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R Software Module

rwasp_spectrum.wasp

Title produced by software

Spectral Analysis

Date of computation

Sat, 06 Dec 2008 05:07:42 -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/06/t1228565290f13sw3pc58e0f89.htm/, Retrieved Sun, 19 May 2024 12:15:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29535, Retrieved Sun, 19 May 2024 12:15:14 +0000

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Estimated Impact

234

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

F       [Spectral Analysis] [Diff Spectral] [2008-12-06 12:07:42] [d41d8cd98f00b204e9800998ecf8427e] [Current]
F RMP     [(Partial) Autocorrelation Function] [] [2008-12-06 12:12:15] [74be16979710d4c4e7c6647856088456] 
F RMP     [ARIMA Backward Selection] [Arima backward] [2008-12-06 14:19:09] [74be16979710d4c4e7c6647856088456] 
- RMPD      [Standard Deviation-Mean Plot] [inter productie m...] [2008-12-08 19:46:48] [11edab5c4db3615abbf782b1c6e7cacf] 
- RMPD      [Variance Reduction Matrix] [VRM inter prod] [2008-12-08 19:51:53] [11edab5c4db3615abbf782b1c6e7cacf] 
- RMPD      [(Partial) Autocorrelation Function] [ACF int prod] [2008-12-08 19:55:18] [11edab5c4db3615abbf782b1c6e7cacf] 
-   P         [(Partial) Autocorrelation Function] [ACF en PACF inter...] [2008-12-08 20:06:19] [11edab5c4db3615abbf782b1c6e7cacf] 
- RMPD      [Spectral Analysis] [cumulative inter ...] [2008-12-08 19:57:17] [11edab5c4db3615abbf782b1c6e7cacf] 
-             [Spectral Analysis] [] [2008-12-08 20:09:41] [11edab5c4db3615abbf782b1c6e7cacf] 
- RM          [ARIMA Backward Selection] [arima backward in...] [2008-12-08 20:21:03] [11edab5c4db3615abbf782b1c6e7cacf] 
- RMPD      [(Partial) Autocorrelation Function] [] [2008-12-09 10:52:15] [74be16979710d4c4e7c6647856088456] 
-   PD        [(Partial) Autocorrelation Function] [] [2008-12-09 10:56:43] [74be16979710d4c4e7c6647856088456] 
- RMPD        [Spectral Analysis] [] [2008-12-09 11:01:22] [74be16979710d4c4e7c6647856088456] 
F   P           [Spectral Analysis] [] [2008-12-09 11:05:55] [74be16979710d4c4e7c6647856088456] 
F RMP           [ARIMA Backward Selection] [] [2008-12-09 11:11:19] [74be16979710d4c4e7c6647856088456] 
F   PD        [(Partial) Autocorrelation Function] [] [2008-12-09 11:16:28] [74be16979710d4c4e7c6647856088456] 
F   PD        [(Partial) Autocorrelation Function] [] [2008-12-09 11:18:29] [74be16979710d4c4e7c6647856088456] 

Feedback Forum

2008-12-13 13:54:02 [Julie Govaerts] [reply] 
op het cumulatief periodogram zien we dat een deel in het betrouwbaarheidsinterval ligt --> deze patronen kunnen we niet meer voorspellen MAAR een deel ligt wel nog buiten het betrouwbaarheidsinterval, dit betekent dat er nog steeds golfbewegingen zijn die we kunnen voorspellen MAAR niet door de saisonaliteit of de lange termijn trend (hebben we eruit gehaald --> er is dus nog ruimte om te verbeteren (bv door de conjunctuur) 
doel = dat alleen het toeval overblijft (we halen 1 voor 1 de componenten eruit) 
dus het cumulatief periodogram moet dan tussen het betrouwbaarheidsinterval liggen 
 
er is een grote kans dat we dit met de arma processen kunnen verklaren --> hier is het de bovenkant (cumulatief periodogram) dat afwijkt = meestal AR processen (als vanonder = meestal MA processen) 
2008-12-13 13:58:26 [Julie Govaerts] [reply] 
stap 4 --> 
ACF: we kijken naar de eerste 5 coëfficiënten --> we mogen aan het tweede staafje trekken omdat de modellen zuiver theoretisch zijn dus er mag een beetje van afgeweken worden 
- Niet saisonaal AR proces DUS P =0 
- AR (3) owv 3 staafjes significant (boven betrouwbaarheidsinterval)--> p = 3 
2008-12-15 13:20:50 [Katja van Hek] [reply] 
De cumulatieve periodogram laat zien dat er geen sprake is van toeval aangezien er nog altijd waarden zijn die niet binnen de betrouwbaarheidsinterval liggen. Omdat ze boven het interval liggen kun je zeggen dat er mogelijk sprake is van AR proces.
2008-12-15 13:33:44 [Katja van Hek] [reply] 
De cumulatieve periodogram heeft nog zichtbare trapbewegingen die kunnen wijzen op seizoenaliteit.Omdat er waarden zijn die boven het betrouwbaarheidsinterval liggen lijkt het logisch om te zeggen dat er sprake is van een AR proces, omdat er nog seizoenale componenten in zitten heb je een SAR proces.
2008-12-15 15:04:34 [An Knapen] [reply] 
OP het raw periodogram kunnen we duidelijk zien dat er geen trend meer aanwezig is. De pieken bevinden zich snel na elkaar en er is ook geen duidelijk patroon meer te herkennen. 
OP het cumulatief periodogram is er geen enkele indicatie meer voor een lange termijn trend. Ook de zogenaamde ‘trappen’ ,zijn verdwenen. Verder kunnen we opmerken dat de curve niet op de diagonaal gelegen is, wat er op wijst dat er toch nog golven in de curve zitten die bepaalde zaken kunnen verklaren. De afwijking(van de diagonaal) bevindt zich aan de bovenkant. Dit wijst erop dat we hier waarschijnlijk te maken hebben met een AR proces.
2008-12-15 15:26:55 [An Knapen] [reply] 
Wanneer we naar de bijhorende tabellen kijken,kunnen we de spectrmwaarde afleiden van periodes die met seizoenaliteit te maken hebben duidelijk herkennen.Bijvoorbeeld 12 maanden, maar ook 6, 4, of 3 maanden, want dit zijn hoeveelheden die juist een bepaald aantal keren in 12 gaan. Deze waarden zijn niet speciaal hoger dan de waarden die er in de buurt liggen. Er is dus geen seizoenaliteit meer.  
 
Ook de veelvouden van 12 hebben geen opvallend hoge spectrumwaarden. Er is dus geen lange termijntrend meer aanwezig. Er zijn wel een aantal hoge spectrumwaarden.Maar deze hebben geen veelvoud van 12 als periode. We spreken hier van een conjunctuurcyclus van zoveel maanden. Dit is logisch aangezien we over werkloosheid spreken. Die is inderdaad afhankelijk van de conjunctuur.  
We kunnen besluiten dat aan de voorwaarden voor een stationaire tijdreeks is voldaan.  
We zien in deze tabel dat de veelvouden van 12 geen uitzonderlijk hoge waarde hebben. Er is dus geen lange termijntrend meer.  
 
We zien ook dat de periodes die een bepaald aantal keren in 12 kunnen ook geen uitzonderlijk hoge waarden hebben. De seizoenaliteit is dus ook weg.  

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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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29535&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29535&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29535&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Raw Periodogram
Parameter	Value
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=29535&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=29535&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29535&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)	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

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 0.5 ; par2 = 1 ; par3 = 1 ; par4 = 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code