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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 computationTue, 09 Dec 2008 08:55:43 -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/09/t1228838195g4jvqz5jae6tdi8.htm/, Retrieved Sun, 19 May 2024 10:41:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31539, Retrieved Sun, 19 May 2024 10:41:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact147

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] [] [2008-12-09 15:55:43] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum
2008-12-15 13:55:10 [Stefan Temmerman] [reply] 
Het Raw Periodogram vertoont geen trend, maar wel nog seizoenaliteit, te zien aan de pieken op de grafiek. Het Cumulative Periodogram vertelt ons hetzelfde, en laat zien dat er nog voorspellingen aan de hand van het verleden kunnen gedaan worden, omdat de grafiek buiten de stippellijnen komt.
Voor step 3 : De student zegt niets over de voorwaarden voor een stationaire reeks te krijgen. Deze zijn de spreiding wegwerken, door middel van de lambda waarde, en de trend & de seizoenaliteit verwijderen door differentiatie. Bij de unemployment reeks is er nog seizoenaliteit aanwezig, dit door de sterke cyclusgebondenheid.
2008-12-15 18:39:53 [Jasmine Hendrikx] [reply] 
Evaluatie stap 2 en stap 3 Spectral Analysis:
De berekening is goed uitgevoerd. Wel zijn d en D ineens gelijkgesteld aan 1. Eerst zou je dus de spectrale analyse moeten toepassen zonder transformatie, dus met d en D gelijk aan 0. Vervolgens zou je d kunnen gelijk stellen aan 1 en D aan 0 en daarna d en D gelijk stellen aan 1. Zo zie de evolutie beter. De conclusie die hier is gegeven is wel juist. Er is geen sprake van seizoenaliteit (geen trappen) en geen langetermijntrend (geen steile lijn aan de linkerkant van de grafiek). Zoals de student ook correct vermeldt, ligt de curve gedeeltelijk buiten het betrouwbaarheidsinterval. Er zijn dus nog wel wat golfbewegingen die voorspelbaar zijn. We zien vooral een afwijking naar boven. De golfbeweging zal niets te maken hebben met de langetermijntrend of met seizoenaliteit. Waarschijnlijk hebben we te maken met conjunctuur (regelmatige terugkerende periodes). Dit is ook wel logisch, aangezien het hier om werkloosheidscijfers gaat.
De volgende vuistregel is hier belangrijk: indien het cumulatief periodogram van de tijdreeks een afwijking vertoont aan bovenkant van diagonaal, dan is het zeer waarschijnlijk dat we een AR proces zullen hebben. Dit is hier het geval. Wanneer we echter een afwijking onderaan hebben, duidt dit op een MA proces.

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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=31539&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=31539&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31539&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)0.5
Degree of non-seasonal differencing (d)1
Degree of seasonal differencing (D)1
Seasonal Period (s)12
Frequency (Period)Spectrum
0.0028 (360)0.057564
0.0056 (180)1.069301
0.0083 (120)0.220896
0.0111 (90)1.481315
0.0139 (72)0.995928
0.0167 (60)1.648276
0.0194 (51.4286)14.564678
0.0222 (45)1.840394
0.025 (40)12.766487
0.0278 (36)6.105788
0.0306 (32.7273)1.015385
0.0333 (30)0.399904
0.0361 (27.6923)29.526143
0.0389 (25.7143)18.248319
0.0417 (24)3.141788
0.0444 (22.5)10.236947
0.0472 (21.1765)6.590284
0.05 (20)1.145137
0.0528 (18.9474)4.348657
0.0556 (18)4.977999
0.0583 (17.1429)6.398841
0.0611 (16.3636)3.751172
0.0639 (15.6522)2.750313
0.0667 (15)0.533473
0.0694 (14.4)0.00977
0.0722 (13.8462)0.034506
0.075 (13.3333)0.835831
0.0778 (12.8571)0.166592
0.0806 (12.4138)0.261723
0.0833 (12)0.079353
0.0861 (11.6129)0.062316
0.0889 (11.25)0.609494
0.0917 (10.9091)0.130312
0.0944 (10.5882)0.02373
0.0972 (10.2857)0.078748
0.1 (10)2.109489
0.1028 (9.7297)7.511028
0.1056 (9.4737)0.502386
0.1083 (9.2308)2.636419
0.1111 (9)0.092986
0.1139 (8.7805)2.780718
0.1167 (8.5714)1.884332
0.1194 (8.3721)1.066026
0.1222 (8.1818)1.546977
0.125 (8)2.761493
0.1278 (7.8261)1.443971
0.1306 (7.6596)0.494138
0.1333 (7.5)4.404072
0.1361 (7.3469)1.28824
0.1389 (7.2)0.407265
0.1417 (7.0588)2.086069
0.1444 (6.9231)1.529735
0.1472 (6.7925)1.827748
0.15 (6.6667)2.541578
0.1528 (6.5455)0.581608
0.1556 (6.4286)0.640041
0.1583 (6.3158)0.354925
0.1611 (6.2069)0.041893
0.1639 (6.1017)0.246845
0.1667 (6)0.001917
0.1694 (5.9016)0.047417
0.1722 (5.8065)0.266618
0.175 (5.7143)0.018036
0.1778 (5.625)0.255299
0.1806 (5.5385)0.536108
0.1833 (5.4545)0.907431
0.1861 (5.3731)0.109349
0.1889 (5.2941)1.068629
0.1917 (5.2174)0.315716
0.1944 (5.1429)5.500412
0.1972 (5.0704)0.278307
0.2 (5)1.697187
0.2028 (4.9315)3.67589
0.2056 (4.8649)7.05649
0.2083 (4.8)4.592939
0.2111 (4.7368)0.587473
0.2139 (4.6753)2.068199
0.2167 (4.6154)1.642435
0.2194 (4.557)1.211529
0.2222 (4.5)0.365791
0.225 (4.4444)0.408188
0.2278 (4.3902)0.823555
0.2306 (4.3373)1.102988
0.2333 (4.2857)0.288742
0.2361 (4.2353)0.282547
0.2389 (4.186)0.008686
0.2417 (4.1379)1.972778
0.2444 (4.0909)0.059989
0.2472 (4.0449)0.165035
0.25 (4)0.022804
0.2528 (3.956)0.269391
0.2556 (3.913)0.052386
0.2583 (3.871)0.817169
0.2611 (3.8298)0.109156
0.2639 (3.7895)0.857574
0.2667 (3.75)0.854041
0.2694 (3.7113)4.952492
0.2722 (3.6735)0.965341
0.275 (3.6364)1.409417
0.2778 (3.6)0.052283
0.2806 (3.5644)0.016725
0.2833 (3.5294)1.605788
0.2861 (3.4951)7.08246
0.2889 (3.4615)0.107544
0.2917 (3.4286)1.354278
0.2944 (3.3962)1.166439
0.2972 (3.3645)0.596559
0.3 (3.3333)0.522582
0.3028 (3.3028)0.661809
0.3056 (3.2727)1.12578
0.3083 (3.2432)0.863734
0.3111 (3.2143)0.797993
0.3139 (3.1858)1.358446
0.3167 (3.1579)0.223895
0.3194 (3.1304)0.085736
0.3222 (3.1034)1.264808
0.325 (3.0769)0.247023
0.3278 (3.0508)0.188419
0.3306 (3.0252)0.337802
0.3333 (3)0.043553
0.3361 (2.9752)0.034062
0.3389 (2.9508)0.018071
0.3417 (2.9268)0.344637
0.3444 (2.9032)0.060212
0.3472 (2.88)0.69594
0.35 (2.8571)2.590298
0.3528 (2.8346)1.002245
0.3556 (2.8125)1.35004
0.3583 (2.7907)2.291366
0.3611 (2.7692)2.001674
0.3639 (2.7481)7.119634
0.3667 (2.7273)0.569299
0.3694 (2.7068)0.577886
0.3722 (2.6866)2.447876
0.375 (2.6667)0.716116
0.3778 (2.6471)0.754038
0.3806 (2.6277)4.874199
0.3833 (2.6087)1.824984
0.3861 (2.5899)0.549589
0.3889 (2.5714)1.235879
0.3917 (2.5532)4.102519
0.3944 (2.5352)2.003635
0.3972 (2.5175)0.620427
0.4 (2.5)0.204581
0.4028 (2.4828)0.515653
0.4056 (2.4658)0.019598
0.4083 (2.449)0.154699
0.4111 (2.4324)0.626278
0.4139 (2.4161)0.139812
0.4167 (2.4)0.167326
0.4194 (2.3841)0.084877
0.4222 (2.3684)0.196339
0.425 (2.3529)0.182845
0.4278 (2.3377)0.190421
0.4306 (2.3226)1.683037
0.4333 (2.3077)1.275025
0.4361 (2.293)0.342482
0.4389 (2.2785)1.607396
0.4417 (2.2642)1.564525
0.4444 (2.25)0.621786
0.4472 (2.236)4.467569
0.45 (2.2222)0.658739
0.4528 (2.2086)2.469759
0.4556 (2.1951)10.543687
0.4583 (2.1818)2.885492
0.4611 (2.1687)1.395165
0.4639 (2.1557)1.616309
0.4667 (2.1429)2.382695
0.4694 (2.1302)0.116625
0.4722 (2.1176)14.787816
0.475 (2.1053)0.485626
0.4778 (2.093)2.266653
0.4806 (2.0809)3.693014
0.4833 (2.069)0.066857
0.4861 (2.0571)0.987105
0.4889 (2.0455)0.06478
0.4917 (2.0339)0.528923
0.4944 (2.0225)0.340026
0.4972 (2.0112)0.36196
0.5 (2)0.070405

\begin{tabular}{lllllllll}
\hline
Raw Periodogram \tabularnewline
Parameter & Value \tabularnewline
Box-Cox transformation parameter (lambda) & 0.5 \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) & 0.057564 \tabularnewline
0.0056 (180) & 1.069301 \tabularnewline
0.0083 (120) & 0.220896 \tabularnewline
0.0111 (90) & 1.481315 \tabularnewline
0.0139 (72) & 0.995928 \tabularnewline
0.0167 (60) & 1.648276 \tabularnewline
0.0194 (51.4286) & 14.564678 \tabularnewline
0.0222 (45) & 1.840394 \tabularnewline
0.025 (40) & 12.766487 \tabularnewline
0.0278 (36) & 6.105788 \tabularnewline
0.0306 (32.7273) & 1.015385 \tabularnewline
0.0333 (30) & 0.399904 \tabularnewline
0.0361 (27.6923) & 29.526143 \tabularnewline
0.0389 (25.7143) & 18.248319 \tabularnewline
0.0417 (24) & 3.141788 \tabularnewline
0.0444 (22.5) & 10.236947 \tabularnewline
0.0472 (21.1765) & 6.590284 \tabularnewline
0.05 (20) & 1.145137 \tabularnewline
0.0528 (18.9474) & 4.348657 \tabularnewline
0.0556 (18) & 4.977999 \tabularnewline
0.0583 (17.1429) & 6.398841 \tabularnewline
0.0611 (16.3636) & 3.751172 \tabularnewline
0.0639 (15.6522) & 2.750313 \tabularnewline
0.0667 (15) & 0.533473 \tabularnewline
0.0694 (14.4) & 0.00977 \tabularnewline
0.0722 (13.8462) & 0.034506 \tabularnewline
0.075 (13.3333) & 0.835831 \tabularnewline
0.0778 (12.8571) & 0.166592 \tabularnewline
0.0806 (12.4138) & 0.261723 \tabularnewline
0.0833 (12) & 0.079353 \tabularnewline
0.0861 (11.6129) & 0.062316 \tabularnewline
0.0889 (11.25) & 0.609494 \tabularnewline
0.0917 (10.9091) & 0.130312 \tabularnewline
0.0944 (10.5882) & 0.02373 \tabularnewline
0.0972 (10.2857) & 0.078748 \tabularnewline
0.1 (10) & 2.109489 \tabularnewline
0.1028 (9.7297) & 7.511028 \tabularnewline
0.1056 (9.4737) & 0.502386 \tabularnewline
0.1083 (9.2308) & 2.636419 \tabularnewline
0.1111 (9) & 0.092986 \tabularnewline
0.1139 (8.7805) & 2.780718 \tabularnewline
0.1167 (8.5714) & 1.884332 \tabularnewline
0.1194 (8.3721) & 1.066026 \tabularnewline
0.1222 (8.1818) & 1.546977 \tabularnewline
0.125 (8) & 2.761493 \tabularnewline
0.1278 (7.8261) & 1.443971 \tabularnewline
0.1306 (7.6596) & 0.494138 \tabularnewline
0.1333 (7.5) & 4.404072 \tabularnewline
0.1361 (7.3469) & 1.28824 \tabularnewline
0.1389 (7.2) & 0.407265 \tabularnewline
0.1417 (7.0588) & 2.086069 \tabularnewline
0.1444 (6.9231) & 1.529735 \tabularnewline
0.1472 (6.7925) & 1.827748 \tabularnewline
0.15 (6.6667) & 2.541578 \tabularnewline
0.1528 (6.5455) & 0.581608 \tabularnewline
0.1556 (6.4286) & 0.640041 \tabularnewline
0.1583 (6.3158) & 0.354925 \tabularnewline
0.1611 (6.2069) & 0.041893 \tabularnewline
0.1639 (6.1017) & 0.246845 \tabularnewline
0.1667 (6) & 0.001917 \tabularnewline
0.1694 (5.9016) & 0.047417 \tabularnewline
0.1722 (5.8065) & 0.266618 \tabularnewline
0.175 (5.7143) & 0.018036 \tabularnewline
0.1778 (5.625) & 0.255299 \tabularnewline
0.1806 (5.5385) & 0.536108 \tabularnewline
0.1833 (5.4545) & 0.907431 \tabularnewline
0.1861 (5.3731) & 0.109349 \tabularnewline
0.1889 (5.2941) & 1.068629 \tabularnewline
0.1917 (5.2174) & 0.315716 \tabularnewline
0.1944 (5.1429) & 5.500412 \tabularnewline
0.1972 (5.0704) & 0.278307 \tabularnewline
0.2 (5) & 1.697187 \tabularnewline
0.2028 (4.9315) & 3.67589 \tabularnewline
0.2056 (4.8649) & 7.05649 \tabularnewline
0.2083 (4.8) & 4.592939 \tabularnewline
0.2111 (4.7368) & 0.587473 \tabularnewline
0.2139 (4.6753) & 2.068199 \tabularnewline
0.2167 (4.6154) & 1.642435 \tabularnewline
0.2194 (4.557) & 1.211529 \tabularnewline
0.2222 (4.5) & 0.365791 \tabularnewline
0.225 (4.4444) & 0.408188 \tabularnewline
0.2278 (4.3902) & 0.823555 \tabularnewline
0.2306 (4.3373) & 1.102988 \tabularnewline
0.2333 (4.2857) & 0.288742 \tabularnewline
0.2361 (4.2353) & 0.282547 \tabularnewline
0.2389 (4.186) & 0.008686 \tabularnewline
0.2417 (4.1379) & 1.972778 \tabularnewline
0.2444 (4.0909) & 0.059989 \tabularnewline
0.2472 (4.0449) & 0.165035 \tabularnewline
0.25 (4) & 0.022804 \tabularnewline
0.2528 (3.956) & 0.269391 \tabularnewline
0.2556 (3.913) & 0.052386 \tabularnewline
0.2583 (3.871) & 0.817169 \tabularnewline
0.2611 (3.8298) & 0.109156 \tabularnewline
0.2639 (3.7895) & 0.857574 \tabularnewline
0.2667 (3.75) & 0.854041 \tabularnewline
0.2694 (3.7113) & 4.952492 \tabularnewline
0.2722 (3.6735) & 0.965341 \tabularnewline
0.275 (3.6364) & 1.409417 \tabularnewline
0.2778 (3.6) & 0.052283 \tabularnewline
0.2806 (3.5644) & 0.016725 \tabularnewline
0.2833 (3.5294) & 1.605788 \tabularnewline
0.2861 (3.4951) & 7.08246 \tabularnewline
0.2889 (3.4615) & 0.107544 \tabularnewline
0.2917 (3.4286) & 1.354278 \tabularnewline
0.2944 (3.3962) & 1.166439 \tabularnewline
0.2972 (3.3645) & 0.596559 \tabularnewline
0.3 (3.3333) & 0.522582 \tabularnewline
0.3028 (3.3028) & 0.661809 \tabularnewline
0.3056 (3.2727) & 1.12578 \tabularnewline
0.3083 (3.2432) & 0.863734 \tabularnewline
0.3111 (3.2143) & 0.797993 \tabularnewline
0.3139 (3.1858) & 1.358446 \tabularnewline
0.3167 (3.1579) & 0.223895 \tabularnewline
0.3194 (3.1304) & 0.085736 \tabularnewline
0.3222 (3.1034) & 1.264808 \tabularnewline
0.325 (3.0769) & 0.247023 \tabularnewline
0.3278 (3.0508) & 0.188419 \tabularnewline
0.3306 (3.0252) & 0.337802 \tabularnewline
0.3333 (3) & 0.043553 \tabularnewline
0.3361 (2.9752) & 0.034062 \tabularnewline
0.3389 (2.9508) & 0.018071 \tabularnewline
0.3417 (2.9268) & 0.344637 \tabularnewline
0.3444 (2.9032) & 0.060212 \tabularnewline
0.3472 (2.88) & 0.69594 \tabularnewline
0.35 (2.8571) & 2.590298 \tabularnewline
0.3528 (2.8346) & 1.002245 \tabularnewline
0.3556 (2.8125) & 1.35004 \tabularnewline
0.3583 (2.7907) & 2.291366 \tabularnewline
0.3611 (2.7692) & 2.001674 \tabularnewline
0.3639 (2.7481) & 7.119634 \tabularnewline
0.3667 (2.7273) & 0.569299 \tabularnewline
0.3694 (2.7068) & 0.577886 \tabularnewline
0.3722 (2.6866) & 2.447876 \tabularnewline
0.375 (2.6667) & 0.716116 \tabularnewline
0.3778 (2.6471) & 0.754038 \tabularnewline
0.3806 (2.6277) & 4.874199 \tabularnewline
0.3833 (2.6087) & 1.824984 \tabularnewline
0.3861 (2.5899) & 0.549589 \tabularnewline
0.3889 (2.5714) & 1.235879 \tabularnewline
0.3917 (2.5532) & 4.102519 \tabularnewline
0.3944 (2.5352) & 2.003635 \tabularnewline
0.3972 (2.5175) & 0.620427 \tabularnewline
0.4 (2.5) & 0.204581 \tabularnewline
0.4028 (2.4828) & 0.515653 \tabularnewline
0.4056 (2.4658) & 0.019598 \tabularnewline
0.4083 (2.449) & 0.154699 \tabularnewline
0.4111 (2.4324) & 0.626278 \tabularnewline
0.4139 (2.4161) & 0.139812 \tabularnewline
0.4167 (2.4) & 0.167326 \tabularnewline
0.4194 (2.3841) & 0.084877 \tabularnewline
0.4222 (2.3684) & 0.196339 \tabularnewline
0.425 (2.3529) & 0.182845 \tabularnewline
0.4278 (2.3377) & 0.190421 \tabularnewline
0.4306 (2.3226) & 1.683037 \tabularnewline
0.4333 (2.3077) & 1.275025 \tabularnewline
0.4361 (2.293) & 0.342482 \tabularnewline
0.4389 (2.2785) & 1.607396 \tabularnewline
0.4417 (2.2642) & 1.564525 \tabularnewline
0.4444 (2.25) & 0.621786 \tabularnewline
0.4472 (2.236) & 4.467569 \tabularnewline
0.45 (2.2222) & 0.658739 \tabularnewline
0.4528 (2.2086) & 2.469759 \tabularnewline
0.4556 (2.1951) & 10.543687 \tabularnewline
0.4583 (2.1818) & 2.885492 \tabularnewline
0.4611 (2.1687) & 1.395165 \tabularnewline
0.4639 (2.1557) & 1.616309 \tabularnewline
0.4667 (2.1429) & 2.382695 \tabularnewline
0.4694 (2.1302) & 0.116625 \tabularnewline
0.4722 (2.1176) & 14.787816 \tabularnewline
0.475 (2.1053) & 0.485626 \tabularnewline
0.4778 (2.093) & 2.266653 \tabularnewline
0.4806 (2.0809) & 3.693014 \tabularnewline
0.4833 (2.069) & 0.066857 \tabularnewline
0.4861 (2.0571) & 0.987105 \tabularnewline
0.4889 (2.0455) & 0.06478 \tabularnewline
0.4917 (2.0339) & 0.528923 \tabularnewline
0.4944 (2.0225) & 0.340026 \tabularnewline
0.4972 (2.0112) & 0.36196 \tabularnewline
0.5 (2) & 0.070405 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31539&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]0.5[/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]0.057564[/C][/ROW]
[ROW][C]0.0056 (180)[/C][C]1.069301[/C][/ROW]
[ROW][C]0.0083 (120)[/C][C]0.220896[/C][/ROW]
[ROW][C]0.0111 (90)[/C][C]1.481315[/C][/ROW]
[ROW][C]0.0139 (72)[/C][C]0.995928[/C][/ROW]
[ROW][C]0.0167 (60)[/C][C]1.648276[/C][/ROW]
[ROW][C]0.0194 (51.4286)[/C][C]14.564678[/C][/ROW]
[ROW][C]0.0222 (45)[/C][C]1.840394[/C][/ROW]
[ROW][C]0.025 (40)[/C][C]12.766487[/C][/ROW]
[ROW][C]0.0278 (36)[/C][C]6.105788[/C][/ROW]
[ROW][C]0.0306 (32.7273)[/C][C]1.015385[/C][/ROW]
[ROW][C]0.0333 (30)[/C][C]0.399904[/C][/ROW]
[ROW][C]0.0361 (27.6923)[/C][C]29.526143[/C][/ROW]
[ROW][C]0.0389 (25.7143)[/C][C]18.248319[/C][/ROW]
[ROW][C]0.0417 (24)[/C][C]3.141788[/C][/ROW]
[ROW][C]0.0444 (22.5)[/C][C]10.236947[/C][/ROW]
[ROW][C]0.0472 (21.1765)[/C][C]6.590284[/C][/ROW]
[ROW][C]0.05 (20)[/C][C]1.145137[/C][/ROW]
[ROW][C]0.0528 (18.9474)[/C][C]4.348657[/C][/ROW]
[ROW][C]0.0556 (18)[/C][C]4.977999[/C][/ROW]
[ROW][C]0.0583 (17.1429)[/C][C]6.398841[/C][/ROW]
[ROW][C]0.0611 (16.3636)[/C][C]3.751172[/C][/ROW]
[ROW][C]0.0639 (15.6522)[/C][C]2.750313[/C][/ROW]
[ROW][C]0.0667 (15)[/C][C]0.533473[/C][/ROW]
[ROW][C]0.0694 (14.4)[/C][C]0.00977[/C][/ROW]
[ROW][C]0.0722 (13.8462)[/C][C]0.034506[/C][/ROW]
[ROW][C]0.075 (13.3333)[/C][C]0.835831[/C][/ROW]
[ROW][C]0.0778 (12.8571)[/C][C]0.166592[/C][/ROW]
[ROW][C]0.0806 (12.4138)[/C][C]0.261723[/C][/ROW]
[ROW][C]0.0833 (12)[/C][C]0.079353[/C][/ROW]
[ROW][C]0.0861 (11.6129)[/C][C]0.062316[/C][/ROW]
[ROW][C]0.0889 (11.25)[/C][C]0.609494[/C][/ROW]
[ROW][C]0.0917 (10.9091)[/C][C]0.130312[/C][/ROW]
[ROW][C]0.0944 (10.5882)[/C][C]0.02373[/C][/ROW]
[ROW][C]0.0972 (10.2857)[/C][C]0.078748[/C][/ROW]
[ROW][C]0.1 (10)[/C][C]2.109489[/C][/ROW]
[ROW][C]0.1028 (9.7297)[/C][C]7.511028[/C][/ROW]
[ROW][C]0.1056 (9.4737)[/C][C]0.502386[/C][/ROW]
[ROW][C]0.1083 (9.2308)[/C][C]2.636419[/C][/ROW]
[ROW][C]0.1111 (9)[/C][C]0.092986[/C][/ROW]
[ROW][C]0.1139 (8.7805)[/C][C]2.780718[/C][/ROW]
[ROW][C]0.1167 (8.5714)[/C][C]1.884332[/C][/ROW]
[ROW][C]0.1194 (8.3721)[/C][C]1.066026[/C][/ROW]
[ROW][C]0.1222 (8.1818)[/C][C]1.546977[/C][/ROW]
[ROW][C]0.125 (8)[/C][C]2.761493[/C][/ROW]
[ROW][C]0.1278 (7.8261)[/C][C]1.443971[/C][/ROW]
[ROW][C]0.1306 (7.6596)[/C][C]0.494138[/C][/ROW]
[ROW][C]0.1333 (7.5)[/C][C]4.404072[/C][/ROW]
[ROW][C]0.1361 (7.3469)[/C][C]1.28824[/C][/ROW]
[ROW][C]0.1389 (7.2)[/C][C]0.407265[/C][/ROW]
[ROW][C]0.1417 (7.0588)[/C][C]2.086069[/C][/ROW]
[ROW][C]0.1444 (6.9231)[/C][C]1.529735[/C][/ROW]
[ROW][C]0.1472 (6.7925)[/C][C]1.827748[/C][/ROW]
[ROW][C]0.15 (6.6667)[/C][C]2.541578[/C][/ROW]
[ROW][C]0.1528 (6.5455)[/C][C]0.581608[/C][/ROW]
[ROW][C]0.1556 (6.4286)[/C][C]0.640041[/C][/ROW]
[ROW][C]0.1583 (6.3158)[/C][C]0.354925[/C][/ROW]
[ROW][C]0.1611 (6.2069)[/C][C]0.041893[/C][/ROW]
[ROW][C]0.1639 (6.1017)[/C][C]0.246845[/C][/ROW]
[ROW][C]0.1667 (6)[/C][C]0.001917[/C][/ROW]
[ROW][C]0.1694 (5.9016)[/C][C]0.047417[/C][/ROW]
[ROW][C]0.1722 (5.8065)[/C][C]0.266618[/C][/ROW]
[ROW][C]0.175 (5.7143)[/C][C]0.018036[/C][/ROW]
[ROW][C]0.1778 (5.625)[/C][C]0.255299[/C][/ROW]
[ROW][C]0.1806 (5.5385)[/C][C]0.536108[/C][/ROW]
[ROW][C]0.1833 (5.4545)[/C][C]0.907431[/C][/ROW]
[ROW][C]0.1861 (5.3731)[/C][C]0.109349[/C][/ROW]
[ROW][C]0.1889 (5.2941)[/C][C]1.068629[/C][/ROW]
[ROW][C]0.1917 (5.2174)[/C][C]0.315716[/C][/ROW]
[ROW][C]0.1944 (5.1429)[/C][C]5.500412[/C][/ROW]
[ROW][C]0.1972 (5.0704)[/C][C]0.278307[/C][/ROW]
[ROW][C]0.2 (5)[/C][C]1.697187[/C][/ROW]
[ROW][C]0.2028 (4.9315)[/C][C]3.67589[/C][/ROW]
[ROW][C]0.2056 (4.8649)[/C][C]7.05649[/C][/ROW]
[ROW][C]0.2083 (4.8)[/C][C]4.592939[/C][/ROW]
[ROW][C]0.2111 (4.7368)[/C][C]0.587473[/C][/ROW]
[ROW][C]0.2139 (4.6753)[/C][C]2.068199[/C][/ROW]
[ROW][C]0.2167 (4.6154)[/C][C]1.642435[/C][/ROW]
[ROW][C]0.2194 (4.557)[/C][C]1.211529[/C][/ROW]
[ROW][C]0.2222 (4.5)[/C][C]0.365791[/C][/ROW]
[ROW][C]0.225 (4.4444)[/C][C]0.408188[/C][/ROW]
[ROW][C]0.2278 (4.3902)[/C][C]0.823555[/C][/ROW]
[ROW][C]0.2306 (4.3373)[/C][C]1.102988[/C][/ROW]
[ROW][C]0.2333 (4.2857)[/C][C]0.288742[/C][/ROW]
[ROW][C]0.2361 (4.2353)[/C][C]0.282547[/C][/ROW]
[ROW][C]0.2389 (4.186)[/C][C]0.008686[/C][/ROW]
[ROW][C]0.2417 (4.1379)[/C][C]1.972778[/C][/ROW]
[ROW][C]0.2444 (4.0909)[/C][C]0.059989[/C][/ROW]
[ROW][C]0.2472 (4.0449)[/C][C]0.165035[/C][/ROW]
[ROW][C]0.25 (4)[/C][C]0.022804[/C][/ROW]
[ROW][C]0.2528 (3.956)[/C][C]0.269391[/C][/ROW]
[ROW][C]0.2556 (3.913)[/C][C]0.052386[/C][/ROW]
[ROW][C]0.2583 (3.871)[/C][C]0.817169[/C][/ROW]
[ROW][C]0.2611 (3.8298)[/C][C]0.109156[/C][/ROW]
[ROW][C]0.2639 (3.7895)[/C][C]0.857574[/C][/ROW]
[ROW][C]0.2667 (3.75)[/C][C]0.854041[/C][/ROW]
[ROW][C]0.2694 (3.7113)[/C][C]4.952492[/C][/ROW]
[ROW][C]0.2722 (3.6735)[/C][C]0.965341[/C][/ROW]
[ROW][C]0.275 (3.6364)[/C][C]1.409417[/C][/ROW]
[ROW][C]0.2778 (3.6)[/C][C]0.052283[/C][/ROW]
[ROW][C]0.2806 (3.5644)[/C][C]0.016725[/C][/ROW]
[ROW][C]0.2833 (3.5294)[/C][C]1.605788[/C][/ROW]
[ROW][C]0.2861 (3.4951)[/C][C]7.08246[/C][/ROW]
[ROW][C]0.2889 (3.4615)[/C][C]0.107544[/C][/ROW]
[ROW][C]0.2917 (3.4286)[/C][C]1.354278[/C][/ROW]
[ROW][C]0.2944 (3.3962)[/C][C]1.166439[/C][/ROW]
[ROW][C]0.2972 (3.3645)[/C][C]0.596559[/C][/ROW]
[ROW][C]0.3 (3.3333)[/C][C]0.522582[/C][/ROW]
[ROW][C]0.3028 (3.3028)[/C][C]0.661809[/C][/ROW]
[ROW][C]0.3056 (3.2727)[/C][C]1.12578[/C][/ROW]
[ROW][C]0.3083 (3.2432)[/C][C]0.863734[/C][/ROW]
[ROW][C]0.3111 (3.2143)[/C][C]0.797993[/C][/ROW]
[ROW][C]0.3139 (3.1858)[/C][C]1.358446[/C][/ROW]
[ROW][C]0.3167 (3.1579)[/C][C]0.223895[/C][/ROW]
[ROW][C]0.3194 (3.1304)[/C][C]0.085736[/C][/ROW]
[ROW][C]0.3222 (3.1034)[/C][C]1.264808[/C][/ROW]
[ROW][C]0.325 (3.0769)[/C][C]0.247023[/C][/ROW]
[ROW][C]0.3278 (3.0508)[/C][C]0.188419[/C][/ROW]
[ROW][C]0.3306 (3.0252)[/C][C]0.337802[/C][/ROW]
[ROW][C]0.3333 (3)[/C][C]0.043553[/C][/ROW]
[ROW][C]0.3361 (2.9752)[/C][C]0.034062[/C][/ROW]
[ROW][C]0.3389 (2.9508)[/C][C]0.018071[/C][/ROW]
[ROW][C]0.3417 (2.9268)[/C][C]0.344637[/C][/ROW]
[ROW][C]0.3444 (2.9032)[/C][C]0.060212[/C][/ROW]
[ROW][C]0.3472 (2.88)[/C][C]0.69594[/C][/ROW]
[ROW][C]0.35 (2.8571)[/C][C]2.590298[/C][/ROW]
[ROW][C]0.3528 (2.8346)[/C][C]1.002245[/C][/ROW]
[ROW][C]0.3556 (2.8125)[/C][C]1.35004[/C][/ROW]
[ROW][C]0.3583 (2.7907)[/C][C]2.291366[/C][/ROW]
[ROW][C]0.3611 (2.7692)[/C][C]2.001674[/C][/ROW]
[ROW][C]0.3639 (2.7481)[/C][C]7.119634[/C][/ROW]
[ROW][C]0.3667 (2.7273)[/C][C]0.569299[/C][/ROW]
[ROW][C]0.3694 (2.7068)[/C][C]0.577886[/C][/ROW]
[ROW][C]0.3722 (2.6866)[/C][C]2.447876[/C][/ROW]
[ROW][C]0.375 (2.6667)[/C][C]0.716116[/C][/ROW]
[ROW][C]0.3778 (2.6471)[/C][C]0.754038[/C][/ROW]
[ROW][C]0.3806 (2.6277)[/C][C]4.874199[/C][/ROW]
[ROW][C]0.3833 (2.6087)[/C][C]1.824984[/C][/ROW]
[ROW][C]0.3861 (2.5899)[/C][C]0.549589[/C][/ROW]
[ROW][C]0.3889 (2.5714)[/C][C]1.235879[/C][/ROW]
[ROW][C]0.3917 (2.5532)[/C][C]4.102519[/C][/ROW]
[ROW][C]0.3944 (2.5352)[/C][C]2.003635[/C][/ROW]
[ROW][C]0.3972 (2.5175)[/C][C]0.620427[/C][/ROW]
[ROW][C]0.4 (2.5)[/C][C]0.204581[/C][/ROW]
[ROW][C]0.4028 (2.4828)[/C][C]0.515653[/C][/ROW]
[ROW][C]0.4056 (2.4658)[/C][C]0.019598[/C][/ROW]
[ROW][C]0.4083 (2.449)[/C][C]0.154699[/C][/ROW]
[ROW][C]0.4111 (2.4324)[/C][C]0.626278[/C][/ROW]
[ROW][C]0.4139 (2.4161)[/C][C]0.139812[/C][/ROW]
[ROW][C]0.4167 (2.4)[/C][C]0.167326[/C][/ROW]
[ROW][C]0.4194 (2.3841)[/C][C]0.084877[/C][/ROW]
[ROW][C]0.4222 (2.3684)[/C][C]0.196339[/C][/ROW]
[ROW][C]0.425 (2.3529)[/C][C]0.182845[/C][/ROW]
[ROW][C]0.4278 (2.3377)[/C][C]0.190421[/C][/ROW]
[ROW][C]0.4306 (2.3226)[/C][C]1.683037[/C][/ROW]
[ROW][C]0.4333 (2.3077)[/C][C]1.275025[/C][/ROW]
[ROW][C]0.4361 (2.293)[/C][C]0.342482[/C][/ROW]
[ROW][C]0.4389 (2.2785)[/C][C]1.607396[/C][/ROW]
[ROW][C]0.4417 (2.2642)[/C][C]1.564525[/C][/ROW]
[ROW][C]0.4444 (2.25)[/C][C]0.621786[/C][/ROW]
[ROW][C]0.4472 (2.236)[/C][C]4.467569[/C][/ROW]
[ROW][C]0.45 (2.2222)[/C][C]0.658739[/C][/ROW]
[ROW][C]0.4528 (2.2086)[/C][C]2.469759[/C][/ROW]
[ROW][C]0.4556 (2.1951)[/C][C]10.543687[/C][/ROW]
[ROW][C]0.4583 (2.1818)[/C][C]2.885492[/C][/ROW]
[ROW][C]0.4611 (2.1687)[/C][C]1.395165[/C][/ROW]
[ROW][C]0.4639 (2.1557)[/C][C]1.616309[/C][/ROW]
[ROW][C]0.4667 (2.1429)[/C][C]2.382695[/C][/ROW]
[ROW][C]0.4694 (2.1302)[/C][C]0.116625[/C][/ROW]
[ROW][C]0.4722 (2.1176)[/C][C]14.787816[/C][/ROW]
[ROW][C]0.475 (2.1053)[/C][C]0.485626[/C][/ROW]
[ROW][C]0.4778 (2.093)[/C][C]2.266653[/C][/ROW]
[ROW][C]0.4806 (2.0809)[/C][C]3.693014[/C][/ROW]
[ROW][C]0.4833 (2.069)[/C][C]0.066857[/C][/ROW]
[ROW][C]0.4861 (2.0571)[/C][C]0.987105[/C][/ROW]
[ROW][C]0.4889 (2.0455)[/C][C]0.06478[/C][/ROW]
[ROW][C]0.4917 (2.0339)[/C][C]0.528923[/C][/ROW]
[ROW][C]0.4944 (2.0225)[/C][C]0.340026[/C][/ROW]
[ROW][C]0.4972 (2.0112)[/C][C]0.36196[/C][/ROW]
[ROW][C]0.5 (2)[/C][C]0.070405[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31539&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31539&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)0.5
Degree of non-seasonal differencing (d)1
Degree of seasonal differencing (D)1
Seasonal Period (s)12
Frequency (Period)Spectrum
0.0028 (360)0.057564
0.0056 (180)1.069301
0.0083 (120)0.220896
0.0111 (90)1.481315
0.0139 (72)0.995928
0.0167 (60)1.648276
0.0194 (51.4286)14.564678
0.0222 (45)1.840394
0.025 (40)12.766487
0.0278 (36)6.105788
0.0306 (32.7273)1.015385
0.0333 (30)0.399904
0.0361 (27.6923)29.526143
0.0389 (25.7143)18.248319
0.0417 (24)3.141788
0.0444 (22.5)10.236947
0.0472 (21.1765)6.590284
0.05 (20)1.145137
0.0528 (18.9474)4.348657
0.0556 (18)4.977999
0.0583 (17.1429)6.398841
0.0611 (16.3636)3.751172
0.0639 (15.6522)2.750313
0.0667 (15)0.533473
0.0694 (14.4)0.00977
0.0722 (13.8462)0.034506
0.075 (13.3333)0.835831
0.0778 (12.8571)0.166592
0.0806 (12.4138)0.261723
0.0833 (12)0.079353
0.0861 (11.6129)0.062316
0.0889 (11.25)0.609494
0.0917 (10.9091)0.130312
0.0944 (10.5882)0.02373
0.0972 (10.2857)0.078748
0.1 (10)2.109489
0.1028 (9.7297)7.511028
0.1056 (9.4737)0.502386
0.1083 (9.2308)2.636419
0.1111 (9)0.092986
0.1139 (8.7805)2.780718
0.1167 (8.5714)1.884332
0.1194 (8.3721)1.066026
0.1222 (8.1818)1.546977
0.125 (8)2.761493
0.1278 (7.8261)1.443971
0.1306 (7.6596)0.494138
0.1333 (7.5)4.404072
0.1361 (7.3469)1.28824
0.1389 (7.2)0.407265
0.1417 (7.0588)2.086069
0.1444 (6.9231)1.529735
0.1472 (6.7925)1.827748
0.15 (6.6667)2.541578
0.1528 (6.5455)0.581608
0.1556 (6.4286)0.640041
0.1583 (6.3158)0.354925
0.1611 (6.2069)0.041893
0.1639 (6.1017)0.246845
0.1667 (6)0.001917
0.1694 (5.9016)0.047417
0.1722 (5.8065)0.266618
0.175 (5.7143)0.018036
0.1778 (5.625)0.255299
0.1806 (5.5385)0.536108
0.1833 (5.4545)0.907431
0.1861 (5.3731)0.109349
0.1889 (5.2941)1.068629
0.1917 (5.2174)0.315716
0.1944 (5.1429)5.500412
0.1972 (5.0704)0.278307
0.2 (5)1.697187
0.2028 (4.9315)3.67589
0.2056 (4.8649)7.05649
0.2083 (4.8)4.592939
0.2111 (4.7368)0.587473
0.2139 (4.6753)2.068199
0.2167 (4.6154)1.642435
0.2194 (4.557)1.211529
0.2222 (4.5)0.365791
0.225 (4.4444)0.408188
0.2278 (4.3902)0.823555
0.2306 (4.3373)1.102988
0.2333 (4.2857)0.288742
0.2361 (4.2353)0.282547
0.2389 (4.186)0.008686
0.2417 (4.1379)1.972778
0.2444 (4.0909)0.059989
0.2472 (4.0449)0.165035
0.25 (4)0.022804
0.2528 (3.956)0.269391
0.2556 (3.913)0.052386
0.2583 (3.871)0.817169
0.2611 (3.8298)0.109156
0.2639 (3.7895)0.857574
0.2667 (3.75)0.854041
0.2694 (3.7113)4.952492
0.2722 (3.6735)0.965341
0.275 (3.6364)1.409417
0.2778 (3.6)0.052283
0.2806 (3.5644)0.016725
0.2833 (3.5294)1.605788
0.2861 (3.4951)7.08246
0.2889 (3.4615)0.107544
0.2917 (3.4286)1.354278
0.2944 (3.3962)1.166439
0.2972 (3.3645)0.596559
0.3 (3.3333)0.522582
0.3028 (3.3028)0.661809
0.3056 (3.2727)1.12578
0.3083 (3.2432)0.863734
0.3111 (3.2143)0.797993
0.3139 (3.1858)1.358446
0.3167 (3.1579)0.223895
0.3194 (3.1304)0.085736
0.3222 (3.1034)1.264808
0.325 (3.0769)0.247023
0.3278 (3.0508)0.188419
0.3306 (3.0252)0.337802
0.3333 (3)0.043553
0.3361 (2.9752)0.034062
0.3389 (2.9508)0.018071
0.3417 (2.9268)0.344637
0.3444 (2.9032)0.060212
0.3472 (2.88)0.69594
0.35 (2.8571)2.590298
0.3528 (2.8346)1.002245
0.3556 (2.8125)1.35004
0.3583 (2.7907)2.291366
0.3611 (2.7692)2.001674
0.3639 (2.7481)7.119634
0.3667 (2.7273)0.569299
0.3694 (2.7068)0.577886
0.3722 (2.6866)2.447876
0.375 (2.6667)0.716116
0.3778 (2.6471)0.754038
0.3806 (2.6277)4.874199
0.3833 (2.6087)1.824984
0.3861 (2.5899)0.549589
0.3889 (2.5714)1.235879
0.3917 (2.5532)4.102519
0.3944 (2.5352)2.003635
0.3972 (2.5175)0.620427
0.4 (2.5)0.204581
0.4028 (2.4828)0.515653
0.4056 (2.4658)0.019598
0.4083 (2.449)0.154699
0.4111 (2.4324)0.626278
0.4139 (2.4161)0.139812
0.4167 (2.4)0.167326
0.4194 (2.3841)0.084877
0.4222 (2.3684)0.196339
0.425 (2.3529)0.182845
0.4278 (2.3377)0.190421
0.4306 (2.3226)1.683037
0.4333 (2.3077)1.275025
0.4361 (2.293)0.342482
0.4389 (2.2785)1.607396
0.4417 (2.2642)1.564525
0.4444 (2.25)0.621786
0.4472 (2.236)4.467569
0.45 (2.2222)0.658739
0.4528 (2.2086)2.469759
0.4556 (2.1951)10.543687
0.4583 (2.1818)2.885492
0.4611 (2.1687)1.395165
0.4639 (2.1557)1.616309
0.4667 (2.1429)2.382695
0.4694 (2.1302)0.116625
0.4722 (2.1176)14.787816
0.475 (2.1053)0.485626
0.4778 (2.093)2.266653
0.4806 (2.0809)3.693014
0.4833 (2.069)0.066857
0.4861 (2.0571)0.987105
0.4889 (2.0455)0.06478
0.4917 (2.0339)0.528923
0.4944 (2.0225)0.340026
0.4972 (2.0112)0.36196
0.5 (2)0.070405


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 0.5 ; 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')