4615)[/C][C]0.005138[/C][/ROW]
[ROW][C]0.4167 (2.4)[/C][C]0.018998[/C][/ROW]
[ROW][C]0.4271 (2.3415)[/C][C]0.000492[/C][/ROW]
[ROW][C]0.4375 (2.2857)[/C][C]0.002281[/C][/ROW]
[ROW][C]0.4479 (2.2326)[/C][C]0.004674[/C][/ROW]
[ROW][C]0.4583 (2.1818)[/C][C]0.001044[/C][/ROW]
[ROW][C]0.4688 (2.1333)[/C][C]0.000882[/C][/ROW]
[ROW][C]0.4792 (2.087)[/C][C]0.000736[/C][/ROW]
[ROW][C]0.4896 (2.0426)[/C][C]0.009085[/C][/ROW]
[ROW][C]0.5 (2)[/C][C]0.001276[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31751&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31751&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)	0
Degree of seasonal differencing (D)	0
Seasonal Period (s)	12
Frequency (Period)	Spectrum
0.0104 (96)	8.141179
0.0208 (48)	0.118558
0.0312 (32)	0.836753
0.0417 (24)	0.817624
0.0521 (19.2)	0.324226
0.0625 (16)	0.280321
0.0729 (13.7143)	0.327721
0.0833 (12)	1.910449
0.0938 (10.6667)	0.579633
0.1042 (9.6)	0.17249
0.1146 (8.7273)	0.345452
0.125 (8)	0.256207
0.1354 (7.3846)	0.013111
0.1458 (6.8571)	0.409241
0.1562 (6.4)	0.408242
0.1667 (6)	0.220707
0.1771 (5.6471)	0.249688
0.1875 (5.3333)	0.082225
0.1979 (5.0526)	0.022774
0.2083 (4.8)	0.024909
0.2187 (4.5714)	0.011834
0.2292 (4.3636)	0.001919
0.2396 (4.1739)	0.013885
0.25 (4)	0.003316
0.2604 (3.84)	0.005768
0.2708 (3.6923)	0.010046
0.2812 (3.5556)	0.001903
0.2917 (3.4286)	0.000453
0.3021 (3.3103)	0.004497
0.3125 (3.2)	9.4e-05
0.3229 (3.0968)	0.001596
0.3333 (3)	0.014791
0.3438 (2.9091)	0.001029
0.3542 (2.8235)	0.007696
0.3646 (2.7429)	0.0023
0.375 (2.6667)	0.00305
0.3854 (2.5946)	0.003109
0.3958 (2.5263)	0.001706
0.4062 (2.4615)	0.005138
0.4167 (2.4)	0.018998
0.4271 (2.3415)	0.000492
0.4375 (2.2857)	0.002281
0.4479 (2.2326)	0.004674
0.4583 (2.1818)	0.001044
0.4688 (2.1333)	0.000882
0.4792 (2.087)	0.000736
0.4896 (2.0426)	0.009085
0.5 (2)	0.001276

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 12 ;

Parameters (R input):

par1 = 1 ; par2 = 0 ; par3 = 0 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code