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R Software Module

rwasp_spectrum.wasp

Title produced by software

Spectral Analysis

Date of computation

Tue, 09 Dec 2008 06:49:38 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/09/t1228830684tsh46e7dvqigomt.htm/, Retrieved Tue, 28 May 2024 12:25:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31392, Retrieved Tue, 28 May 2024 12:25:53 +0000

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Estimated Impact

159

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

F       [Spectral Analysis] [step3 spectral] [2008-12-09 13:49:38] [a413cf7744efd6bb212437a3916e2f23] [Current]

Feedback Forum

2008-12-13 19:46:33 [006ad2c49b6a7c2ad6ab685cfc1dae56] [reply] 
Op het cumulatieve periodogram zien we een heel sterke stijging, dit wijst op een LT-trend. 70 % van de gegevens wordt verklaard door de LT- beweging. 
2008-12-13 19:49:48 [006ad2c49b6a7c2ad6ab685cfc1dae56] [reply] 
Je moest bij step 2 ook een spectraalanalyse uitvoeren.  
Voorbeeld: http://www.freestatistics.org/blog/index.php?v=date/2008/Dec/07/t1228662610gk9enh23oepp19a.htm  
In de tabel vinden we de grootste spectrumwaarde in het begin bij de laagste frequenties (hoogste periodes), dit wijst op een LT-trend. 
Op deze grafiek zien we dat het spectrum de grootste waarde heeft aan de linkerkant, dit wijst op een LT-trend (laagste frequenties). Er is ook seizoenaliteit (pieken bij seizoenale coëfficiënten).
2008-12-15 14:19:00 [Jonas Scheltjens] [reply] 
De spectrale analyse werd ook niet goed uitgevoerd door de student. De bedoeling van de spectraal analyse is dat de tijdreeks ontbonden wordt in regelmatige golfbewegingen. In de tabel kunnen we de golfbewegingen met verschillende periodes nakijken. In de kolom die daar op volgt vinden we dan de spectrumwaarde, die aangeeft hoe sterk een golfbeweging voorkomt. 
Enkel het cumulative periodogram werd besproken door de student. Wel is deze juist: de snelle stijging in het begin duidt inderdaad op lange termijn trend. En de (ietwat kleine) trapbeweging duidt op seizoenaliteit. Verder zien we in het raw periodogram duidelijke pieken verschijnen. Ook dit wijst er op dat er sprake is van seizoenaliteit. Wat we ook in het raw periodogram zien is dat er een duidelijke langzaam dalende trend aanwezig is, wat duidt op de aanwezigheid van een lange termijn trend. 
 
Wanneer we dan de veranderingen ook opnemen in Step 2: 
De verbeterde spectraalanalyse werd ook niet opgenomen en besproken. We kunnen hieruit opmaken: 
Achtereenvolgens bespreek ik wat er zich voordoet wanneer we niet-seizoenaal en seizoneaal differentiëren. 
Bij de niet-seizoenale differentiatie hebben we de parameter d ingesteld op 1 en kunnen zien in het raw periodogram dat de lange termijn trend verdwenen is. We zien echter wel nog de seizoenaliteit (hoge pieken). Dit zien we ook in het het cumulative periodogram: een steil begin is niet langer aanwezig. De beweging gebeurt hier wel trapsgewijs, wat betekend dat er sprake is van seizoenaliteit, welke hier wel significant verschillend is van 0 (te zien aan de ligging t.o.v. het betrouwbaarheidsinterval). Om nu ook de seizoenaliteit uit de tijdreeks te halen gaan we nu ook aan parameter D de waarde 1 toekennen.  
 
 Nadat we dus de seizoenale differentiatie hebben uitgevoerd (D=1) besluiten we dat de seizoenaliteit uit de tijdreeks is verdwenen. Ook de pieken van in het raw periodogram zijn nu verdwenen en dit valt ook te merken in het cumulative periodogram: het trapsgewijze verloop is nu verdwenen. We kunnen dus niet meer spreken over seizoenaliteit. Wat opvalt is het feit dat er toch nog een zekere voorspelbaarheid aanwezig is, aangezien we kunnen stellen dat als er niets meer te verklaren zou zijn, het cumulative periodogram zou samenvallen met de diagonaal, die op even grote afstand van beide lijnen ligt die het betrouwbaarheidsinterval belichamen. We kunnen dus zien dat er nog steeds golfbewegingen aanwezig zijn die we kunnen verklaren en patronen die we kunnen voorspellen. Hier is bijkomend onderzoek voor nodig. Er zijn nog golfbewegingen aanwezig met redelijke lange periodes, dit kan op conjunctuurbewegingen duiden. 
2008-12-16 23:42:55 [Gert-Jan Geudens] [reply] 
Correct. We zien hier (in de cumulative periodogram) een zeer steil verloop. Dit wijst op een lange termijntrend. Via deze trend kunnen we tevens 70% van de gegevens verklaren.

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31392&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=31392&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31392&T=0

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The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Raw Periodogram
Parameter	Value
Box-Cox transformation parameter (lambda)	1
Degree of non-seasonal differencing (d)	0
Degree of seasonal differencing (D)	0
Seasonal Period (s)	12
Frequency (Period)	Spectrum
0.0027 (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=31392&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=31392&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31392&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Raw Periodogram
Parameter	Value
Box-Cox transformation parameter (lambda)	1
Degree of non-seasonal differencing (d)	0
Degree of seasonal differencing (D)	0
Seasonal Period (s)	12
Frequency (Period)	Spectrum
0.0027 (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

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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

R code (references can be found in the software module):

par1 <- as.numeric(par1)
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
if (par1 == 0) {
x <- log(x)
} else {
x <- (x ^ par1 - 1) / par1
}
if (par2 > 0) x <- diff(x,lag=1,difference=par2)
if (par3 > 0) x <- diff(x,lag=par4,difference=par3)
bitmap(file='test1.png')
r <- spectrum(x,main='Raw Periodogram')
dev.off()
bitmap(file='test2.png')
cpgram(x,main='Cumulative Periodogram')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Raw Periodogram',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Box-Cox transformation parameter (lambda)',header=TRUE)
a<-table.element(a,par1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Degree of non-seasonal differencing (d)',header=TRUE)
a<-table.element(a,par2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Degree of seasonal differencing (D)',header=TRUE)
a<-table.element(a,par3)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Seasonal Period (s)',header=TRUE)
a<-table.element(a,par4)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Frequency (Period)',header=TRUE)
a<-table.element(a,'Spectrum',header=TRUE)
a<-table.row.end(a)
for (i in 1:length(r$freq)) {
a<-table.row.start(a)
mylab <- round(r$freq[i],4)
mylab <- paste(mylab,' (',sep='')
mylab <- paste(mylab,round(1/r$freq[i],4),sep='')
mylab <- paste(mylab,')',sep='')
a<-table.element(a,mylab,header=TRUE)
a<-table.element(a,round(r$spec[i],6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code