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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 computationFri, 05 Dec 2008 08:24:03 -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/05/t1228490686y3df70vtydr6fgw.htm/, Retrieved Thu, 16 May 2024 23:39:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29315, Retrieved Thu, 16 May 2024 23:39:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSeverijns Britt
Estimated Impact177

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] [spectraal unemplo...] [2008-12-05 15:24:03] [78308c9f3efc33d1da821bcd963df161] [Current]
Feedback Forum
2008-12-13 14:39:41 [Loïque Verhasselt] [reply] 
STEP 2:Via spectrum: We zien duidelijk dat de student alle stappen onderneemt om de output van de spectrale analyse goed te interpreteren. Zowel bij het ruwe als de cumulatieve periodogram. Bij het cumulatieve periodogram zien we duidelijk de steil stijgende grafiek die wijst op de lange termijn trend en de trapsgewijze stijging die de seizoenaliteit beschrijft. De student voert de transformatie stap per stap door zodat we goed de veranderingen kunnen waarnemen. In elke methode komt de student een gelijke conclusie uit zoals het zou moeten zijn.
2008-12-13 14:42:00 [Loïque Verhasselt] [reply] 
STEP 3: Een juiste beantwoording van deze stap is nergens te vinden in de workshop. Het was hier de bedoeling om de voorwaarden van stationariteit te controleren via het spectrum en via de ACF. De student geeft alleen maar de output doorheen de workshop,geen specifieke behandeling van deze stap.Wanneer een reeks stationair is, moet ze voldoen aan twee voorwaarden:Eerste voorwaarde: de tijdreeks mag niet geïntegreerd zijn.
Dit wil zeggen dat de ACF (Auto Correlation Function) geen langzaam dalende niet - seizoenale autocorrelatiecoëfficiënten of seizoenale autocorrelatiecoëfficiënten mag bevatten.Dit impliceert eveneens dat het spectrum geen aanwijzing geeft van (sterke) cyclische golven van lage frequentie (lange periodes)of het spectrum geen (sterke) cyclische golven van seizoenale frequentie vertoont.Tweede voorwaarde: de meest waarschijnlijke verandering door toeval is constant over de tijd. Dit betekent een constante standaardfout over de ganse tijdreeks. Dit impliceert een constante spreiding. Deze conditie is nodig om gemakkelijk te kunnen differentiëren tussen veranderingen te wijten aan toeval, en veranderingen die toegeschreven kunnen worden aan exogene factoren.De eerste voorwaarde is zoals gezegd in step 3, niet voldaan. De tijdreeks vertoont nog seizoenaliteit door de cyclusgebondenheid van werkloosheid.De tweede voorwaarde is wel voldaan. We hebben door middel van de gevonden lambda - waarde in step 1 de spreiding constant gemaakt. De betrouwbare p – waarde zegt ons dat de regressie helling niet aan het toeval te wijten is, en zo dus significant is.
2008-12-15 17:19:48 [Steven Vercammen] [reply] 
Dit klopt.Het feit dat de curve nog buiten de 95% Kolmogorov-Smirnov betrouwbaarheidsintervallen ligt wijst erop dat er nog golfbewegingen in de tijdreeks aanwezig zijn die we kunnen verklaren, voorspellen. Het uiteindelijke doel zou moeten zijn dat de curve volledig binnen deze intervallen ligt zodat we elke voorspelbare golfbeweging eruit hebben gehaald. We zien hier een soort van conjunctuurcyclus wat logisch is omdat de werkloosheid nauw verband houdt met de conjunctuur. Het feit dat de curve aan de bovenkant afwijkt is een indicatie dat er hier een AR-proces aanwezig is.
2008-12-15 17:26:26 [Steven Vercammen] [reply] 
STEP 3 wordt nergens besproken. We passen in deze stap echter ook de spectraal analyse toe. Spectraalanalyse wordt gebruikt om willekeurige tijdreeksen te ontbinden in regelmatige golfbewegingen. Een lange termijntrend betekent dat er sprake is van een lange periode en een trage frequentie. Het spectrum geeft de intensiteit van een golfperiode aan, maw hoe belangrijk is deze golfbeweging. We zien hier dat de waarden allemaal zeer laag zijn. Wanneer er nog een lange termijn trend in de reeks aanwezig zou zijn dan zouden we zeer hoge waarde zien bij de lange periodes, dit is echter niet het geval. Er zijn ook geen hoge waarden te vinden bij periodes 6,12, 24,… wat er op wijst dat er ook geen seizonaliteit aanwezig is in de tijdreeks.
Op het raw en cumulative periodogram zien we ook geen aanwijzingen meer dat de tijdreeks niet stationair zou zijn. Er zijn maw geen indicaties voor een lange termijn trend of seizonaliteit.


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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
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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
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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
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148
159.4
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153.6
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151.2
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201.7
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356.1
398.3
403.7
384.6
365.8
368.1
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343.3
292.9
311.5
300.9
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329.7
316.2
269
289.3
266.2
253.6
233.8
228.4
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260.1
306.6
309.2
309.5
271
279.9
317.9
298.4
246.7
227.3
209.1
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320.6
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282.2
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284.3
252.6
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246.5
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511.6
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509.8
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371.1
331.5
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533.5
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462.1
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432.3
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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
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362.8
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289.5
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290.3
272
307.4
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249.1
230.4
361.5
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257.6
241.8
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292.3
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254.2
230
339
318.2
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295.8
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271
262.7
340.6
379.4
373.3
355.2
338.4
466.9
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429.2
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544.2
517.5
469.4
439.4
549
533
506.1
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481.5
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544.7
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434.4
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517.3
485.7
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426.6
411.6
467.5
484.5
451.2
417.4
379.9
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455
420.8
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376.3
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475.5
430.1
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538
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488.5
520.2
504.4
568.5
610.6
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830.9
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762.3
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769.6
752.2
724.4
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803.3
752.5
689
630.4
765.5
757.7
732.2
702.6
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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=29315&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=29315&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29315&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)1
Degree of seasonal differencing (D)1
Seasonal Period (s)12
Frequency (Period)Spectrum
0.0028 (360)28.47367
0.0056 (180)414.292161
0.0083 (120)104.659583
0.0111 (90)527.62959
0.0139 (72)436.831196
0.0167 (60)631.528207
0.0194 (51.4286)5839.526931
0.0222 (45)1169.573349
0.025 (40)5072.18807
0.0278 (36)2213.515735
0.0306 (32.7273)852.336707
0.0333 (30)530.526269
0.0361 (27.6923)11261.18092
0.0389 (25.7143)6978.078336
0.0417 (24)459.614366
0.0444 (22.5)3692.814056
0.0472 (21.1765)2628.95551
0.05 (20)775.979553
0.0528 (18.9474)2893.995714
0.0556 (18)2214.011437
0.0583 (17.1429)3355.14256
0.0611 (16.3636)1307.491068
0.0639 (15.6522)1376.503128
0.0667 (15)267.588572
0.0694 (14.4)51.710806
0.0722 (13.8462)0.898643
0.075 (13.3333)261.375885
0.0778 (12.8571)119.199203
0.0806 (12.4138)87.080052
0.0833 (12)19.728341
0.0861 (11.6129)20.250833
0.0889 (11.25)412.746472
0.0917 (10.9091)55.508656
0.0944 (10.5882)1.792884
0.0972 (10.2857)67.226566
0.1 (10)1059.920249
0.1028 (9.7297)3108.735703
0.1056 (9.4737)139.152789
0.1083 (9.2308)635.633722
0.1111 (9)1.215956
0.1139 (8.7805)1017.652401
0.1167 (8.5714)518.062615
0.1194 (8.3721)975.699483
0.1222 (8.1818)1066.396239
0.125 (8)1180.319748
0.1278 (7.8261)351.203644
0.1306 (7.6596)286.661143
0.1333 (7.5)1571.981167
0.1361 (7.3469)725.70512
0.1389 (7.2)60.092625
0.1417 (7.0588)900.764046
0.1444 (6.9231)667.595856
0.1472 (6.7925)993.521882
0.15 (6.6667)475.721172
0.1528 (6.5455)195.122165
0.1556 (6.4286)98.909622
0.1583 (6.3158)97.311996
0.1611 (6.2069)164.320589
0.1639 (6.1017)98.431157
0.1667 (6)33.698325
0.1694 (5.9016)50.550402
0.1722 (5.8065)375.472754
0.175 (5.7143)8.511937
0.1778 (5.625)160.861268
0.1806 (5.5385)127.439707
0.1833 (5.4545)551.137581
0.1861 (5.3731)297.839469
0.1889 (5.2941)260.703525
0.1917 (5.2174)7.981103
0.1944 (5.1429)1564.389383
0.1972 (5.0704)239.758911
0.2 (5)625.813898
0.2028 (4.9315)2321.90262
0.2056 (4.8649)2869.556434
0.2083 (4.8)1573.859437
0.2111 (4.7368)108.639417
0.2139 (4.6753)935.298211
0.2167 (4.6154)842.467548
0.2194 (4.557)227.504124
0.2222 (4.5)148.088231
0.225 (4.4444)95.643432
0.2278 (4.3902)341.770836
0.2306 (4.3373)536.17233
0.2333 (4.2857)107.567867
0.2361 (4.2353)130.38183
0.2389 (4.186)8.213225
0.2417 (4.1379)745.338556
0.2444 (4.0909)29.698788
0.2472 (4.0449)43.691722
0.25 (4)41.908876
0.2528 (3.956)54.567587
0.2556 (3.913)38.196879
0.2583 (3.871)255.528431
0.2611 (3.8298)16.929041
0.2639 (3.7895)221.37186
0.2667 (3.75)278.820051
0.2694 (3.7113)1154.124681
0.2722 (3.6735)358.15741
0.275 (3.6364)801.474987
0.2778 (3.6)75.938049
0.2806 (3.5644)142.783243
0.2833 (3.5294)356.177064
0.2861 (3.4951)3060.81221
0.2889 (3.4615)20.760888
0.2917 (3.4286)182.723581
0.2944 (3.3962)370.419856
0.2972 (3.3645)63.884539
0.3 (3.3333)117.921087
0.3028 (3.3028)315.866478
0.3056 (3.2727)379.132894
0.3083 (3.2432)345.283894
0.3111 (3.2143)424.96728
0.3139 (3.1858)409.982604
0.3167 (3.1579)145.028319
0.3194 (3.1304)15.430093
0.3222 (3.1034)399.788866
0.325 (3.0769)31.899729
0.3278 (3.0508)62.383933
0.3306 (3.0252)118.884177
0.3333 (3)27.373487
0.3361 (2.9752)21.638867
0.3389 (2.9508)14.244087
0.3417 (2.9268)127.687918
0.3444 (2.9032)28.359501
0.3472 (2.88)112.571672
0.35 (2.8571)1019.932187
0.3528 (2.8346)473.066131
0.3556 (2.8125)489.421993
0.3583 (2.7907)473.937598
0.3611 (2.7692)560.319681
0.3639 (2.7481)2248.32203
0.3667 (2.7273)116.734055
0.3694 (2.7068)238.708351
0.3722 (2.6866)660.480161
0.375 (2.6667)246.379527
0.3778 (2.6471)540.346449
0.3806 (2.6277)1259.722361
0.3833 (2.6087)788.06859
0.3861 (2.5899)196.688116
0.3889 (2.5714)668.642704
0.3917 (2.5532)1188.229112
0.3944 (2.5352)933.439352
0.3972 (2.5175)62.193625
0.4 (2.5)13.350142
0.4028 (2.4828)94.248396
0.4056 (2.4658)50.198259
0.4083 (2.449)81.026515
0.4111 (2.4324)114.513619
0.4139 (2.4161)20.642128
0.4167 (2.4)146.287264
0.4194 (2.3841)44.979104
0.4222 (2.3684)31.638169
0.425 (2.3529)60.237249
0.4278 (2.3377)43.173649
0.4306 (2.3226)589.170987
0.4333 (2.3077)622.959985
0.4361 (2.293)8.900882
0.4389 (2.2785)771.085924
0.4417 (2.2642)1006.968599
0.4444 (2.25)304.823593
0.4472 (2.236)1605.527866
0.45 (2.2222)261.96916
0.4528 (2.2086)505.50468
0.4556 (2.1951)3999.710889
0.4583 (2.1818)718.42606
0.4611 (2.1687)751.190363
0.4639 (2.1557)678.418759
0.4667 (2.1429)933.95044
0.4694 (2.1302)43.074796
0.4722 (2.1176)5855.746814
0.475 (2.1053)32.815179
0.4778 (2.093)1311.654262
0.4806 (2.0809)1699.615978
0.4833 (2.069)159.171774
0.4861 (2.0571)456.965247
0.4889 (2.0455)60.234123
0.4917 (2.0339)167.225704
0.4944 (2.0225)180.46487
0.4972 (2.0112)97.224213
0.5 (2)24.253402

\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
0.0028 (360) & 28.47367 \tabularnewline
0.0056 (180) & 414.292161 \tabularnewline
0.0083 (120) & 104.659583 \tabularnewline
0.0111 (90) & 527.62959 \tabularnewline
0.0139 (72) & 436.831196 \tabularnewline
0.0167 (60) & 631.528207 \tabularnewline
0.0194 (51.4286) & 5839.526931 \tabularnewline
0.0222 (45) & 1169.573349 \tabularnewline
0.025 (40) & 5072.18807 \tabularnewline
0.0278 (36) & 2213.515735 \tabularnewline
0.0306 (32.7273) & 852.336707 \tabularnewline
0.0333 (30) & 530.526269 \tabularnewline
0.0361 (27.6923) & 11261.18092 \tabularnewline
0.0389 (25.7143) & 6978.078336 \tabularnewline
0.0417 (24) & 459.614366 \tabularnewline
0.0444 (22.5) & 3692.814056 \tabularnewline
0.0472 (21.1765) & 2628.95551 \tabularnewline
0.05 (20) & 775.979553 \tabularnewline
0.0528 (18.9474) & 2893.995714 \tabularnewline
0.0556 (18) & 2214.011437 \tabularnewline
0.0583 (17.1429) & 3355.14256 \tabularnewline
0.0611 (16.3636) & 1307.491068 \tabularnewline
0.0639 (15.6522) & 1376.503128 \tabularnewline
0.0667 (15) & 267.588572 \tabularnewline
0.0694 (14.4) & 51.710806 \tabularnewline
0.0722 (13.8462) & 0.898643 \tabularnewline
0.075 (13.3333) & 261.375885 \tabularnewline
0.0778 (12.8571) & 119.199203 \tabularnewline
0.0806 (12.4138) & 87.080052 \tabularnewline
0.0833 (12) & 19.728341 \tabularnewline
0.0861 (11.6129) & 20.250833 \tabularnewline
0.0889 (11.25) & 412.746472 \tabularnewline
0.0917 (10.9091) & 55.508656 \tabularnewline
0.0944 (10.5882) & 1.792884 \tabularnewline
0.0972 (10.2857) & 67.226566 \tabularnewline
0.1 (10) & 1059.920249 \tabularnewline
0.1028 (9.7297) & 3108.735703 \tabularnewline
0.1056 (9.4737) & 139.152789 \tabularnewline
0.1083 (9.2308) & 635.633722 \tabularnewline
0.1111 (9) & 1.215956 \tabularnewline
0.1139 (8.7805) & 1017.652401 \tabularnewline
0.1167 (8.5714) & 518.062615 \tabularnewline
0.1194 (8.3721) & 975.699483 \tabularnewline
0.1222 (8.1818) & 1066.396239 \tabularnewline
0.125 (8) & 1180.319748 \tabularnewline
0.1278 (7.8261) & 351.203644 \tabularnewline
0.1306 (7.6596) & 286.661143 \tabularnewline
0.1333 (7.5) & 1571.981167 \tabularnewline
0.1361 (7.3469) & 725.70512 \tabularnewline
0.1389 (7.2) & 60.092625 \tabularnewline
0.1417 (7.0588) & 900.764046 \tabularnewline
0.1444 (6.9231) & 667.595856 \tabularnewline
0.1472 (6.7925) & 993.521882 \tabularnewline
0.15 (6.6667) & 475.721172 \tabularnewline
0.1528 (6.5455) & 195.122165 \tabularnewline
0.1556 (6.4286) & 98.909622 \tabularnewline
0.1583 (6.3158) & 97.311996 \tabularnewline
0.1611 (6.2069) & 164.320589 \tabularnewline
0.1639 (6.1017) & 98.431157 \tabularnewline
0.1667 (6) & 33.698325 \tabularnewline
0.1694 (5.9016) & 50.550402 \tabularnewline
0.1722 (5.8065) & 375.472754 \tabularnewline
0.175 (5.7143) & 8.511937 \tabularnewline
0.1778 (5.625) & 160.861268 \tabularnewline
0.1806 (5.5385) & 127.439707 \tabularnewline
0.1833 (5.4545) & 551.137581 \tabularnewline
0.1861 (5.3731) & 297.839469 \tabularnewline
0.1889 (5.2941) & 260.703525 \tabularnewline
0.1917 (5.2174) & 7.981103 \tabularnewline
0.1944 (5.1429) & 1564.389383 \tabularnewline
0.1972 (5.0704) & 239.758911 \tabularnewline
0.2 (5) & 625.813898 \tabularnewline
0.2028 (4.9315) & 2321.90262 \tabularnewline
0.2056 (4.8649) & 2869.556434 \tabularnewline
0.2083 (4.8) & 1573.859437 \tabularnewline
0.2111 (4.7368) & 108.639417 \tabularnewline
0.2139 (4.6753) & 935.298211 \tabularnewline
0.2167 (4.6154) & 842.467548 \tabularnewline
0.2194 (4.557) & 227.504124 \tabularnewline
0.2222 (4.5) & 148.088231 \tabularnewline
0.225 (4.4444) & 95.643432 \tabularnewline
0.2278 (4.3902) & 341.770836 \tabularnewline
0.2306 (4.3373) & 536.17233 \tabularnewline
0.2333 (4.2857) & 107.567867 \tabularnewline
0.2361 (4.2353) & 130.38183 \tabularnewline
0.2389 (4.186) & 8.213225 \tabularnewline
0.2417 (4.1379) & 745.338556 \tabularnewline
0.2444 (4.0909) & 29.698788 \tabularnewline
0.2472 (4.0449) & 43.691722 \tabularnewline
0.25 (4) & 41.908876 \tabularnewline
0.2528 (3.956) & 54.567587 \tabularnewline
0.2556 (3.913) & 38.196879 \tabularnewline
0.2583 (3.871) & 255.528431 \tabularnewline
0.2611 (3.8298) & 16.929041 \tabularnewline
0.2639 (3.7895) & 221.37186 \tabularnewline
0.2667 (3.75) & 278.820051 \tabularnewline
0.2694 (3.7113) & 1154.124681 \tabularnewline
0.2722 (3.6735) & 358.15741 \tabularnewline
0.275 (3.6364) & 801.474987 \tabularnewline
0.2778 (3.6) & 75.938049 \tabularnewline
0.2806 (3.5644) & 142.783243 \tabularnewline
0.2833 (3.5294) & 356.177064 \tabularnewline
0.2861 (3.4951) & 3060.81221 \tabularnewline
0.2889 (3.4615) & 20.760888 \tabularnewline
0.2917 (3.4286) & 182.723581 \tabularnewline
0.2944 (3.3962) & 370.419856 \tabularnewline
0.2972 (3.3645) & 63.884539 \tabularnewline
0.3 (3.3333) & 117.921087 \tabularnewline
0.3028 (3.3028) & 315.866478 \tabularnewline
0.3056 (3.2727) & 379.132894 \tabularnewline
0.3083 (3.2432) & 345.283894 \tabularnewline
0.3111 (3.2143) & 424.96728 \tabularnewline
0.3139 (3.1858) & 409.982604 \tabularnewline
0.3167 (3.1579) & 145.028319 \tabularnewline
0.3194 (3.1304) & 15.430093 \tabularnewline
0.3222 (3.1034) & 399.788866 \tabularnewline
0.325 (3.0769) & 31.899729 \tabularnewline
0.3278 (3.0508) & 62.383933 \tabularnewline
0.3306 (3.0252) & 118.884177 \tabularnewline
0.3333 (3) & 27.373487 \tabularnewline
0.3361 (2.9752) & 21.638867 \tabularnewline
0.3389 (2.9508) & 14.244087 \tabularnewline
0.3417 (2.9268) & 127.687918 \tabularnewline
0.3444 (2.9032) & 28.359501 \tabularnewline
0.3472 (2.88) & 112.571672 \tabularnewline
0.35 (2.8571) & 1019.932187 \tabularnewline
0.3528 (2.8346) & 473.066131 \tabularnewline
0.3556 (2.8125) & 489.421993 \tabularnewline
0.3583 (2.7907) & 473.937598 \tabularnewline
0.3611 (2.7692) & 560.319681 \tabularnewline
0.3639 (2.7481) & 2248.32203 \tabularnewline
0.3667 (2.7273) & 116.734055 \tabularnewline
0.3694 (2.7068) & 238.708351 \tabularnewline
0.3722 (2.6866) & 660.480161 \tabularnewline
0.375 (2.6667) & 246.379527 \tabularnewline
0.3778 (2.6471) & 540.346449 \tabularnewline
0.3806 (2.6277) & 1259.722361 \tabularnewline
0.3833 (2.6087) & 788.06859 \tabularnewline
0.3861 (2.5899) & 196.688116 \tabularnewline
0.3889 (2.5714) & 668.642704 \tabularnewline
0.3917 (2.5532) & 1188.229112 \tabularnewline
0.3944 (2.5352) & 933.439352 \tabularnewline
0.3972 (2.5175) & 62.193625 \tabularnewline
0.4 (2.5) & 13.350142 \tabularnewline
0.4028 (2.4828) & 94.248396 \tabularnewline
0.4056 (2.4658) & 50.198259 \tabularnewline
0.4083 (2.449) & 81.026515 \tabularnewline
0.4111 (2.4324) & 114.513619 \tabularnewline
0.4139 (2.4161) & 20.642128 \tabularnewline
0.4167 (2.4) & 146.287264 \tabularnewline
0.4194 (2.3841) & 44.979104 \tabularnewline
0.4222 (2.3684) & 31.638169 \tabularnewline
0.425 (2.3529) & 60.237249 \tabularnewline
0.4278 (2.3377) & 43.173649 \tabularnewline
0.4306 (2.3226) & 589.170987 \tabularnewline
0.4333 (2.3077) & 622.959985 \tabularnewline
0.4361 (2.293) & 8.900882 \tabularnewline
0.4389 (2.2785) & 771.085924 \tabularnewline
0.4417 (2.2642) & 1006.968599 \tabularnewline
0.4444 (2.25) & 304.823593 \tabularnewline
0.4472 (2.236) & 1605.527866 \tabularnewline
0.45 (2.2222) & 261.96916 \tabularnewline
0.4528 (2.2086) & 505.50468 \tabularnewline
0.4556 (2.1951) & 3999.710889 \tabularnewline
0.4583 (2.1818) & 718.42606 \tabularnewline
0.4611 (2.1687) & 751.190363 \tabularnewline
0.4639 (2.1557) & 678.418759 \tabularnewline
0.4667 (2.1429) & 933.95044 \tabularnewline
0.4694 (2.1302) & 43.074796 \tabularnewline
0.4722 (2.1176) & 5855.746814 \tabularnewline
0.475 (2.1053) & 32.815179 \tabularnewline
0.4778 (2.093) & 1311.654262 \tabularnewline
0.4806 (2.0809) & 1699.615978 \tabularnewline
0.4833 (2.069) & 159.171774 \tabularnewline
0.4861 (2.0571) & 456.965247 \tabularnewline
0.4889 (2.0455) & 60.234123 \tabularnewline
0.4917 (2.0339) & 167.225704 \tabularnewline
0.4944 (2.0225) & 180.46487 \tabularnewline
0.4972 (2.0112) & 97.224213 \tabularnewline
0.5 (2) & 24.253402 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29315&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]0.0028 (360)[/C][C]28.47367[/C][/ROW]
[ROW][C]0.0056 (180)[/C][C]414.292161[/C][/ROW]
[ROW][C]0.0083 (120)[/C][C]104.659583[/C][/ROW]
[ROW][C]0.0111 (90)[/C][C]527.62959[/C][/ROW]
[ROW][C]0.0139 (72)[/C][C]436.831196[/C][/ROW]
[ROW][C]0.0167 (60)[/C][C]631.528207[/C][/ROW]
[ROW][C]0.0194 (51.4286)[/C][C]5839.526931[/C][/ROW]
[ROW][C]0.0222 (45)[/C][C]1169.573349[/C][/ROW]
[ROW][C]0.025 (40)[/C][C]5072.18807[/C][/ROW]
[ROW][C]0.0278 (36)[/C][C]2213.515735[/C][/ROW]
[ROW][C]0.0306 (32.7273)[/C][C]852.336707[/C][/ROW]
[ROW][C]0.0333 (30)[/C][C]530.526269[/C][/ROW]
[ROW][C]0.0361 (27.6923)[/C][C]11261.18092[/C][/ROW]
[ROW][C]0.0389 (25.7143)[/C][C]6978.078336[/C][/ROW]
[ROW][C]0.0417 (24)[/C][C]459.614366[/C][/ROW]
[ROW][C]0.0444 (22.5)[/C][C]3692.814056[/C][/ROW]
[ROW][C]0.0472 (21.1765)[/C][C]2628.95551[/C][/ROW]
[ROW][C]0.05 (20)[/C][C]775.979553[/C][/ROW]
[ROW][C]0.0528 (18.9474)[/C][C]2893.995714[/C][/ROW]
[ROW][C]0.0556 (18)[/C][C]2214.011437[/C][/ROW]
[ROW][C]0.0583 (17.1429)[/C][C]3355.14256[/C][/ROW]
[ROW][C]0.0611 (16.3636)[/C][C]1307.491068[/C][/ROW]
[ROW][C]0.0639 (15.6522)[/C][C]1376.503128[/C][/ROW]
[ROW][C]0.0667 (15)[/C][C]267.588572[/C][/ROW]
[ROW][C]0.0694 (14.4)[/C][C]51.710806[/C][/ROW]
[ROW][C]0.0722 (13.8462)[/C][C]0.898643[/C][/ROW]
[ROW][C]0.075 (13.3333)[/C][C]261.375885[/C][/ROW]
[ROW][C]0.0778 (12.8571)[/C][C]119.199203[/C][/ROW]
[ROW][C]0.0806 (12.4138)[/C][C]87.080052[/C][/ROW]
[ROW][C]0.0833 (12)[/C][C]19.728341[/C][/ROW]
[ROW][C]0.0861 (11.6129)[/C][C]20.250833[/C][/ROW]
[ROW][C]0.0889 (11.25)[/C][C]412.746472[/C][/ROW]
[ROW][C]0.0917 (10.9091)[/C][C]55.508656[/C][/ROW]
[ROW][C]0.0944 (10.5882)[/C][C]1.792884[/C][/ROW]
[ROW][C]0.0972 (10.2857)[/C][C]67.226566[/C][/ROW]
[ROW][C]0.1 (10)[/C][C]1059.920249[/C][/ROW]
[ROW][C]0.1028 (9.7297)[/C][C]3108.735703[/C][/ROW]
[ROW][C]0.1056 (9.4737)[/C][C]139.152789[/C][/ROW]
[ROW][C]0.1083 (9.2308)[/C][C]635.633722[/C][/ROW]
[ROW][C]0.1111 (9)[/C][C]1.215956[/C][/ROW]
[ROW][C]0.1139 (8.7805)[/C][C]1017.652401[/C][/ROW]
[ROW][C]0.1167 (8.5714)[/C][C]518.062615[/C][/ROW]
[ROW][C]0.1194 (8.3721)[/C][C]975.699483[/C][/ROW]
[ROW][C]0.1222 (8.1818)[/C][C]1066.396239[/C][/ROW]
[ROW][C]0.125 (8)[/C][C]1180.319748[/C][/ROW]
[ROW][C]0.1278 (7.8261)[/C][C]351.203644[/C][/ROW]
[ROW][C]0.1306 (7.6596)[/C][C]286.661143[/C][/ROW]
[ROW][C]0.1333 (7.5)[/C][C]1571.981167[/C][/ROW]
[ROW][C]0.1361 (7.3469)[/C][C]725.70512[/C][/ROW]
[ROW][C]0.1389 (7.2)[/C][C]60.092625[/C][/ROW]
[ROW][C]0.1417 (7.0588)[/C][C]900.764046[/C][/ROW]
[ROW][C]0.1444 (6.9231)[/C][C]667.595856[/C][/ROW]
[ROW][C]0.1472 (6.7925)[/C][C]993.521882[/C][/ROW]
[ROW][C]0.15 (6.6667)[/C][C]475.721172[/C][/ROW]
[ROW][C]0.1528 (6.5455)[/C][C]195.122165[/C][/ROW]
[ROW][C]0.1556 (6.4286)[/C][C]98.909622[/C][/ROW]
[ROW][C]0.1583 (6.3158)[/C][C]97.311996[/C][/ROW]
[ROW][C]0.1611 (6.2069)[/C][C]164.320589[/C][/ROW]
[ROW][C]0.1639 (6.1017)[/C][C]98.431157[/C][/ROW]
[ROW][C]0.1667 (6)[/C][C]33.698325[/C][/ROW]
[ROW][C]0.1694 (5.9016)[/C][C]50.550402[/C][/ROW]
[ROW][C]0.1722 (5.8065)[/C][C]375.472754[/C][/ROW]
[ROW][C]0.175 (5.7143)[/C][C]8.511937[/C][/ROW]
[ROW][C]0.1778 (5.625)[/C][C]160.861268[/C][/ROW]
[ROW][C]0.1806 (5.5385)[/C][C]127.439707[/C][/ROW]
[ROW][C]0.1833 (5.4545)[/C][C]551.137581[/C][/ROW]
[ROW][C]0.1861 (5.3731)[/C][C]297.839469[/C][/ROW]
[ROW][C]0.1889 (5.2941)[/C][C]260.703525[/C][/ROW]
[ROW][C]0.1917 (5.2174)[/C][C]7.981103[/C][/ROW]
[ROW][C]0.1944 (5.1429)[/C][C]1564.389383[/C][/ROW]
[ROW][C]0.1972 (5.0704)[/C][C]239.758911[/C][/ROW]
[ROW][C]0.2 (5)[/C][C]625.813898[/C][/ROW]
[ROW][C]0.2028 (4.9315)[/C][C]2321.90262[/C][/ROW]
[ROW][C]0.2056 (4.8649)[/C][C]2869.556434[/C][/ROW]
[ROW][C]0.2083 (4.8)[/C][C]1573.859437[/C][/ROW]
[ROW][C]0.2111 (4.7368)[/C][C]108.639417[/C][/ROW]
[ROW][C]0.2139 (4.6753)[/C][C]935.298211[/C][/ROW]
[ROW][C]0.2167 (4.6154)[/C][C]842.467548[/C][/ROW]
[ROW][C]0.2194 (4.557)[/C][C]227.504124[/C][/ROW]
[ROW][C]0.2222 (4.5)[/C][C]148.088231[/C][/ROW]
[ROW][C]0.225 (4.4444)[/C][C]95.643432[/C][/ROW]
[ROW][C]0.2278 (4.3902)[/C][C]341.770836[/C][/ROW]
[ROW][C]0.2306 (4.3373)[/C][C]536.17233[/C][/ROW]
[ROW][C]0.2333 (4.2857)[/C][C]107.567867[/C][/ROW]
[ROW][C]0.2361 (4.2353)[/C][C]130.38183[/C][/ROW]
[ROW][C]0.2389 (4.186)[/C][C]8.213225[/C][/ROW]
[ROW][C]0.2417 (4.1379)[/C][C]745.338556[/C][/ROW]
[ROW][C]0.2444 (4.0909)[/C][C]29.698788[/C][/ROW]
[ROW][C]0.2472 (4.0449)[/C][C]43.691722[/C][/ROW]
[ROW][C]0.25 (4)[/C][C]41.908876[/C][/ROW]
[ROW][C]0.2528 (3.956)[/C][C]54.567587[/C][/ROW]
[ROW][C]0.2556 (3.913)[/C][C]38.196879[/C][/ROW]
[ROW][C]0.2583 (3.871)[/C][C]255.528431[/C][/ROW]
[ROW][C]0.2611 (3.8298)[/C][C]16.929041[/C][/ROW]
[ROW][C]0.2639 (3.7895)[/C][C]221.37186[/C][/ROW]
[ROW][C]0.2667 (3.75)[/C][C]278.820051[/C][/ROW]
[ROW][C]0.2694 (3.7113)[/C][C]1154.124681[/C][/ROW]
[ROW][C]0.2722 (3.6735)[/C][C]358.15741[/C][/ROW]
[ROW][C]0.275 (3.6364)[/C][C]801.474987[/C][/ROW]
[ROW][C]0.2778 (3.6)[/C][C]75.938049[/C][/ROW]
[ROW][C]0.2806 (3.5644)[/C][C]142.783243[/C][/ROW]
[ROW][C]0.2833 (3.5294)[/C][C]356.177064[/C][/ROW]
[ROW][C]0.2861 (3.4951)[/C][C]3060.81221[/C][/ROW]
[ROW][C]0.2889 (3.4615)[/C][C]20.760888[/C][/ROW]
[ROW][C]0.2917 (3.4286)[/C][C]182.723581[/C][/ROW]
[ROW][C]0.2944 (3.3962)[/C][C]370.419856[/C][/ROW]
[ROW][C]0.2972 (3.3645)[/C][C]63.884539[/C][/ROW]
[ROW][C]0.3 (3.3333)[/C][C]117.921087[/C][/ROW]
[ROW][C]0.3028 (3.3028)[/C][C]315.866478[/C][/ROW]
[ROW][C]0.3056 (3.2727)[/C][C]379.132894[/C][/ROW]
[ROW][C]0.3083 (3.2432)[/C][C]345.283894[/C][/ROW]
[ROW][C]0.3111 (3.2143)[/C][C]424.96728[/C][/ROW]
[ROW][C]0.3139 (3.1858)[/C][C]409.982604[/C][/ROW]
[ROW][C]0.3167 (3.1579)[/C][C]145.028319[/C][/ROW]
[ROW][C]0.3194 (3.1304)[/C][C]15.430093[/C][/ROW]
[ROW][C]0.3222 (3.1034)[/C][C]399.788866[/C][/ROW]
[ROW][C]0.325 (3.0769)[/C][C]31.899729[/C][/ROW]
[ROW][C]0.3278 (3.0508)[/C][C]62.383933[/C][/ROW]
[ROW][C]0.3306 (3.0252)[/C][C]118.884177[/C][/ROW]
[ROW][C]0.3333 (3)[/C][C]27.373487[/C][/ROW]
[ROW][C]0.3361 (2.9752)[/C][C]21.638867[/C][/ROW]
[ROW][C]0.3389 (2.9508)[/C][C]14.244087[/C][/ROW]
[ROW][C]0.3417 (2.9268)[/C][C]127.687918[/C][/ROW]
[ROW][C]0.3444 (2.9032)[/C][C]28.359501[/C][/ROW]
[ROW][C]0.3472 (2.88)[/C][C]112.571672[/C][/ROW]
[ROW][C]0.35 (2.8571)[/C][C]1019.932187[/C][/ROW]
[ROW][C]0.3528 (2.8346)[/C][C]473.066131[/C][/ROW]
[ROW][C]0.3556 (2.8125)[/C][C]489.421993[/C][/ROW]
[ROW][C]0.3583 (2.7907)[/C][C]473.937598[/C][/ROW]
[ROW][C]0.3611 (2.7692)[/C][C]560.319681[/C][/ROW]
[ROW][C]0.3639 (2.7481)[/C][C]2248.32203[/C][/ROW]
[ROW][C]0.3667 (2.7273)[/C][C]116.734055[/C][/ROW]
[ROW][C]0.3694 (2.7068)[/C][C]238.708351[/C][/ROW]
[ROW][C]0.3722 (2.6866)[/C][C]660.480161[/C][/ROW]
[ROW][C]0.375 (2.6667)[/C][C]246.379527[/C][/ROW]
[ROW][C]0.3778 (2.6471)[/C][C]540.346449[/C][/ROW]
[ROW][C]0.3806 (2.6277)[/C][C]1259.722361[/C][/ROW]
[ROW][C]0.3833 (2.6087)[/C][C]788.06859[/C][/ROW]
[ROW][C]0.3861 (2.5899)[/C][C]196.688116[/C][/ROW]
[ROW][C]0.3889 (2.5714)[/C][C]668.642704[/C][/ROW]
[ROW][C]0.3917 (2.5532)[/C][C]1188.229112[/C][/ROW]
[ROW][C]0.3944 (2.5352)[/C][C]933.439352[/C][/ROW]
[ROW][C]0.3972 (2.5175)[/C][C]62.193625[/C][/ROW]
[ROW][C]0.4 (2.5)[/C][C]13.350142[/C][/ROW]
[ROW][C]0.4028 (2.4828)[/C][C]94.248396[/C][/ROW]
[ROW][C]0.4056 (2.4658)[/C][C]50.198259[/C][/ROW]
[ROW][C]0.4083 (2.449)[/C][C]81.026515[/C][/ROW]
[ROW][C]0.4111 (2.4324)[/C][C]114.513619[/C][/ROW]
[ROW][C]0.4139 (2.4161)[/C][C]20.642128[/C][/ROW]
[ROW][C]0.4167 (2.4)[/C][C]146.287264[/C][/ROW]
[ROW][C]0.4194 (2.3841)[/C][C]44.979104[/C][/ROW]
[ROW][C]0.4222 (2.3684)[/C][C]31.638169[/C][/ROW]
[ROW][C]0.425 (2.3529)[/C][C]60.237249[/C][/ROW]
[ROW][C]0.4278 (2.3377)[/C][C]43.173649[/C][/ROW]
[ROW][C]0.4306 (2.3226)[/C][C]589.170987[/C][/ROW]
[ROW][C]0.4333 (2.3077)[/C][C]622.959985[/C][/ROW]
[ROW][C]0.4361 (2.293)[/C][C]8.900882[/C][/ROW]
[ROW][C]0.4389 (2.2785)[/C][C]771.085924[/C][/ROW]
[ROW][C]0.4417 (2.2642)[/C][C]1006.968599[/C][/ROW]
[ROW][C]0.4444 (2.25)[/C][C]304.823593[/C][/ROW]
[ROW][C]0.4472 (2.236)[/C][C]1605.527866[/C][/ROW]
[ROW][C]0.45 (2.2222)[/C][C]261.96916[/C][/ROW]
[ROW][C]0.4528 (2.2086)[/C][C]505.50468[/C][/ROW]
[ROW][C]0.4556 (2.1951)[/C][C]3999.710889[/C][/ROW]
[ROW][C]0.4583 (2.1818)[/C][C]718.42606[/C][/ROW]
[ROW][C]0.4611 (2.1687)[/C][C]751.190363[/C][/ROW]
[ROW][C]0.4639 (2.1557)[/C][C]678.418759[/C][/ROW]
[ROW][C]0.4667 (2.1429)[/C][C]933.95044[/C][/ROW]
[ROW][C]0.4694 (2.1302)[/C][C]43.074796[/C][/ROW]
[ROW][C]0.4722 (2.1176)[/C][C]5855.746814[/C][/ROW]
[ROW][C]0.475 (2.1053)[/C][C]32.815179[/C][/ROW]
[ROW][C]0.4778 (2.093)[/C][C]1311.654262[/C][/ROW]
[ROW][C]0.4806 (2.0809)[/C][C]1699.615978[/C][/ROW]
[ROW][C]0.4833 (2.069)[/C][C]159.171774[/C][/ROW]
[ROW][C]0.4861 (2.0571)[/C][C]456.965247[/C][/ROW]
[ROW][C]0.4889 (2.0455)[/C][C]60.234123[/C][/ROW]
[ROW][C]0.4917 (2.0339)[/C][C]167.225704[/C][/ROW]
[ROW][C]0.4944 (2.0225)[/C][C]180.46487[/C][/ROW]
[ROW][C]0.4972 (2.0112)[/C][C]97.224213[/C][/ROW]
[ROW][C]0.5 (2)[/C][C]24.253402[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29315&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29315&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
0.0028 (360)28.47367
0.0056 (180)414.292161
0.0083 (120)104.659583
0.0111 (90)527.62959
0.0139 (72)436.831196
0.0167 (60)631.528207
0.0194 (51.4286)5839.526931
0.0222 (45)1169.573349
0.025 (40)5072.18807
0.0278 (36)2213.515735
0.0306 (32.7273)852.336707
0.0333 (30)530.526269
0.0361 (27.6923)11261.18092
0.0389 (25.7143)6978.078336
0.0417 (24)459.614366
0.0444 (22.5)3692.814056
0.0472 (21.1765)2628.95551
0.05 (20)775.979553
0.0528 (18.9474)2893.995714
0.0556 (18)2214.011437
0.0583 (17.1429)3355.14256
0.0611 (16.3636)1307.491068
0.0639 (15.6522)1376.503128
0.0667 (15)267.588572
0.0694 (14.4)51.710806
0.0722 (13.8462)0.898643
0.075 (13.3333)261.375885
0.0778 (12.8571)119.199203
0.0806 (12.4138)87.080052
0.0833 (12)19.728341
0.0861 (11.6129)20.250833
0.0889 (11.25)412.746472
0.0917 (10.9091)55.508656
0.0944 (10.5882)1.792884
0.0972 (10.2857)67.226566
0.1 (10)1059.920249
0.1028 (9.7297)3108.735703
0.1056 (9.4737)139.152789
0.1083 (9.2308)635.633722
0.1111 (9)1.215956
0.1139 (8.7805)1017.652401
0.1167 (8.5714)518.062615
0.1194 (8.3721)975.699483
0.1222 (8.1818)1066.396239
0.125 (8)1180.319748
0.1278 (7.8261)351.203644
0.1306 (7.6596)286.661143
0.1333 (7.5)1571.981167
0.1361 (7.3469)725.70512
0.1389 (7.2)60.092625
0.1417 (7.0588)900.764046
0.1444 (6.9231)667.595856
0.1472 (6.7925)993.521882
0.15 (6.6667)475.721172
0.1528 (6.5455)195.122165
0.1556 (6.4286)98.909622
0.1583 (6.3158)97.311996
0.1611 (6.2069)164.320589
0.1639 (6.1017)98.431157
0.1667 (6)33.698325
0.1694 (5.9016)50.550402
0.1722 (5.8065)375.472754
0.175 (5.7143)8.511937
0.1778 (5.625)160.861268
0.1806 (5.5385)127.439707
0.1833 (5.4545)551.137581
0.1861 (5.3731)297.839469
0.1889 (5.2941)260.703525
0.1917 (5.2174)7.981103
0.1944 (5.1429)1564.389383
0.1972 (5.0704)239.758911
0.2 (5)625.813898
0.2028 (4.9315)2321.90262
0.2056 (4.8649)2869.556434
0.2083 (4.8)1573.859437
0.2111 (4.7368)108.639417
0.2139 (4.6753)935.298211
0.2167 (4.6154)842.467548
0.2194 (4.557)227.504124
0.2222 (4.5)148.088231
0.225 (4.4444)95.643432
0.2278 (4.3902)341.770836
0.2306 (4.3373)536.17233
0.2333 (4.2857)107.567867
0.2361 (4.2353)130.38183
0.2389 (4.186)8.213225
0.2417 (4.1379)745.338556
0.2444 (4.0909)29.698788
0.2472 (4.0449)43.691722
0.25 (4)41.908876
0.2528 (3.956)54.567587
0.2556 (3.913)38.196879
0.2583 (3.871)255.528431
0.2611 (3.8298)16.929041
0.2639 (3.7895)221.37186
0.2667 (3.75)278.820051
0.2694 (3.7113)1154.124681
0.2722 (3.6735)358.15741
0.275 (3.6364)801.474987
0.2778 (3.6)75.938049
0.2806 (3.5644)142.783243
0.2833 (3.5294)356.177064
0.2861 (3.4951)3060.81221
0.2889 (3.4615)20.760888
0.2917 (3.4286)182.723581
0.2944 (3.3962)370.419856
0.2972 (3.3645)63.884539
0.3 (3.3333)117.921087
0.3028 (3.3028)315.866478
0.3056 (3.2727)379.132894
0.3083 (3.2432)345.283894
0.3111 (3.2143)424.96728
0.3139 (3.1858)409.982604
0.3167 (3.1579)145.028319
0.3194 (3.1304)15.430093
0.3222 (3.1034)399.788866
0.325 (3.0769)31.899729
0.3278 (3.0508)62.383933
0.3306 (3.0252)118.884177
0.3333 (3)27.373487
0.3361 (2.9752)21.638867
0.3389 (2.9508)14.244087
0.3417 (2.9268)127.687918
0.3444 (2.9032)28.359501
0.3472 (2.88)112.571672
0.35 (2.8571)1019.932187
0.3528 (2.8346)473.066131
0.3556 (2.8125)489.421993
0.3583 (2.7907)473.937598
0.3611 (2.7692)560.319681
0.3639 (2.7481)2248.32203
0.3667 (2.7273)116.734055
0.3694 (2.7068)238.708351
0.3722 (2.6866)660.480161
0.375 (2.6667)246.379527
0.3778 (2.6471)540.346449
0.3806 (2.6277)1259.722361
0.3833 (2.6087)788.06859
0.3861 (2.5899)196.688116
0.3889 (2.5714)668.642704
0.3917 (2.5532)1188.229112
0.3944 (2.5352)933.439352
0.3972 (2.5175)62.193625
0.4 (2.5)13.350142
0.4028 (2.4828)94.248396
0.4056 (2.4658)50.198259
0.4083 (2.449)81.026515
0.4111 (2.4324)114.513619
0.4139 (2.4161)20.642128
0.4167 (2.4)146.287264
0.4194 (2.3841)44.979104
0.4222 (2.3684)31.638169
0.425 (2.3529)60.237249
0.4278 (2.3377)43.173649
0.4306 (2.3226)589.170987
0.4333 (2.3077)622.959985
0.4361 (2.293)8.900882
0.4389 (2.2785)771.085924
0.4417 (2.2642)1006.968599
0.4444 (2.25)304.823593
0.4472 (2.236)1605.527866
0.45 (2.2222)261.96916
0.4528 (2.2086)505.50468
0.4556 (2.1951)3999.710889
0.4583 (2.1818)718.42606
0.4611 (2.1687)751.190363
0.4639 (2.1557)678.418759
0.4667 (2.1429)933.95044
0.4694 (2.1302)43.074796
0.4722 (2.1176)5855.746814
0.475 (2.1053)32.815179
0.4778 (2.093)1311.654262
0.4806 (2.0809)1699.615978
0.4833 (2.069)159.171774
0.4861 (2.0571)456.965247
0.4889 (2.0455)60.234123
0.4917 (2.0339)167.225704
0.4944 (2.0225)180.46487
0.4972 (2.0112)97.224213
0.5 (2)24.253402


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 1 ; par3 = 1 ; 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')