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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_spectrum.wasp
Title produced by softwareSpectral Analysis
Date of computationSun, 07 Dec 2008 05:10:49 -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/07/t122865205696f5pht197n4yrb.htm/, Retrieved Sun, 19 May 2024 10:08:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29893, Retrieved Sun, 19 May 2024 10:08:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact217

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   [Standard Deviation-Mean Plot] [q1] [2008-12-07 11:50:18] [1b742211e88d1643c42c5773474321b2]
F RM      [Variance Reduction Matrix] [step 2] [2008-12-07 11:57:32] [1b742211e88d1643c42c5773474321b2]
F RMP       [(Partial) Autocorrelation Function] [ste^2] [2008-12-07 12:04:39] [1b742211e88d1643c42c5773474321b2]
F RM            [Spectral Analysis] [step 2] [2008-12-07 12:10:49] [607bd9e9685911f7e343f7bc0bf7bdf9] [Current]
-                 [Spectral Analysis] [step 3] [2008-12-07 12:17:09] [1b742211e88d1643c42c5773474321b2]
F RM                [(Partial) Autocorrelation Function] [step 3] [2008-12-07 12:22:25] [1b742211e88d1643c42c5773474321b2]
F RM                  [ARIMA Backward Selection] [step 4] [2008-12-07 12:41:04] [1b742211e88d1643c42c5773474321b2]
Feedback Forum
2008-12-13 11:38:22 [Nicolaj Wuyts] [reply] 
VRM: We zoeken hier de d en D-waarden met de kleinste variatie. Hoe kleiner de variatie, hoe meer zekerheid dit ons biedt. Indien er twijfel is bij de gewone variatie, moet er gekeken worden naar de getrimde variatie.
ACF: De autocorrelatie functie geeft het herkenbaar patroon van een hanglat weer.
Spectraal analyse: Aan de hand van de lange termijntrend kan ongeveer 70% van de gegevens verklaard worden. Ook uit het raw periodogram kunnen we afleiden dat d=1 en D=1. De lange termijntrend tekent zich af in het langzaam dalend verloop naar het einde van de grafiek toe. De seizoenale trend zit verdoken in de regelmatig wederkerende pieken.
2008-12-14 12:33:01 [Carole Thielens] [reply] 
* De analyses met de partial autocorrelation function, de variance reduction matrix en de spectraalanalyse waren wel juist, maar onvolledig. De student gebruikte elke methode om te herkennen dat er sprake is van seizonaliteit en een lange termijntrend, maar zocht niet naar de juiste waarden voor de parameters d en D om te gebruikten bij de differentiatie. Het was immers de bedoeling om d en D goed te gebruiken opdat deze niet-stationaire tijdsreeks getransformeerd kan worden tot een stationaire tijdsreeks. Enkel bij de variance reduction matrix vond de student de juiste waarden voor d en D door te kijken welke waarden gepaard gingen met de kleinste variantie. Er werd niet bij de partial autocorrelation en evenmin bij de spectraalanalyse gekeken naar het effect van deze transformatie op de tijdsreeks.


Ook hier zien we enkel het cumulative periodogram van voor de differentiatie, zonder dat de student onderzocht wat het effect was van differentiatie met d=1 en D=1.

De student merkt hier wel correct op dat een snel stijgende cumulative periodogram duidt op een lange termijn trend en dat een trapmatig verloop wijst op seizonaliteit. De raw periodogram wordt niet beschreven.
Deze moet als volgt geïnterpreteerd worden:
-De curve ligt het hoogst in het begin, dus bij een lage frequentie. Dit wijst op een lange termijn trend. Ook zien we om de 12 maanden een piek, wat wijst op seizonaliteit.

Ook de tabel wordt niet omschreven ! Een mogelijke uitleg hierbij zou kunnen zijn:
Uit de tabel kunnen we aan de hand van de frequentie en bijhorende spectrumwaarden afleiden of er sprake is van een lange termijn trend of seizonaliteit.
*Spectrum= de intensiteit waarmee de golfbeweging voorkomt in de tijdsreeks. Dit geeft een indicatie over wat wel en niet sterk voorkomt.
* Ook moet vermeld worden dat de meest dominante frequentie gekenmerkt wordt door de langste periode.
* Bovendien kan gesteld worden dat indien de eerste waarde, deze met de meest dominante frequentie(375) ook een zeer hoge spectrumwaarde heeft, dan is er duidelijk sprake van een lange termijn trend. Dit is ook duidelijk af te lezen uit de tabel. De eerste frequentie
*Seizonaliteit kan vastgesteld worden wanneer de spectrumwaarde bij de periodes 4,6 en 12 het hoogst zijn. Dit is hier eveneens overduidelijk het geval.


2008-12-14 16:52:29 [Jasmine Hendrikx] [reply] 
Evaluatie stap 2 Spectral Analysis:
De berekening is goed uitgevoerd en de conclusie is inderdaad juist. Uit het cumulatieve periodogram kunnen we afleiden dat er een langetermijntrend is (het zeer steile verloop aan de linkerkant) en zien we ook een trapfunctie, wat duidt op seizoenaliteit. Hier zou nog het volgende vermeld kunnen worden: op de x-as kunnen we de frequentie aflezen. De y-as is geschaald tussen 0 en 1.
De getallen op de y-as kun je interpreteren als R-squared. Het getal 0.2 op de y-as wil zeggen dat je 20% kunt verklaren van de reeks. Het getal 0.8 wil zeggen dat je 80% kunt verklaren van de reeks. Hier zien we dat de langetermijtrend 70% van de tijdreeks verklaard. De stippellijnen in de grafiek wijzen op het betrouwbaarheidsinterval.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
235.1
280.7
264.6
240.7
201.4
240.8
241.1
223.8
206.1
174.7
203.3
220.5
299.5
347.4
338.3
327.7
351.6
396.6
438.8
395.6
363.5
378.8
357
369
464.8
479.1
431.3
366.5
326.3
355.1
331.6
261.3
249
205.5
235.6
240.9
264.9
253.8
232.3
193.8
177
213.2
207.2
180.6
188.6
175.4
199
179.6
225.8
234
200.2
183.6
178.2
203.2
208.5
191.8
172.8
148
159.4
154.5
213.2
196.4
182.8
176.4
153.6
173.2
171
151.2
161.9
157.2
201.7
236.4
356.1
398.3
403.7
384.6
365.8
368.1
367.9
347
343.3
292.9
311.5
300.9
366.9
356.9
329.7
316.2
269
289.3
266.2
253.6
233.8
228.4
253.6
260.1
306.6
309.2
309.5
271
279.9
317.9
298.4
246.7
227.3
209.1
259.9
266
320.6
308.5
282.2
262.7
263.5
313.1
284.3
252.6
250.3
246.5
312.7
333.2
446.4
511.6
515.5
506.4
483.2
522.3
509.8
460.7
405.8
375
378.5
406.8
467.8
469.8
429.8
355.8
332.7
378
360.5
334.7
319.5
323.1
363.6
352.1
411.9
388.6
416.4
360.7
338
417.2
388.4
371.1
331.5
353.7
396.7
447
533.5
565.4
542.3
488.7
467.1
531.3
496.1
444
403.4
386.3
394.1
404.1
462.1
448.1
432.3
386.3
395.2
421.9
382.9
384.2
345.5
323.4
372.6
376
462.7
487
444.2
399.3
394.9
455.4
414
375.5
347
339.4
385.8
378.8
451.8
446.1
422.5
383.1
352.8
445.3
367.5
355.1
326.2
319.8
331.8
340.9
394.1
417.2
369.9
349.2
321.4
405.7
342.9
316.5
284.2
270.9
288.8
278.8
324.4
310.9
299
273
279.3
359.2
305
282.1
250.3
246.5
257.9
266.5
315.9
318.4
295.4
266.4
245.8
362.8
324.9
294.2
289.5
295.2
290.3
272
307.4
328.7
292.9
249.1
230.4
361.5
321.7
277.2
260.7
251
257.6
241.8
287.5
292.3
274.7
254.2
230
339
318.2
287
295.8
284
271
262.7
340.6
379.4
373.3
355.2
338.4
466.9
451
422
429.2
425.9
460.7
463.6
541.4
544.2
517.5
469.4
439.4
549
533
506.1
484
457
481.5
469.5
544.7
541.2
521.5
469.7
434.4
542.6
517.3
485.7
465.8
447
426.6
411.6
467.5
484.5
451.2
417.4
379.9
484.7
455
420.8
416.5
376.3
405.6
405.8
500.8
514
475.5
430.1
414.4
538
526
488.5
520.2
504.4
568.5
610.6
818
830.9
835.9
782
762.3
856.9
820.9
769.6
752.2
724.4
723.1
719.5
817.4
803.3
752.5
689
630.4
765.5
757.7
732.2
702.6
683.3
709.5
702.2
784.8
810.9
755.6
656.8
615.1
745.3
694.1
675.7
643.7
622.1
634.6
588
689.7
673.9
647.9
568.8
545.7
632.6
643.8
593.1
579.7
546
562.9
572.5

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=29893&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=29893&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29893&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






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
0.0027 (375)305412.921088
0.0053 (187.5)836275.153364
0.008 (125)25924.242345
0.0107 (93.75)2438.46743
0.0133 (75)60760.562241
0.016 (62.5)248643.39661
0.0187 (53.5714)219726.382379
0.0213 (46.875)5307.430043
0.024 (41.6667)113169.995526
0.0267 (37.5)5632.434995
0.0293 (34.0909)42000.731998
0.032 (31.25)3933.834892
0.0347 (28.8462)23380.749897
0.0373 (26.7857)22184.263032
0.04 (25)45594.791384
0.0427 (23.4375)7580.338001
0.0453 (22.0588)1925.794887
0.048 (20.8333)10964.663604
0.0507 (19.7368)73.73535
0.0533 (18.75)7972.451053
0.056 (17.8571)4058.376269
0.0587 (17.0455)13467.282847
0.0613 (16.3043)2553.825299
0.064 (15.625)3514.172006
0.0667 (15)869.704069
0.0693 (14.4231)466.697005
0.072 (13.8889)87.138234
0.0747 (13.3929)2892.663869
0.0773 (12.931)1907.11472
0.08 (12.5)8035.783217
0.0827 (12.0968)66353.069789
0.0853 (11.7188)12243.133634
0.088 (11.3636)8330.071062
0.0907 (11.0294)3501.405105
0.0933 (10.7143)1215.317187
0.096 (10.4167)648.858007
0.0987 (10.1351)1713.000747
0.1013 (9.8684)56.922523
0.104 (9.6154)4656.230622
0.1067 (9.375)726.147395
0.1093 (9.1463)125.422037
0.112 (8.9286)162.342283
0.1147 (8.7209)463.861461
0.1173 (8.5227)417.84533
0.12 (8.3333)290.424129
0.1227 (8.1522)762.717422
0.1253 (7.9787)327.88452
0.128 (7.8125)169.692982
0.1307 (7.6531)104.31067
0.1333 (7.5)732.145538
0.136 (7.3529)373.506985
0.1387 (7.2115)7.604551
0.1413 (7.0755)220.553988
0.144 (6.9444)839.521161
0.1467 (6.8182)393.246535
0.1493 (6.6964)507.301466
0.152 (6.5789)618.82861
0.1547 (6.4655)78.631513
0.1573 (6.3559)1100.788506
0.16 (6.25)2816.708611
0.1627 (6.1475)5497.013382
0.1653 (6.0484)43080.497912
0.168 (5.9524)38220.275597
0.1707 (5.8594)5263.218754
0.1733 (5.7692)3175.089709
0.176 (5.6818)422.105705
0.1787 (5.597)404.262665
0.1813 (5.5147)96.929115
0.184 (5.4348)268.407257
0.1867 (5.3571)471.357965
0.1893 (5.2817)4.602399
0.192 (5.2083)6.226613
0.1947 (5.137)555.477218
0.1973 (5.0676)105.562383
0.2 (5)106.693124
0.2027 (4.9342)365.21339
0.2053 (4.8701)578.006014
0.208 (4.8077)301.856887
0.2107 (4.7468)12.160869
0.2133 (4.6875)167.999597
0.216 (4.6296)87.634774
0.2187 (4.5732)94.207363
0.2213 (4.5181)72.898752
0.224 (4.4643)40.872729
0.2267 (4.4118)58.267977
0.2293 (4.3605)153.166385
0.232 (4.3103)63.576578
0.2347 (4.2614)142.78437
0.2373 (4.2135)539.460232
0.24 (4.1667)1045.83448
0.2427 (4.1209)68.339186
0.2453 (4.0761)710.483462
0.248 (4.0323)5855.827504
0.2507 (3.9894)21873.575727
0.2533 (3.9474)1517.513805
0.256 (3.9063)411.931544
0.2587 (3.866)61.893128
0.2613 (3.8265)62.82269
0.264 (3.7879)158.711251
0.2667 (3.75)8.586587
0.2693 (3.7129)164.013297
0.272 (3.6765)155.577936
0.2747 (3.6408)168.014205
0.2773 (3.6058)67.286502
0.28 (3.5714)29.916694
0.2827 (3.5377)85.6302
0.2853 (3.5047)203.985743
0.288 (3.4722)59.484349
0.2907 (3.4404)63.294866
0.2933 (3.4091)47.798787
0.296 (3.3784)24.847116
0.2987 (3.3482)3.142518
0.3013 (3.3186)74.742853
0.304 (3.2895)26.040169
0.3067 (3.2609)5.481305
0.3093 (3.2328)64.169891
0.312 (3.2051)52.334359
0.3147 (3.178)105.19286
0.3173 (3.1513)25.478031
0.32 (3.125)9.412664
0.3227 (3.0992)237.788005
0.3253 (3.0738)16.770133
0.328 (3.0488)125.738512
0.3307 (3.0242)1395.603276
0.3333 (3)2117.716663
0.336 (2.9762)198.222107
0.3387 (2.9528)213.673282
0.3413 (2.9297)0.477349
0.344 (2.907)110.526313
0.3467 (2.8846)21.56702
0.3493 (2.8626)314.476129
0.352 (2.8409)78.326184
0.3547 (2.8195)10.083297
0.3573 (2.7985)26.371526
0.36 (2.7778)36.85968
0.3627 (2.7574)379.688317
0.3653 (2.7372)50.55697
0.368 (2.7174)8.913881
0.3707 (2.6978)52.245281
0.3733 (2.6786)20.549021
0.376 (2.6596)29.521128
0.3787 (2.6408)36.3016
0.3813 (2.6224)99.851191
0.384 (2.6042)71.236474
0.3867 (2.5862)5.140791
0.3893 (2.5685)89.996982
0.392 (2.551)136.158383
0.3947 (2.5338)113.464136
0.3973 (2.5168)33.103213
0.4 (2.5)31.900626
0.4027 (2.4834)57.379425
0.4053 (2.4671)18.361649
0.408 (2.451)173.511546
0.4107 (2.4351)85.783267
0.4133 (2.4194)940.594929
0.416 (2.4038)14079.701652
0.4187 (2.3885)3526.560495
0.4213 (2.3734)1423.339742
0.424 (2.3585)350.478199
0.4267 (2.3438)117.237258
0.4293 (2.3292)47.144303
0.432 (2.3148)266.375549
0.4347 (2.3006)27.963408
0.4373 (2.2866)60.379971
0.44 (2.2727)5.396099
0.4427 (2.259)94.141278
0.4453 (2.2455)99.625457
0.448 (2.2321)62.36076
0.4507 (2.2189)48.873597
0.4533 (2.2059)48.579614
0.456 (2.193)240.690985
0.4587 (2.1802)34.443563
0.4613 (2.1676)49.575728
0.464 (2.1552)42.522978
0.4667 (2.1429)50.508575
0.4693 (2.1307)0.683834
0.472 (2.1186)515.801934
0.4747 (2.1067)3.437625
0.4773 (2.095)126.939257
0.48 (2.0833)292.405694
0.4827 (2.0718)31.544685
0.4853 (2.0604)97.324859
0.488 (2.0492)26.196496
0.4907 (2.038)23.824451
0.4933 (2.027)77.919946
0.496 (2.0161)853.237673
0.4987 (2.0053)326.881288

\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
0.0027 (375) & 305412.921088 \tabularnewline
0.0053 (187.5) & 836275.153364 \tabularnewline
0.008 (125) & 25924.242345 \tabularnewline
0.0107 (93.75) & 2438.46743 \tabularnewline
0.0133 (75) & 60760.562241 \tabularnewline
0.016 (62.5) & 248643.39661 \tabularnewline
0.0187 (53.5714) & 219726.382379 \tabularnewline
0.0213 (46.875) & 5307.430043 \tabularnewline
0.024 (41.6667) & 113169.995526 \tabularnewline
0.0267 (37.5) & 5632.434995 \tabularnewline
0.0293 (34.0909) & 42000.731998 \tabularnewline
0.032 (31.25) & 3933.834892 \tabularnewline
0.0347 (28.8462) & 23380.749897 \tabularnewline
0.0373 (26.7857) & 22184.263032 \tabularnewline
0.04 (25) & 45594.791384 \tabularnewline
0.0427 (23.4375) & 7580.338001 \tabularnewline
0.0453 (22.0588) & 1925.794887 \tabularnewline
0.048 (20.8333) & 10964.663604 \tabularnewline
0.0507 (19.7368) & 73.73535 \tabularnewline
0.0533 (18.75) & 7972.451053 \tabularnewline
0.056 (17.8571) & 4058.376269 \tabularnewline
0.0587 (17.0455) & 13467.282847 \tabularnewline
0.0613 (16.3043) & 2553.825299 \tabularnewline
0.064 (15.625) & 3514.172006 \tabularnewline
0.0667 (15) & 869.704069 \tabularnewline
0.0693 (14.4231) & 466.697005 \tabularnewline
0.072 (13.8889) & 87.138234 \tabularnewline
0.0747 (13.3929) & 2892.663869 \tabularnewline
0.0773 (12.931) & 1907.11472 \tabularnewline
0.08 (12.5) & 8035.783217 \tabularnewline
0.0827 (12.0968) & 66353.069789 \tabularnewline
0.0853 (11.7188) & 12243.133634 \tabularnewline
0.088 (11.3636) & 8330.071062 \tabularnewline
0.0907 (11.0294) & 3501.405105 \tabularnewline
0.0933 (10.7143) & 1215.317187 \tabularnewline
0.096 (10.4167) & 648.858007 \tabularnewline
0.0987 (10.1351) & 1713.000747 \tabularnewline
0.1013 (9.8684) & 56.922523 \tabularnewline
0.104 (9.6154) & 4656.230622 \tabularnewline
0.1067 (9.375) & 726.147395 \tabularnewline
0.1093 (9.1463) & 125.422037 \tabularnewline
0.112 (8.9286) & 162.342283 \tabularnewline
0.1147 (8.7209) & 463.861461 \tabularnewline
0.1173 (8.5227) & 417.84533 \tabularnewline
0.12 (8.3333) & 290.424129 \tabularnewline
0.1227 (8.1522) & 762.717422 \tabularnewline
0.1253 (7.9787) & 327.88452 \tabularnewline
0.128 (7.8125) & 169.692982 \tabularnewline
0.1307 (7.6531) & 104.31067 \tabularnewline
0.1333 (7.5) & 732.145538 \tabularnewline
0.136 (7.3529) & 373.506985 \tabularnewline
0.1387 (7.2115) & 7.604551 \tabularnewline
0.1413 (7.0755) & 220.553988 \tabularnewline
0.144 (6.9444) & 839.521161 \tabularnewline
0.1467 (6.8182) & 393.246535 \tabularnewline
0.1493 (6.6964) & 507.301466 \tabularnewline
0.152 (6.5789) & 618.82861 \tabularnewline
0.1547 (6.4655) & 78.631513 \tabularnewline
0.1573 (6.3559) & 1100.788506 \tabularnewline
0.16 (6.25) & 2816.708611 \tabularnewline
0.1627 (6.1475) & 5497.013382 \tabularnewline
0.1653 (6.0484) & 43080.497912 \tabularnewline
0.168 (5.9524) & 38220.275597 \tabularnewline
0.1707 (5.8594) & 5263.218754 \tabularnewline
0.1733 (5.7692) & 3175.089709 \tabularnewline
0.176 (5.6818) & 422.105705 \tabularnewline
0.1787 (5.597) & 404.262665 \tabularnewline
0.1813 (5.5147) & 96.929115 \tabularnewline
0.184 (5.4348) & 268.407257 \tabularnewline
0.1867 (5.3571) & 471.357965 \tabularnewline
0.1893 (5.2817) & 4.602399 \tabularnewline
0.192 (5.2083) & 6.226613 \tabularnewline
0.1947 (5.137) & 555.477218 \tabularnewline
0.1973 (5.0676) & 105.562383 \tabularnewline
0.2 (5) & 106.693124 \tabularnewline
0.2027 (4.9342) & 365.21339 \tabularnewline
0.2053 (4.8701) & 578.006014 \tabularnewline
0.208 (4.8077) & 301.856887 \tabularnewline
0.2107 (4.7468) & 12.160869 \tabularnewline
0.2133 (4.6875) & 167.999597 \tabularnewline
0.216 (4.6296) & 87.634774 \tabularnewline
0.2187 (4.5732) & 94.207363 \tabularnewline
0.2213 (4.5181) & 72.898752 \tabularnewline
0.224 (4.4643) & 40.872729 \tabularnewline
0.2267 (4.4118) & 58.267977 \tabularnewline
0.2293 (4.3605) & 153.166385 \tabularnewline
0.232 (4.3103) & 63.576578 \tabularnewline
0.2347 (4.2614) & 142.78437 \tabularnewline
0.2373 (4.2135) & 539.460232 \tabularnewline
0.24 (4.1667) & 1045.83448 \tabularnewline
0.2427 (4.1209) & 68.339186 \tabularnewline
0.2453 (4.0761) & 710.483462 \tabularnewline
0.248 (4.0323) & 5855.827504 \tabularnewline
0.2507 (3.9894) & 21873.575727 \tabularnewline
0.2533 (3.9474) & 1517.513805 \tabularnewline
0.256 (3.9063) & 411.931544 \tabularnewline
0.2587 (3.866) & 61.893128 \tabularnewline
0.2613 (3.8265) & 62.82269 \tabularnewline
0.264 (3.7879) & 158.711251 \tabularnewline
0.2667 (3.75) & 8.586587 \tabularnewline
0.2693 (3.7129) & 164.013297 \tabularnewline
0.272 (3.6765) & 155.577936 \tabularnewline
0.2747 (3.6408) & 168.014205 \tabularnewline
0.2773 (3.6058) & 67.286502 \tabularnewline
0.28 (3.5714) & 29.916694 \tabularnewline
0.2827 (3.5377) & 85.6302 \tabularnewline
0.2853 (3.5047) & 203.985743 \tabularnewline
0.288 (3.4722) & 59.484349 \tabularnewline
0.2907 (3.4404) & 63.294866 \tabularnewline
0.2933 (3.4091) & 47.798787 \tabularnewline
0.296 (3.3784) & 24.847116 \tabularnewline
0.2987 (3.3482) & 3.142518 \tabularnewline
0.3013 (3.3186) & 74.742853 \tabularnewline
0.304 (3.2895) & 26.040169 \tabularnewline
0.3067 (3.2609) & 5.481305 \tabularnewline
0.3093 (3.2328) & 64.169891 \tabularnewline
0.312 (3.2051) & 52.334359 \tabularnewline
0.3147 (3.178) & 105.19286 \tabularnewline
0.3173 (3.1513) & 25.478031 \tabularnewline
0.32 (3.125) & 9.412664 \tabularnewline
0.3227 (3.0992) & 237.788005 \tabularnewline
0.3253 (3.0738) & 16.770133 \tabularnewline
0.328 (3.0488) & 125.738512 \tabularnewline
0.3307 (3.0242) & 1395.603276 \tabularnewline
0.3333 (3) & 2117.716663 \tabularnewline
0.336 (2.9762) & 198.222107 \tabularnewline
0.3387 (2.9528) & 213.673282 \tabularnewline
0.3413 (2.9297) & 0.477349 \tabularnewline
0.344 (2.907) & 110.526313 \tabularnewline
0.3467 (2.8846) & 21.56702 \tabularnewline
0.3493 (2.8626) & 314.476129 \tabularnewline
0.352 (2.8409) & 78.326184 \tabularnewline
0.3547 (2.8195) & 10.083297 \tabularnewline
0.3573 (2.7985) & 26.371526 \tabularnewline
0.36 (2.7778) & 36.85968 \tabularnewline
0.3627 (2.7574) & 379.688317 \tabularnewline
0.3653 (2.7372) & 50.55697 \tabularnewline
0.368 (2.7174) & 8.913881 \tabularnewline
0.3707 (2.6978) & 52.245281 \tabularnewline
0.3733 (2.6786) & 20.549021 \tabularnewline
0.376 (2.6596) & 29.521128 \tabularnewline
0.3787 (2.6408) & 36.3016 \tabularnewline
0.3813 (2.6224) & 99.851191 \tabularnewline
0.384 (2.6042) & 71.236474 \tabularnewline
0.3867 (2.5862) & 5.140791 \tabularnewline
0.3893 (2.5685) & 89.996982 \tabularnewline
0.392 (2.551) & 136.158383 \tabularnewline
0.3947 (2.5338) & 113.464136 \tabularnewline
0.3973 (2.5168) & 33.103213 \tabularnewline
0.4 (2.5) & 31.900626 \tabularnewline
0.4027 (2.4834) & 57.379425 \tabularnewline
0.4053 (2.4671) & 18.361649 \tabularnewline
0.408 (2.451) & 173.511546 \tabularnewline
0.4107 (2.4351) & 85.783267 \tabularnewline
0.4133 (2.4194) & 940.594929 \tabularnewline
0.416 (2.4038) & 14079.701652 \tabularnewline
0.4187 (2.3885) & 3526.560495 \tabularnewline
0.4213 (2.3734) & 1423.339742 \tabularnewline
0.424 (2.3585) & 350.478199 \tabularnewline
0.4267 (2.3438) & 117.237258 \tabularnewline
0.4293 (2.3292) & 47.144303 \tabularnewline
0.432 (2.3148) & 266.375549 \tabularnewline
0.4347 (2.3006) & 27.963408 \tabularnewline
0.4373 (2.2866) & 60.379971 \tabularnewline
0.44 (2.2727) & 5.396099 \tabularnewline
0.4427 (2.259) & 94.141278 \tabularnewline
0.4453 (2.2455) & 99.625457 \tabularnewline
0.448 (2.2321) & 62.36076 \tabularnewline
0.4507 (2.2189) & 48.873597 \tabularnewline
0.4533 (2.2059) & 48.579614 \tabularnewline
0.456 (2.193) & 240.690985 \tabularnewline
0.4587 (2.1802) & 34.443563 \tabularnewline
0.4613 (2.1676) & 49.575728 \tabularnewline
0.464 (2.1552) & 42.522978 \tabularnewline
0.4667 (2.1429) & 50.508575 \tabularnewline
0.4693 (2.1307) & 0.683834 \tabularnewline
0.472 (2.1186) & 515.801934 \tabularnewline
0.4747 (2.1067) & 3.437625 \tabularnewline
0.4773 (2.095) & 126.939257 \tabularnewline
0.48 (2.0833) & 292.405694 \tabularnewline
0.4827 (2.0718) & 31.544685 \tabularnewline
0.4853 (2.0604) & 97.324859 \tabularnewline
0.488 (2.0492) & 26.196496 \tabularnewline
0.4907 (2.038) & 23.824451 \tabularnewline
0.4933 (2.027) & 77.919946 \tabularnewline
0.496 (2.0161) & 853.237673 \tabularnewline
0.4987 (2.0053) & 326.881288 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29893&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]0.0027 (375)[/C][C]305412.921088[/C][/ROW]
[ROW][C]0.0053 (187.5)[/C][C]836275.153364[/C][/ROW]
[ROW][C]0.008 (125)[/C][C]25924.242345[/C][/ROW]
[ROW][C]0.0107 (93.75)[/C][C]2438.46743[/C][/ROW]
[ROW][C]0.0133 (75)[/C][C]60760.562241[/C][/ROW]
[ROW][C]0.016 (62.5)[/C][C]248643.39661[/C][/ROW]
[ROW][C]0.0187 (53.5714)[/C][C]219726.382379[/C][/ROW]
[ROW][C]0.0213 (46.875)[/C][C]5307.430043[/C][/ROW]
[ROW][C]0.024 (41.6667)[/C][C]113169.995526[/C][/ROW]
[ROW][C]0.0267 (37.5)[/C][C]5632.434995[/C][/ROW]
[ROW][C]0.0293 (34.0909)[/C][C]42000.731998[/C][/ROW]
[ROW][C]0.032 (31.25)[/C][C]3933.834892[/C][/ROW]
[ROW][C]0.0347 (28.8462)[/C][C]23380.749897[/C][/ROW]
[ROW][C]0.0373 (26.7857)[/C][C]22184.263032[/C][/ROW]
[ROW][C]0.04 (25)[/C][C]45594.791384[/C][/ROW]
[ROW][C]0.0427 (23.4375)[/C][C]7580.338001[/C][/ROW]
[ROW][C]0.0453 (22.0588)[/C][C]1925.794887[/C][/ROW]
[ROW][C]0.048 (20.8333)[/C][C]10964.663604[/C][/ROW]
[ROW][C]0.0507 (19.7368)[/C][C]73.73535[/C][/ROW]
[ROW][C]0.0533 (18.75)[/C][C]7972.451053[/C][/ROW]
[ROW][C]0.056 (17.8571)[/C][C]4058.376269[/C][/ROW]
[ROW][C]0.0587 (17.0455)[/C][C]13467.282847[/C][/ROW]
[ROW][C]0.0613 (16.3043)[/C][C]2553.825299[/C][/ROW]
[ROW][C]0.064 (15.625)[/C][C]3514.172006[/C][/ROW]
[ROW][C]0.0667 (15)[/C][C]869.704069[/C][/ROW]
[ROW][C]0.0693 (14.4231)[/C][C]466.697005[/C][/ROW]
[ROW][C]0.072 (13.8889)[/C][C]87.138234[/C][/ROW]
[ROW][C]0.0747 (13.3929)[/C][C]2892.663869[/C][/ROW]
[ROW][C]0.0773 (12.931)[/C][C]1907.11472[/C][/ROW]
[ROW][C]0.08 (12.5)[/C][C]8035.783217[/C][/ROW]
[ROW][C]0.0827 (12.0968)[/C][C]66353.069789[/C][/ROW]
[ROW][C]0.0853 (11.7188)[/C][C]12243.133634[/C][/ROW]
[ROW][C]0.088 (11.3636)[/C][C]8330.071062[/C][/ROW]
[ROW][C]0.0907 (11.0294)[/C][C]3501.405105[/C][/ROW]
[ROW][C]0.0933 (10.7143)[/C][C]1215.317187[/C][/ROW]
[ROW][C]0.096 (10.4167)[/C][C]648.858007[/C][/ROW]
[ROW][C]0.0987 (10.1351)[/C][C]1713.000747[/C][/ROW]
[ROW][C]0.1013 (9.8684)[/C][C]56.922523[/C][/ROW]
[ROW][C]0.104 (9.6154)[/C][C]4656.230622[/C][/ROW]
[ROW][C]0.1067 (9.375)[/C][C]726.147395[/C][/ROW]
[ROW][C]0.1093 (9.1463)[/C][C]125.422037[/C][/ROW]
[ROW][C]0.112 (8.9286)[/C][C]162.342283[/C][/ROW]
[ROW][C]0.1147 (8.7209)[/C][C]463.861461[/C][/ROW]
[ROW][C]0.1173 (8.5227)[/C][C]417.84533[/C][/ROW]
[ROW][C]0.12 (8.3333)[/C][C]290.424129[/C][/ROW]
[ROW][C]0.1227 (8.1522)[/C][C]762.717422[/C][/ROW]
[ROW][C]0.1253 (7.9787)[/C][C]327.88452[/C][/ROW]
[ROW][C]0.128 (7.8125)[/C][C]169.692982[/C][/ROW]
[ROW][C]0.1307 (7.6531)[/C][C]104.31067[/C][/ROW]
[ROW][C]0.1333 (7.5)[/C][C]732.145538[/C][/ROW]
[ROW][C]0.136 (7.3529)[/C][C]373.506985[/C][/ROW]
[ROW][C]0.1387 (7.2115)[/C][C]7.604551[/C][/ROW]
[ROW][C]0.1413 (7.0755)[/C][C]220.553988[/C][/ROW]
[ROW][C]0.144 (6.9444)[/C][C]839.521161[/C][/ROW]
[ROW][C]0.1467 (6.8182)[/C][C]393.246535[/C][/ROW]
[ROW][C]0.1493 (6.6964)[/C][C]507.301466[/C][/ROW]
[ROW][C]0.152 (6.5789)[/C][C]618.82861[/C][/ROW]
[ROW][C]0.1547 (6.4655)[/C][C]78.631513[/C][/ROW]
[ROW][C]0.1573 (6.3559)[/C][C]1100.788506[/C][/ROW]
[ROW][C]0.16 (6.25)[/C][C]2816.708611[/C][/ROW]
[ROW][C]0.1627 (6.1475)[/C][C]5497.013382[/C][/ROW]
[ROW][C]0.1653 (6.0484)[/C][C]43080.497912[/C][/ROW]
[ROW][C]0.168 (5.9524)[/C][C]38220.275597[/C][/ROW]
[ROW][C]0.1707 (5.8594)[/C][C]5263.218754[/C][/ROW]
[ROW][C]0.1733 (5.7692)[/C][C]3175.089709[/C][/ROW]
[ROW][C]0.176 (5.6818)[/C][C]422.105705[/C][/ROW]
[ROW][C]0.1787 (5.597)[/C][C]404.262665[/C][/ROW]
[ROW][C]0.1813 (5.5147)[/C][C]96.929115[/C][/ROW]
[ROW][C]0.184 (5.4348)[/C][C]268.407257[/C][/ROW]
[ROW][C]0.1867 (5.3571)[/C][C]471.357965[/C][/ROW]
[ROW][C]0.1893 (5.2817)[/C][C]4.602399[/C][/ROW]
[ROW][C]0.192 (5.2083)[/C][C]6.226613[/C][/ROW]
[ROW][C]0.1947 (5.137)[/C][C]555.477218[/C][/ROW]
[ROW][C]0.1973 (5.0676)[/C][C]105.562383[/C][/ROW]
[ROW][C]0.2 (5)[/C][C]106.693124[/C][/ROW]
[ROW][C]0.2027 (4.9342)[/C][C]365.21339[/C][/ROW]
[ROW][C]0.2053 (4.8701)[/C][C]578.006014[/C][/ROW]
[ROW][C]0.208 (4.8077)[/C][C]301.856887[/C][/ROW]
[ROW][C]0.2107 (4.7468)[/C][C]12.160869[/C][/ROW]
[ROW][C]0.2133 (4.6875)[/C][C]167.999597[/C][/ROW]
[ROW][C]0.216 (4.6296)[/C][C]87.634774[/C][/ROW]
[ROW][C]0.2187 (4.5732)[/C][C]94.207363[/C][/ROW]
[ROW][C]0.2213 (4.5181)[/C][C]72.898752[/C][/ROW]
[ROW][C]0.224 (4.4643)[/C][C]40.872729[/C][/ROW]
[ROW][C]0.2267 (4.4118)[/C][C]58.267977[/C][/ROW]
[ROW][C]0.2293 (4.3605)[/C][C]153.166385[/C][/ROW]
[ROW][C]0.232 (4.3103)[/C][C]63.576578[/C][/ROW]
[ROW][C]0.2347 (4.2614)[/C][C]142.78437[/C][/ROW]
[ROW][C]0.2373 (4.2135)[/C][C]539.460232[/C][/ROW]
[ROW][C]0.24 (4.1667)[/C][C]1045.83448[/C][/ROW]
[ROW][C]0.2427 (4.1209)[/C][C]68.339186[/C][/ROW]
[ROW][C]0.2453 (4.0761)[/C][C]710.483462[/C][/ROW]
[ROW][C]0.248 (4.0323)[/C][C]5855.827504[/C][/ROW]
[ROW][C]0.2507 (3.9894)[/C][C]21873.575727[/C][/ROW]
[ROW][C]0.2533 (3.9474)[/C][C]1517.513805[/C][/ROW]
[ROW][C]0.256 (3.9063)[/C][C]411.931544[/C][/ROW]
[ROW][C]0.2587 (3.866)[/C][C]61.893128[/C][/ROW]
[ROW][C]0.2613 (3.8265)[/C][C]62.82269[/C][/ROW]
[ROW][C]0.264 (3.7879)[/C][C]158.711251[/C][/ROW]
[ROW][C]0.2667 (3.75)[/C][C]8.586587[/C][/ROW]
[ROW][C]0.2693 (3.7129)[/C][C]164.013297[/C][/ROW]
[ROW][C]0.272 (3.6765)[/C][C]155.577936[/C][/ROW]
[ROW][C]0.2747 (3.6408)[/C][C]168.014205[/C][/ROW]
[ROW][C]0.2773 (3.6058)[/C][C]67.286502[/C][/ROW]
[ROW][C]0.28 (3.5714)[/C][C]29.916694[/C][/ROW]
[ROW][C]0.2827 (3.5377)[/C][C]85.6302[/C][/ROW]
[ROW][C]0.2853 (3.5047)[/C][C]203.985743[/C][/ROW]
[ROW][C]0.288 (3.4722)[/C][C]59.484349[/C][/ROW]
[ROW][C]0.2907 (3.4404)[/C][C]63.294866[/C][/ROW]
[ROW][C]0.2933 (3.4091)[/C][C]47.798787[/C][/ROW]
[ROW][C]0.296 (3.3784)[/C][C]24.847116[/C][/ROW]
[ROW][C]0.2987 (3.3482)[/C][C]3.142518[/C][/ROW]
[ROW][C]0.3013 (3.3186)[/C][C]74.742853[/C][/ROW]
[ROW][C]0.304 (3.2895)[/C][C]26.040169[/C][/ROW]
[ROW][C]0.3067 (3.2609)[/C][C]5.481305[/C][/ROW]
[ROW][C]0.3093 (3.2328)[/C][C]64.169891[/C][/ROW]
[ROW][C]0.312 (3.2051)[/C][C]52.334359[/C][/ROW]
[ROW][C]0.3147 (3.178)[/C][C]105.19286[/C][/ROW]
[ROW][C]0.3173 (3.1513)[/C][C]25.478031[/C][/ROW]
[ROW][C]0.32 (3.125)[/C][C]9.412664[/C][/ROW]
[ROW][C]0.3227 (3.0992)[/C][C]237.788005[/C][/ROW]
[ROW][C]0.3253 (3.0738)[/C][C]16.770133[/C][/ROW]
[ROW][C]0.328 (3.0488)[/C][C]125.738512[/C][/ROW]
[ROW][C]0.3307 (3.0242)[/C][C]1395.603276[/C][/ROW]
[ROW][C]0.3333 (3)[/C][C]2117.716663[/C][/ROW]
[ROW][C]0.336 (2.9762)[/C][C]198.222107[/C][/ROW]
[ROW][C]0.3387 (2.9528)[/C][C]213.673282[/C][/ROW]
[ROW][C]0.3413 (2.9297)[/C][C]0.477349[/C][/ROW]
[ROW][C]0.344 (2.907)[/C][C]110.526313[/C][/ROW]
[ROW][C]0.3467 (2.8846)[/C][C]21.56702[/C][/ROW]
[ROW][C]0.3493 (2.8626)[/C][C]314.476129[/C][/ROW]
[ROW][C]0.352 (2.8409)[/C][C]78.326184[/C][/ROW]
[ROW][C]0.3547 (2.8195)[/C][C]10.083297[/C][/ROW]
[ROW][C]0.3573 (2.7985)[/C][C]26.371526[/C][/ROW]
[ROW][C]0.36 (2.7778)[/C][C]36.85968[/C][/ROW]
[ROW][C]0.3627 (2.7574)[/C][C]379.688317[/C][/ROW]
[ROW][C]0.3653 (2.7372)[/C][C]50.55697[/C][/ROW]
[ROW][C]0.368 (2.7174)[/C][C]8.913881[/C][/ROW]
[ROW][C]0.3707 (2.6978)[/C][C]52.245281[/C][/ROW]
[ROW][C]0.3733 (2.6786)[/C][C]20.549021[/C][/ROW]
[ROW][C]0.376 (2.6596)[/C][C]29.521128[/C][/ROW]
[ROW][C]0.3787 (2.6408)[/C][C]36.3016[/C][/ROW]
[ROW][C]0.3813 (2.6224)[/C][C]99.851191[/C][/ROW]
[ROW][C]0.384 (2.6042)[/C][C]71.236474[/C][/ROW]
[ROW][C]0.3867 (2.5862)[/C][C]5.140791[/C][/ROW]
[ROW][C]0.3893 (2.5685)[/C][C]89.996982[/C][/ROW]
[ROW][C]0.392 (2.551)[/C][C]136.158383[/C][/ROW]
[ROW][C]0.3947 (2.5338)[/C][C]113.464136[/C][/ROW]
[ROW][C]0.3973 (2.5168)[/C][C]33.103213[/C][/ROW]
[ROW][C]0.4 (2.5)[/C][C]31.900626[/C][/ROW]
[ROW][C]0.4027 (2.4834)[/C][C]57.379425[/C][/ROW]
[ROW][C]0.4053 (2.4671)[/C][C]18.361649[/C][/ROW]
[ROW][C]0.408 (2.451)[/C][C]173.511546[/C][/ROW]
[ROW][C]0.4107 (2.4351)[/C][C]85.783267[/C][/ROW]
[ROW][C]0.4133 (2.4194)[/C][C]940.594929[/C][/ROW]
[ROW][C]0.416 (2.4038)[/C][C]14079.701652[/C][/ROW]
[ROW][C]0.4187 (2.3885)[/C][C]3526.560495[/C][/ROW]
[ROW][C]0.4213 (2.3734)[/C][C]1423.339742[/C][/ROW]
[ROW][C]0.424 (2.3585)[/C][C]350.478199[/C][/ROW]
[ROW][C]0.4267 (2.3438)[/C][C]117.237258[/C][/ROW]
[ROW][C]0.4293 (2.3292)[/C][C]47.144303[/C][/ROW]
[ROW][C]0.432 (2.3148)[/C][C]266.375549[/C][/ROW]
[ROW][C]0.4347 (2.3006)[/C][C]27.963408[/C][/ROW]
[ROW][C]0.4373 (2.2866)[/C][C]60.379971[/C][/ROW]
[ROW][C]0.44 (2.2727)[/C][C]5.396099[/C][/ROW]
[ROW][C]0.4427 (2.259)[/C][C]94.141278[/C][/ROW]
[ROW][C]0.4453 (2.2455)[/C][C]99.625457[/C][/ROW]
[ROW][C]0.448 (2.2321)[/C][C]62.36076[/C][/ROW]
[ROW][C]0.4507 (2.2189)[/C][C]48.873597[/C][/ROW]
[ROW][C]0.4533 (2.2059)[/C][C]48.579614[/C][/ROW]
[ROW][C]0.456 (2.193)[/C][C]240.690985[/C][/ROW]
[ROW][C]0.4587 (2.1802)[/C][C]34.443563[/C][/ROW]
[ROW][C]0.4613 (2.1676)[/C][C]49.575728[/C][/ROW]
[ROW][C]0.464 (2.1552)[/C][C]42.522978[/C][/ROW]
[ROW][C]0.4667 (2.1429)[/C][C]50.508575[/C][/ROW]
[ROW][C]0.4693 (2.1307)[/C][C]0.683834[/C][/ROW]
[ROW][C]0.472 (2.1186)[/C][C]515.801934[/C][/ROW]
[ROW][C]0.4747 (2.1067)[/C][C]3.437625[/C][/ROW]
[ROW][C]0.4773 (2.095)[/C][C]126.939257[/C][/ROW]
[ROW][C]0.48 (2.0833)[/C][C]292.405694[/C][/ROW]
[ROW][C]0.4827 (2.0718)[/C][C]31.544685[/C][/ROW]
[ROW][C]0.4853 (2.0604)[/C][C]97.324859[/C][/ROW]
[ROW][C]0.488 (2.0492)[/C][C]26.196496[/C][/ROW]
[ROW][C]0.4907 (2.038)[/C][C]23.824451[/C][/ROW]
[ROW][C]0.4933 (2.027)[/C][C]77.919946[/C][/ROW]
[ROW][C]0.496 (2.0161)[/C][C]853.237673[/C][/ROW]
[ROW][C]0.4987 (2.0053)[/C][C]326.881288[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29893&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29893&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
0.0027 (375)305412.921088
0.0053 (187.5)836275.153364
0.008 (125)25924.242345
0.0107 (93.75)2438.46743
0.0133 (75)60760.562241
0.016 (62.5)248643.39661
0.0187 (53.5714)219726.382379
0.0213 (46.875)5307.430043
0.024 (41.6667)113169.995526
0.0267 (37.5)5632.434995
0.0293 (34.0909)42000.731998
0.032 (31.25)3933.834892
0.0347 (28.8462)23380.749897
0.0373 (26.7857)22184.263032
0.04 (25)45594.791384
0.0427 (23.4375)7580.338001
0.0453 (22.0588)1925.794887
0.048 (20.8333)10964.663604
0.0507 (19.7368)73.73535
0.0533 (18.75)7972.451053
0.056 (17.8571)4058.376269
0.0587 (17.0455)13467.282847
0.0613 (16.3043)2553.825299
0.064 (15.625)3514.172006
0.0667 (15)869.704069
0.0693 (14.4231)466.697005
0.072 (13.8889)87.138234
0.0747 (13.3929)2892.663869
0.0773 (12.931)1907.11472
0.08 (12.5)8035.783217
0.0827 (12.0968)66353.069789
0.0853 (11.7188)12243.133634
0.088 (11.3636)8330.071062
0.0907 (11.0294)3501.405105
0.0933 (10.7143)1215.317187
0.096 (10.4167)648.858007
0.0987 (10.1351)1713.000747
0.1013 (9.8684)56.922523
0.104 (9.6154)4656.230622
0.1067 (9.375)726.147395
0.1093 (9.1463)125.422037
0.112 (8.9286)162.342283
0.1147 (8.7209)463.861461
0.1173 (8.5227)417.84533
0.12 (8.3333)290.424129
0.1227 (8.1522)762.717422
0.1253 (7.9787)327.88452
0.128 (7.8125)169.692982
0.1307 (7.6531)104.31067
0.1333 (7.5)732.145538
0.136 (7.3529)373.506985
0.1387 (7.2115)7.604551
0.1413 (7.0755)220.553988
0.144 (6.9444)839.521161
0.1467 (6.8182)393.246535
0.1493 (6.6964)507.301466
0.152 (6.5789)618.82861
0.1547 (6.4655)78.631513
0.1573 (6.3559)1100.788506
0.16 (6.25)2816.708611
0.1627 (6.1475)5497.013382
0.1653 (6.0484)43080.497912
0.168 (5.9524)38220.275597
0.1707 (5.8594)5263.218754
0.1733 (5.7692)3175.089709
0.176 (5.6818)422.105705
0.1787 (5.597)404.262665
0.1813 (5.5147)96.929115
0.184 (5.4348)268.407257
0.1867 (5.3571)471.357965
0.1893 (5.2817)4.602399
0.192 (5.2083)6.226613
0.1947 (5.137)555.477218
0.1973 (5.0676)105.562383
0.2 (5)106.693124
0.2027 (4.9342)365.21339
0.2053 (4.8701)578.006014
0.208 (4.8077)301.856887
0.2107 (4.7468)12.160869
0.2133 (4.6875)167.999597
0.216 (4.6296)87.634774
0.2187 (4.5732)94.207363
0.2213 (4.5181)72.898752
0.224 (4.4643)40.872729
0.2267 (4.4118)58.267977
0.2293 (4.3605)153.166385
0.232 (4.3103)63.576578
0.2347 (4.2614)142.78437
0.2373 (4.2135)539.460232
0.24 (4.1667)1045.83448
0.2427 (4.1209)68.339186
0.2453 (4.0761)710.483462
0.248 (4.0323)5855.827504
0.2507 (3.9894)21873.575727
0.2533 (3.9474)1517.513805
0.256 (3.9063)411.931544
0.2587 (3.866)61.893128
0.2613 (3.8265)62.82269
0.264 (3.7879)158.711251
0.2667 (3.75)8.586587
0.2693 (3.7129)164.013297
0.272 (3.6765)155.577936
0.2747 (3.6408)168.014205
0.2773 (3.6058)67.286502
0.28 (3.5714)29.916694
0.2827 (3.5377)85.6302
0.2853 (3.5047)203.985743
0.288 (3.4722)59.484349
0.2907 (3.4404)63.294866
0.2933 (3.4091)47.798787
0.296 (3.3784)24.847116
0.2987 (3.3482)3.142518
0.3013 (3.3186)74.742853
0.304 (3.2895)26.040169
0.3067 (3.2609)5.481305
0.3093 (3.2328)64.169891
0.312 (3.2051)52.334359
0.3147 (3.178)105.19286
0.3173 (3.1513)25.478031
0.32 (3.125)9.412664
0.3227 (3.0992)237.788005
0.3253 (3.0738)16.770133
0.328 (3.0488)125.738512
0.3307 (3.0242)1395.603276
0.3333 (3)2117.716663
0.336 (2.9762)198.222107
0.3387 (2.9528)213.673282
0.3413 (2.9297)0.477349
0.344 (2.907)110.526313
0.3467 (2.8846)21.56702
0.3493 (2.8626)314.476129
0.352 (2.8409)78.326184
0.3547 (2.8195)10.083297
0.3573 (2.7985)26.371526
0.36 (2.7778)36.85968
0.3627 (2.7574)379.688317
0.3653 (2.7372)50.55697
0.368 (2.7174)8.913881
0.3707 (2.6978)52.245281
0.3733 (2.6786)20.549021
0.376 (2.6596)29.521128
0.3787 (2.6408)36.3016
0.3813 (2.6224)99.851191
0.384 (2.6042)71.236474
0.3867 (2.5862)5.140791
0.3893 (2.5685)89.996982
0.392 (2.551)136.158383
0.3947 (2.5338)113.464136
0.3973 (2.5168)33.103213
0.4 (2.5)31.900626
0.4027 (2.4834)57.379425
0.4053 (2.4671)18.361649
0.408 (2.451)173.511546
0.4107 (2.4351)85.783267
0.4133 (2.4194)940.594929
0.416 (2.4038)14079.701652
0.4187 (2.3885)3526.560495
0.4213 (2.3734)1423.339742
0.424 (2.3585)350.478199
0.4267 (2.3438)117.237258
0.4293 (2.3292)47.144303
0.432 (2.3148)266.375549
0.4347 (2.3006)27.963408
0.4373 (2.2866)60.379971
0.44 (2.2727)5.396099
0.4427 (2.259)94.141278
0.4453 (2.2455)99.625457
0.448 (2.2321)62.36076
0.4507 (2.2189)48.873597
0.4533 (2.2059)48.579614
0.456 (2.193)240.690985
0.4587 (2.1802)34.443563
0.4613 (2.1676)49.575728
0.464 (2.1552)42.522978
0.4667 (2.1429)50.508575
0.4693 (2.1307)0.683834
0.472 (2.1186)515.801934
0.4747 (2.1067)3.437625
0.4773 (2.095)126.939257
0.48 (2.0833)292.405694
0.4827 (2.0718)31.544685
0.4853 (2.0604)97.324859
0.488 (2.0492)26.196496
0.4907 (2.038)23.824451
0.4933 (2.027)77.919946
0.496 (2.0161)853.237673
0.4987 (2.0053)326.881288


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 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')