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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_spectrum.wasp
Title produced by softwareSpectral Analysis
Date of computationWed, 22 Dec 2010 14:47:17 +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/2010/Dec/22/t1293029104a55659h2qzzwxef.htm/, Retrieved Mon, 06 May 2024 01:57:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114280, Retrieved Mon, 06 May 2024 01:57:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact121

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]
- RMP   [(Partial) Autocorrelation Function] [WS8 Autocorolation] [2010-12-01 09:55:45] [b84bdc9bd81e1f02ca0dcc4710c1b790]
- RMPD    [Spectral Analysis] [Spectral Analysis...] [2010-12-21 16:41:30] [fc9068db680cd880760a7c0fccd81a61]
-   P         [Spectral Analysis] [Spectral Analysis...] [2010-12-22 14:47:17] [a8abc7260f3c847aeac0a796e7895a2e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
143827
145191
146832
148577
149873
151847
153252
154292
155657
156523
156416
156693
160312
160438
160882
161668
164391
168556
169738
170387
171294
172202
172651
172770
178366
180014
181067
182586
184957
186417
188599
189490
190264
191221
191110
190674
195438
196393
197172
198760
200945
203845
204613
205487
206100
206315
206291
207801
211653
211325
211893
212056
214696
217455
218884
219816
219984
219062
218550
218179
222218
222196
223393
223292
226236
228831
228745
229140
229270
229359
230006
228810
232677
232961
234629
235660
240024
243554
244368
244356
245126
246321
246797
246735
251083
251786
252732
255051
259022
261698
263891
265247
262228
263429
264305
266371
273248
275472
278146
279506
283991
286794
288703
289285
288869
286942
285833
284095
289229
289389
290793
291454
294733
293853
294056
293982
293075
292391

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114280&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114280&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114280&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 time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk






Raw Periodogram
ParameterValue
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
0.0083 (120)143501427.415761
0.0167 (60)486881116.62625
0.025 (40)34921937.130576
0.0333 (30)9230222.04341
0.0417 (24)42399509.727174
0.05 (20)25364940.46379
0.0583 (17.1429)9118356.775876
0.0667 (15)7376799.094589
0.075 (13.3333)4190544.539395
0.0833 (12)86624676.621892
0.0917 (10.9091)9669852.958275
0.1 (10)6101258.285506
0.1083 (9.2308)2787372.75372
0.1167 (8.5714)194416.740894
0.125 (8)1560875.564952
0.1333 (7.5)74540.740096
0.1417 (7.0588)8221447.008603
0.15 (6.6667)3902240.324194
0.1583 (6.3158)849717.931731
0.1667 (6)20364412.670997
0.175 (5.7143)1086327.896215
0.1833 (5.4545)194376.972649
0.1917 (5.2174)536320.079531
0.2 (5)212563.510598
0.2083 (4.8)356945.003845
0.2167 (4.6154)445486.840783
0.225 (4.4444)375974.90865
0.2333 (4.2857)255512.352971
0.2417 (4.1379)242251.747049
0.25 (4)12554035.536349
0.2583 (3.871)128721.156271
0.2667 (3.75)572572.734074
0.275 (3.6364)147055.606702
0.2833 (3.5294)654946.189827
0.2917 (3.4286)232494.972793
0.3 (3.3333)331108.047614
0.3083 (3.2432)66685.216768
0.3167 (3.1579)715295.234366
0.325 (3.0769)69155.919741
0.3333 (3)2520010.935043
0.3417 (2.9268)355009.281263
0.35 (2.8571)541097.296399
0.3583 (2.7907)35654.622237
0.3667 (2.7273)133694.637837
0.375 (2.6667)17406.734752
0.3833 (2.6087)283438.915355
0.3917 (2.5532)428838.368315
0.4 (2.5)4436.994369
0.4083 (2.449)53741.069319
0.4167 (2.4)5169504.752457
0.425 (2.3529)514763.413561
0.4333 (2.3077)130112.488208
0.4417 (2.2642)33529.621018
0.45 (2.2222)53865.378825
0.4583 (2.1818)329121.63667
0.4667 (2.1429)189247.165784
0.475 (2.1053)707725.571821
0.4833 (2.069)34215.940672
0.4917 (2.0339)114664.538725
0.5 (2)5067965.858574

\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
0.0083 (120) & 143501427.415761 \tabularnewline
0.0167 (60) & 486881116.62625 \tabularnewline
0.025 (40) & 34921937.130576 \tabularnewline
0.0333 (30) & 9230222.04341 \tabularnewline
0.0417 (24) & 42399509.727174 \tabularnewline
0.05 (20) & 25364940.46379 \tabularnewline
0.0583 (17.1429) & 9118356.775876 \tabularnewline
0.0667 (15) & 7376799.094589 \tabularnewline
0.075 (13.3333) & 4190544.539395 \tabularnewline
0.0833 (12) & 86624676.621892 \tabularnewline
0.0917 (10.9091) & 9669852.958275 \tabularnewline
0.1 (10) & 6101258.285506 \tabularnewline
0.1083 (9.2308) & 2787372.75372 \tabularnewline
0.1167 (8.5714) & 194416.740894 \tabularnewline
0.125 (8) & 1560875.564952 \tabularnewline
0.1333 (7.5) & 74540.740096 \tabularnewline
0.1417 (7.0588) & 8221447.008603 \tabularnewline
0.15 (6.6667) & 3902240.324194 \tabularnewline
0.1583 (6.3158) & 849717.931731 \tabularnewline
0.1667 (6) & 20364412.670997 \tabularnewline
0.175 (5.7143) & 1086327.896215 \tabularnewline
0.1833 (5.4545) & 194376.972649 \tabularnewline
0.1917 (5.2174) & 536320.079531 \tabularnewline
0.2 (5) & 212563.510598 \tabularnewline
0.2083 (4.8) & 356945.003845 \tabularnewline
0.2167 (4.6154) & 445486.840783 \tabularnewline
0.225 (4.4444) & 375974.90865 \tabularnewline
0.2333 (4.2857) & 255512.352971 \tabularnewline
0.2417 (4.1379) & 242251.747049 \tabularnewline
0.25 (4) & 12554035.536349 \tabularnewline
0.2583 (3.871) & 128721.156271 \tabularnewline
0.2667 (3.75) & 572572.734074 \tabularnewline
0.275 (3.6364) & 147055.606702 \tabularnewline
0.2833 (3.5294) & 654946.189827 \tabularnewline
0.2917 (3.4286) & 232494.972793 \tabularnewline
0.3 (3.3333) & 331108.047614 \tabularnewline
0.3083 (3.2432) & 66685.216768 \tabularnewline
0.3167 (3.1579) & 715295.234366 \tabularnewline
0.325 (3.0769) & 69155.919741 \tabularnewline
0.3333 (3) & 2520010.935043 \tabularnewline
0.3417 (2.9268) & 355009.281263 \tabularnewline
0.35 (2.8571) & 541097.296399 \tabularnewline
0.3583 (2.7907) & 35654.622237 \tabularnewline
0.3667 (2.7273) & 133694.637837 \tabularnewline
0.375 (2.6667) & 17406.734752 \tabularnewline
0.3833 (2.6087) & 283438.915355 \tabularnewline
0.3917 (2.5532) & 428838.368315 \tabularnewline
0.4 (2.5) & 4436.994369 \tabularnewline
0.4083 (2.449) & 53741.069319 \tabularnewline
0.4167 (2.4) & 5169504.752457 \tabularnewline
0.425 (2.3529) & 514763.413561 \tabularnewline
0.4333 (2.3077) & 130112.488208 \tabularnewline
0.4417 (2.2642) & 33529.621018 \tabularnewline
0.45 (2.2222) & 53865.378825 \tabularnewline
0.4583 (2.1818) & 329121.63667 \tabularnewline
0.4667 (2.1429) & 189247.165784 \tabularnewline
0.475 (2.1053) & 707725.571821 \tabularnewline
0.4833 (2.069) & 34215.940672 \tabularnewline
0.4917 (2.0339) & 114664.538725 \tabularnewline
0.5 (2) & 5067965.858574 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114280&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]0.0083 (120)[/C][C]143501427.415761[/C][/ROW]
[ROW][C]0.0167 (60)[/C][C]486881116.62625[/C][/ROW]
[ROW][C]0.025 (40)[/C][C]34921937.130576[/C][/ROW]
[ROW][C]0.0333 (30)[/C][C]9230222.04341[/C][/ROW]
[ROW][C]0.0417 (24)[/C][C]42399509.727174[/C][/ROW]
[ROW][C]0.05 (20)[/C][C]25364940.46379[/C][/ROW]
[ROW][C]0.0583 (17.1429)[/C][C]9118356.775876[/C][/ROW]
[ROW][C]0.0667 (15)[/C][C]7376799.094589[/C][/ROW]
[ROW][C]0.075 (13.3333)[/C][C]4190544.539395[/C][/ROW]
[ROW][C]0.0833 (12)[/C][C]86624676.621892[/C][/ROW]
[ROW][C]0.0917 (10.9091)[/C][C]9669852.958275[/C][/ROW]
[ROW][C]0.1 (10)[/C][C]6101258.285506[/C][/ROW]
[ROW][C]0.1083 (9.2308)[/C][C]2787372.75372[/C][/ROW]
[ROW][C]0.1167 (8.5714)[/C][C]194416.740894[/C][/ROW]
[ROW][C]0.125 (8)[/C][C]1560875.564952[/C][/ROW]
[ROW][C]0.1333 (7.5)[/C][C]74540.740096[/C][/ROW]
[ROW][C]0.1417 (7.0588)[/C][C]8221447.008603[/C][/ROW]
[ROW][C]0.15 (6.6667)[/C][C]3902240.324194[/C][/ROW]
[ROW][C]0.1583 (6.3158)[/C][C]849717.931731[/C][/ROW]
[ROW][C]0.1667 (6)[/C][C]20364412.670997[/C][/ROW]
[ROW][C]0.175 (5.7143)[/C][C]1086327.896215[/C][/ROW]
[ROW][C]0.1833 (5.4545)[/C][C]194376.972649[/C][/ROW]
[ROW][C]0.1917 (5.2174)[/C][C]536320.079531[/C][/ROW]
[ROW][C]0.2 (5)[/C][C]212563.510598[/C][/ROW]
[ROW][C]0.2083 (4.8)[/C][C]356945.003845[/C][/ROW]
[ROW][C]0.2167 (4.6154)[/C][C]445486.840783[/C][/ROW]
[ROW][C]0.225 (4.4444)[/C][C]375974.90865[/C][/ROW]
[ROW][C]0.2333 (4.2857)[/C][C]255512.352971[/C][/ROW]
[ROW][C]0.2417 (4.1379)[/C][C]242251.747049[/C][/ROW]
[ROW][C]0.25 (4)[/C][C]12554035.536349[/C][/ROW]
[ROW][C]0.2583 (3.871)[/C][C]128721.156271[/C][/ROW]
[ROW][C]0.2667 (3.75)[/C][C]572572.734074[/C][/ROW]
[ROW][C]0.275 (3.6364)[/C][C]147055.606702[/C][/ROW]
[ROW][C]0.2833 (3.5294)[/C][C]654946.189827[/C][/ROW]
[ROW][C]0.2917 (3.4286)[/C][C]232494.972793[/C][/ROW]
[ROW][C]0.3 (3.3333)[/C][C]331108.047614[/C][/ROW]
[ROW][C]0.3083 (3.2432)[/C][C]66685.216768[/C][/ROW]
[ROW][C]0.3167 (3.1579)[/C][C]715295.234366[/C][/ROW]
[ROW][C]0.325 (3.0769)[/C][C]69155.919741[/C][/ROW]
[ROW][C]0.3333 (3)[/C][C]2520010.935043[/C][/ROW]
[ROW][C]0.3417 (2.9268)[/C][C]355009.281263[/C][/ROW]
[ROW][C]0.35 (2.8571)[/C][C]541097.296399[/C][/ROW]
[ROW][C]0.3583 (2.7907)[/C][C]35654.622237[/C][/ROW]
[ROW][C]0.3667 (2.7273)[/C][C]133694.637837[/C][/ROW]
[ROW][C]0.375 (2.6667)[/C][C]17406.734752[/C][/ROW]
[ROW][C]0.3833 (2.6087)[/C][C]283438.915355[/C][/ROW]
[ROW][C]0.3917 (2.5532)[/C][C]428838.368315[/C][/ROW]
[ROW][C]0.4 (2.5)[/C][C]4436.994369[/C][/ROW]
[ROW][C]0.4083 (2.449)[/C][C]53741.069319[/C][/ROW]
[ROW][C]0.4167 (2.4)[/C][C]5169504.752457[/C][/ROW]
[ROW][C]0.425 (2.3529)[/C][C]514763.413561[/C][/ROW]
[ROW][C]0.4333 (2.3077)[/C][C]130112.488208[/C][/ROW]
[ROW][C]0.4417 (2.2642)[/C][C]33529.621018[/C][/ROW]
[ROW][C]0.45 (2.2222)[/C][C]53865.378825[/C][/ROW]
[ROW][C]0.4583 (2.1818)[/C][C]329121.63667[/C][/ROW]
[ROW][C]0.4667 (2.1429)[/C][C]189247.165784[/C][/ROW]
[ROW][C]0.475 (2.1053)[/C][C]707725.571821[/C][/ROW]
[ROW][C]0.4833 (2.069)[/C][C]34215.940672[/C][/ROW]
[ROW][C]0.4917 (2.0339)[/C][C]114664.538725[/C][/ROW]
[ROW][C]0.5 (2)[/C][C]5067965.858574[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114280&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114280&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)0
Degree of seasonal differencing (D)0
Seasonal Period (s)12
Frequency (Period)Spectrum
0.0083 (120)143501427.415761
0.0167 (60)486881116.62625
0.025 (40)34921937.130576
0.0333 (30)9230222.04341
0.0417 (24)42399509.727174
0.05 (20)25364940.46379
0.0583 (17.1429)9118356.775876
0.0667 (15)7376799.094589
0.075 (13.3333)4190544.539395
0.0833 (12)86624676.621892
0.0917 (10.9091)9669852.958275
0.1 (10)6101258.285506
0.1083 (9.2308)2787372.75372
0.1167 (8.5714)194416.740894
0.125 (8)1560875.564952
0.1333 (7.5)74540.740096
0.1417 (7.0588)8221447.008603
0.15 (6.6667)3902240.324194
0.1583 (6.3158)849717.931731
0.1667 (6)20364412.670997
0.175 (5.7143)1086327.896215
0.1833 (5.4545)194376.972649
0.1917 (5.2174)536320.079531
0.2 (5)212563.510598
0.2083 (4.8)356945.003845
0.2167 (4.6154)445486.840783
0.225 (4.4444)375974.90865
0.2333 (4.2857)255512.352971
0.2417 (4.1379)242251.747049
0.25 (4)12554035.536349
0.2583 (3.871)128721.156271
0.2667 (3.75)572572.734074
0.275 (3.6364)147055.606702
0.2833 (3.5294)654946.189827
0.2917 (3.4286)232494.972793
0.3 (3.3333)331108.047614
0.3083 (3.2432)66685.216768
0.3167 (3.1579)715295.234366
0.325 (3.0769)69155.919741
0.3333 (3)2520010.935043
0.3417 (2.9268)355009.281263
0.35 (2.8571)541097.296399
0.3583 (2.7907)35654.622237
0.3667 (2.7273)133694.637837
0.375 (2.6667)17406.734752
0.3833 (2.6087)283438.915355
0.3917 (2.5532)428838.368315
0.4 (2.5)4436.994369
0.4083 (2.449)53741.069319
0.4167 (2.4)5169504.752457
0.425 (2.3529)514763.413561
0.4333 (2.3077)130112.488208
0.4417 (2.2642)33529.621018
0.45 (2.2222)53865.378825
0.4583 (2.1818)329121.63667
0.4667 (2.1429)189247.165784
0.475 (2.1053)707725.571821
0.4833 (2.069)34215.940672
0.4917 (2.0339)114664.538725
0.5 (2)5067965.858574


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 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')