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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 computationThu, 04 Dec 2008 12:46:17 -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/04/t12284200933newe2f0li8c4nh.htm/, Retrieved Wed, 22 May 2024 15:44:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29039, Retrieved Wed, 22 May 2024 15:44:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact191

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Spectral Analysis] [] [2008-12-04 19:46:17] [ba8414dd214a21fbd6c7bde748ac585f] [Current]
F   PD    [Spectral Analysis] [] [2008-12-09 11:08:44] [74be16979710d4c4e7c6647856088456]
Feedback Forum
2008-12-13 12:19:16 [Ken Wright] [reply] 
In deze vraag was het gewoon de bedoeling om seizoenaliteit en LT trend te herkennen, hetgene wat jij hebt geproduceert zijn oplossingen voor step 3

spectral anlysis zonder aanpassing:http://www.freestatistics.org/blog/index.php?v=date/2008/Dec/07/t1228660458xhvkum0awphm7al.htm
je ziet duidelijk een LT trend in het cumulative periodogram door een steile stijgende rechte, ook kan je al seizoenaliteit verwachten : je ziet na de steile rechte dat het cumulative periodogram getrapt is, dit duidt op seizoenaliteit. Je kunt ook de tabel raadplegen, deze gaat de tijdreeks ontbinden in alle mogelijke golfbewegingen. Bij hoge waarde (360) geeft het spectrum hoge waarden, dus er is een LT trend, maar ook op waarden zoals 12,24,… zijn er verhoogde waarden dit duidt op seizoenaliteit.
2008-12-13 12:56:47 [Ken Wright] [reply] 
step 3: correct, de steile helling in het begin en de getrapte curve is weggewerkt door differentiatie
2008-12-13 15:05:14 [Loïque Verhasselt] [reply] 
Step 2: Opnieuw vinden we de correcte output en de correcte conclusies maar we vinden geen interpretatie van de output en ook geen doorloping van de verschillende stappen. We krijgen juist de eindoplossing.
Via spectrum: De student geeft hier alleen de uiteindelijke oplossing en juist het cumulatie periodogram. Wat is juist de spectraal analyse? Door een spectraalanalyse wordt de tijdreeks ontbonden in regelmatige golfbewegingen. We zien een duidelijk patroon van een lange termijn trend in het begin van de grafiek. We kunnen zien dat ongeveer 70% van de tijdreeks wordt verklaard door de lange termijn trend. We gaan dus al 1 maal niet seizoenaal differentiëren. We zien ook duidelijk een trapsgewijs stijging. Dit wil zeggen dat er duidelijk een patroon aanwezig is van seizoenaliteit. We gaan dus ook 1 maal seizoenaal differentiëren. Het uiteindelijke doel is dat : normaal gezien zou een stationaire tijdreeks op de diagonaal moeten liggen tussen het betrouwbaarheidsinterval. We voeren nu de transformatie door en zetten parameters d en D op 1 !We zien dat de afwijking vooral in het begin ervoor zorgt dat er een afwijking is van de diagonaal dit met een redelijk lange periode. Dit heeft waarschijnlijk te maken met een conjunctuur in de tijdreeks. De tijdreeks beschrijft de werkloosheid en is zeker beïnvloed door conjunctuur.
2008-12-13 15:06:12 [Loïque Verhasselt] [reply] 
STEP 3: De student geeft de juiste output weer en geeft de 2 voorwaarden die moeten voldaan zijn voor stationariteit. Erg duidelijk zijn ze niet en daarom geef ik hier nog een algemene voorwaardebeschrijving.Eerste voorwaarde: de tijdreeks mag niet geïntegreerd zijn.
Dit wil zeggen dat de ACF (Auto Correlation Function) geen langzaam dalende niet - seizoenale autocorrelatiecoëfficiënten of seizoenale autocorrelatiecoëfficiënten mag bevatten.Dit impliceert eveneens dat het spectrum geen aanwijzing geeft van (sterke) cyclische golven van lage frequentie (lange periodes)of het spectrum geen (sterke) cyclische golven van seizoenale frequentie vertoont.Tweede voorwaarde: de meest waarschijnlijke verandering door toeval is constant over de tijd. Dit betekent een constante standaardfout over de ganse tijdreeks. Dit impliceert een constante spreiding. Deze conditie is nodig om gemakkelijk te kunnen differentiëren tussen veranderingen te wijten aan toeval.De eerste voorwaarde is zoals gezegd in step 3, niet voldaan. De tijdreeks vertoont nog seizoenaliteit door de cyclusgebondenheid van werkloosheid.De tweede voorwaarde is wel voldaan. We hebben door middel van de gevonden lambda - waarde in step 1 de spreiding constant gemaakt. De betrouwbare p – waarde zegt ons dat de regressie helling niet aan het toeval te wijten is, en zo dus significant is.
2008-12-14 16:11:51 [Thomas Plasschaert] [reply] 
Het Cumulative periodogram geeft hier eerst een verticale curve , wat wijst op een lange termijn trend, en daarna een getrapte curve, dit wijst op seizoenaliteit. Wanneer de differentiatie correct gebeurt, zal deze curve grotendeels binnen het betrouwbaarheidsinterval liggen, dit interval wordt voorgesteld door de stippellijntjes.
2008-12-14 16:14:22 [Thomas Plasschaert] [reply] 
Het Cumulative periodogram geeft hier eerst een verticale curve , wat wijst op een lange termijn trend, en daarna een getrapte curve, dit wijst op seizoenaliteit. Wanneer de differentiatie correct gebeurt, zal deze curve grotendeels binnen het betrouwbaarheidsinterval liggen, dit interval wordt voorgesteld door de stippellijntjes.

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Dataset

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Download CSV
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Boxplots 
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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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29039&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29039&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29039&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'Gwilym Jenkins' @ 72.249.127.135






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=29039&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=29039&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29039&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 = 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')