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*Unverified author*

R Software Module

rwasp_spectrum.wasp

Title produced by software

Spectral Analysis

Date of computation

Tue, 02 Dec 2008 06:19:49 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/02/t1228224065jkobc6q1jajlbe4.htm/, Retrieved Sun, 19 May 2024 10:41:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27738, Retrieved Sun, 19 May 2024 10:41:11 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

194

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

F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
F RMPD    [Spectral Analysis] [q6] [2008-12-02 13:19:49] [d41d8cd98f00b204e9800998ecf8427e] [Current]
F   P       [Spectral Analysis] [q6] [2008-12-02 13:25:30] [74be16979710d4c4e7c6647856088456] 
F   P       [Spectral Analysis] [q6] [2008-12-02 13:30:03] [74be16979710d4c4e7c6647856088456] 
F RMPD      [Cross Correlation Function] [q7] [2008-12-02 13:34:43] [7ab42b4673454531c59df48fbb842b60] 
F   PD        [Cross Correlation Function] [q8] [2008-12-02 13:49:39] [7ab42b4673454531c59df48fbb842b60] 
F RM D          [Variance Reduction Matrix] [q8] [2008-12-02 13:55:29] [7ab42b4673454531c59df48fbb842b60] 
- RMP             [Standard Deviation-Mean Plot] [q9] [2008-12-07 11:33:42] [1b742211e88d1643c42c5773474321b2] 
F RM D          [Variance Reduction Matrix] [q8] [2008-12-02 13:58:13] [7ab42b4673454531c59df48fbb842b60] 
- RMP             [Standard Deviation-Mean Plot] [q9] [2008-12-07 11:28:49] [1b742211e88d1643c42c5773474321b2] 

Feedback Forum

2008-12-07 20:58:31 [Jasmine Hendrikx] [reply] 
Evaluatie Q6: 
De berekening is op de juiste manier uitgevoerd. We beginnen inderdaad door d en D gelijk te stellen aan 0. Bij spectral analysis wordt de tijdreeks ontbonden in regelmatige golfreeksen. De tabel die bij deze berekening hoort, is niet in het document weergegeven, maar is wel erg nuttig. De getallen die tussen haakjes staan in de tabel, is de periode. Als er dus bijvoorbeeld 144 staat, wil dat zeggen dat het hier over 144 maanden gaat, dus over 12 jaar. Het is de periode om van de ene top naar de andere te gaan. De getallen in de tweede kolom wijzen op de intensiteit waarmee die voorkomt in onze tijdreeks. Zo is het eerste getal gelijk aan 3792 (bij een periode van 144 maanden). Dit getal is groter dan de meeste andere getallen. De golfbewegingen met kortere periodes zijn dus meestal minder belangrijk dan golfbeweging met 144 maanden. Dit wijst dus op een langetermijntrend. We kijken ook naar het belang van seizoenaliteit. De golfbeweging van 12 maanden is heel groot, namelijk 68 000 (dit in tegenstelling tot 3792 bij de periode van 144 maanden). We kunnen hieruit dus besluiten dat de seizoenaliteit veel belangrijker is dan de lange termijn. Deze zal een veel hogere amplitude hebben dan de langetermijntrend.  
De bespreking van het raw periodogram is ook goed. Het is inderdaad zo dat we een trendmatig verloop en seizoenaliteit kunnen afleiden uit de grafiek. Op de x-as zien we de frequenties. Op de y-as staat de intensiteit waarmee de golfbewegingen voorkomen (spectrumwaarde). Lage frequenties duiden op lange periodes. Hoge frequenties duiden op korte periodes. We zien in de grafiek een blauwe lijn met een puntje. Deze lijn kunnen we eigenlijk als een meetlatje beschouwen. Om te kijken of pieken en dalen significant van elkaar verschillen moet je kijken naar de lengte van het blauwe lijntje. Is de afstand van dat blauw lijntje kleiner dan de afstand tussen de piek en het dal dan kunnen we stellen dat de piek en het dal significant van elkaar verschillen. De periodes met een lange periode (dus lage frequentie) hebben een grotere intensiteit, dus er is duidelijk sprake van een langetermijntrend. (kun je uit de grafiek afleiden, er is namelijk spraken van een dalend verloop). Ook zegt de student dat er sprake is van seizoenaliteit door de opvallend terugkerende pieken, wat correct is. De conclusie bij het cumulatieve periodogram is ook goed. Trappen wijzen inderdaad op seizoenaliteit en links kunnen we een zeer steile stijgende lijn zien, wat wijst op een langetermijntrend. Hier zou er nog vermeld kunnen orden dat de x-as de frequentie weergeeft en de y-as gecumuleerde spectrumwaarden voorstelt. De getallen op de y-as worden geschaald tussen 0 en 1 en kun je interpreteren als R-squared. Het getal 0.2 op de y-as wil zeggen dat je 20% kunt verklaren van de reeks. Het getal 0.8 wil zeggen dat je 80% kunt verklaren van de reeks. Wanneer we dan kijken naar de grafiek, kunnen we inderdaad zien dat er een langetermijntrend aanwezig is, en dat deze 70% verklaart van de tijdreeks.  Aangezien we onder andere spreken van een langetermijntrend, gaan we 1 keer niet-seizoenaal differentiëren.   

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Dataseries X:

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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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27738&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27738&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27738&T=0

As an alternative you can also use a QR Code:

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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

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
0.0069 (144)	3792.028873
0.0139 (72)	1238.009494
0.0208 (48)	1826.626686
0.0278 (36)	201.90456
0.0347 (28.8)	331.907846
0.0417 (24)	695.956872
0.0486 (20.5714)	189.838038
0.0556 (18)	632.668292
0.0625 (16)	287.593613
0.0694 (14.4)	1791.509224
0.0764 (13.0909)	9958.986159
0.0833 (12)	68001.700911
0.0903 (11.0769)	6339.30519
0.0972 (10.2857)	1529.925619
0.1042 (9.6)	854.106417
0.1111 (9)	454.283437
0.1181 (8.4706)	125.530203
0.125 (8)	30.347246
0.1319 (7.5789)	70.029431
0.1389 (7.2)	204.158401
0.1458 (6.8571)	203.994506
0.1528 (6.5455)	348.864801
0.1597 (6.2609)	1597.138661
0.1667 (6)	18608.352793
0.1736 (5.76)	2154.647278
0.1806 (5.5385)	608.650096
0.1875 (5.3333)	615.202265
0.1944 (5.1429)	120.078527
0.2014 (4.9655)	130.147126
0.2083 (4.8)	121.85189
0.2153 (4.6452)	40.141534
0.2222 (4.5)	217.826943
0.2292 (4.3636)	68.288003
0.2361 (4.2353)	214.055484
0.2431 (4.1143)	331.595519
0.25 (4)	3179.724197
0.2569 (3.8919)	203.863339
0.2639 (3.7895)	64.50686
0.2708 (3.6923)	3.43721
0.2778 (3.6)	31.782121
0.2847 (3.5122)	6.688219
0.2917 (3.4286)	16.986738
0.2986 (3.3488)	42.173804
0.3056 (3.2727)	29.803217
0.3125 (3.2)	33.804933
0.3194 (3.1304)	60.212446
0.3264 (3.0638)	379.911387
0.3333 (3)	2005.72132
0.3403 (2.9388)	75.434588
0.3472 (2.88)	140.072127
0.3542 (2.8235)	9.294066
0.3611 (2.7692)	15.430795
0.3681 (2.717)	10.698128
0.375 (2.6667)	4.21834
0.3819 (2.6182)	35.411804
0.3889 (2.5714)	16.11576
0.3958 (2.5263)	11.881808
0.4028 (2.4828)	183.988521
0.4097 (2.4407)	159.788028
0.4167 (2.4)	1276.34537
0.4236 (2.3607)	113.356981
0.4306 (2.3226)	208.3604
0.4375 (2.2857)	105.674799
0.4444 (2.25)	48.09594
0.4514 (2.2154)	10.461349
0.4583 (2.1818)	50.391079
0.4653 (2.1493)	26.292831
0.4722 (2.1176)	29.647284
0.4792 (2.087)	24.120557
0.4861 (2.0571)	8.778387
0.4931 (2.0282)	8.689016
0.5 (2)	25.907638

\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
0.0069 (144) & 3792.028873 \tabularnewline
0.0139 (72) & 1238.009494 \tabularnewline
0.0208 (48) & 1826.626686 \tabularnewline
0.0278 (36) & 201.90456 \tabularnewline
0.0347 (28.8) & 331.907846 \tabularnewline
0.0417 (24) & 695.956872 \tabularnewline
0.0486 (20.5714) & 189.838038 \tabularnewline
0.0556 (18) & 632.668292 \tabularnewline
0.0625 (16) & 287.593613 \tabularnewline
0.0694 (14.4) & 1791.509224 \tabularnewline
0.0764 (13.0909) & 9958.986159 \tabularnewline
0.0833 (12) & 68001.700911 \tabularnewline
0.0903 (11.0769) & 6339.30519 \tabularnewline
0.0972 (10.2857) & 1529.925619 \tabularnewline
0.1042 (9.6) & 854.106417 \tabularnewline
0.1111 (9) & 454.283437 \tabularnewline
0.1181 (8.4706) & 125.530203 \tabularnewline
0.125 (8) & 30.347246 \tabularnewline
0.1319 (7.5789) & 70.029431 \tabularnewline
0.1389 (7.2) & 204.158401 \tabularnewline
0.1458 (6.8571) & 203.994506 \tabularnewline
0.1528 (6.5455) & 348.864801 \tabularnewline
0.1597 (6.2609) & 1597.138661 \tabularnewline
0.1667 (6) & 18608.352793 \tabularnewline
0.1736 (5.76) & 2154.647278 \tabularnewline
0.1806 (5.5385) & 608.650096 \tabularnewline
0.1875 (5.3333) & 615.202265 \tabularnewline
0.1944 (5.1429) & 120.078527 \tabularnewline
0.2014 (4.9655) & 130.147126 \tabularnewline
0.2083 (4.8) & 121.85189 \tabularnewline
0.2153 (4.6452) & 40.141534 \tabularnewline
0.2222 (4.5) & 217.826943 \tabularnewline
0.2292 (4.3636) & 68.288003 \tabularnewline
0.2361 (4.2353) & 214.055484 \tabularnewline
0.2431 (4.1143) & 331.595519 \tabularnewline
0.25 (4) & 3179.724197 \tabularnewline
0.2569 (3.8919) & 203.863339 \tabularnewline
0.2639 (3.7895) & 64.50686 \tabularnewline
0.2708 (3.6923) & 3.43721 \tabularnewline
0.2778 (3.6) & 31.782121 \tabularnewline
0.2847 (3.5122) & 6.688219 \tabularnewline
0.2917 (3.4286) & 16.986738 \tabularnewline
0.2986 (3.3488) & 42.173804 \tabularnewline
0.3056 (3.2727) & 29.803217 \tabularnewline
0.3125 (3.2) & 33.804933 \tabularnewline
0.3194 (3.1304) & 60.212446 \tabularnewline
0.3264 (3.0638) & 379.911387 \tabularnewline
0.3333 (3) & 2005.72132 \tabularnewline
0.3403 (2.9388) & 75.434588 \tabularnewline
0.3472 (2.88) & 140.072127 \tabularnewline
0.3542 (2.8235) & 9.294066 \tabularnewline
0.3611 (2.7692) & 15.430795 \tabularnewline
0.3681 (2.717) & 10.698128 \tabularnewline
0.375 (2.6667) & 4.21834 \tabularnewline
0.3819 (2.6182) & 35.411804 \tabularnewline
0.3889 (2.5714) & 16.11576 \tabularnewline
0.3958 (2.5263) & 11.881808 \tabularnewline
0.4028 (2.4828) & 183.988521 \tabularnewline
0.4097 (2.4407) & 159.788028 \tabularnewline
0.4167 (2.4) & 1276.34537 \tabularnewline
0.4236 (2.3607) & 113.356981 \tabularnewline
0.4306 (2.3226) & 208.3604 \tabularnewline
0.4375 (2.2857) & 105.674799 \tabularnewline
0.4444 (2.25) & 48.09594 \tabularnewline
0.4514 (2.2154) & 10.461349 \tabularnewline
0.4583 (2.1818) & 50.391079 \tabularnewline
0.4653 (2.1493) & 26.292831 \tabularnewline
0.4722 (2.1176) & 29.647284 \tabularnewline
0.4792 (2.087) & 24.120557 \tabularnewline
0.4861 (2.0571) & 8.778387 \tabularnewline
0.4931 (2.0282) & 8.689016 \tabularnewline
0.5 (2) & 25.907638 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27738&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]0.0069 (144)[/C][C]3792.028873[/C][/ROW]
[ROW][C]0.0139 (72)[/C][C]1238.009494[/C][/ROW]
[ROW][C]0.0208 (48)[/C][C]1826.626686[/C][/ROW]
[ROW][C]0.0278 (36)[/C][C]201.90456[/C][/ROW]
[ROW][C]0.0347 (28.8)[/C][C]331.907846[/C][/ROW]
[ROW][C]0.0417 (24)[/C][C]695.956872[/C][/ROW]
[ROW][C]0.0486 (20.5714)[/C][C]189.838038[/C][/ROW]
[ROW][C]0.0556 (18)[/C][C]632.668292[/C][/ROW]
[ROW][C]0.0625 (16)[/C][C]287.593613[/C][/ROW]
[ROW][C]0.0694 (14.4)[/C][C]1791.509224[/C][/ROW]
[ROW][C]0.0764 (13.0909)[/C][C]9958.986159[/C][/ROW]
[ROW][C]0.0833 (12)[/C][C]68001.700911[/C][/ROW]
[ROW][C]0.0903 (11.0769)[/C][C]6339.30519[/C][/ROW]
[ROW][C]0.0972 (10.2857)[/C][C]1529.925619[/C][/ROW]
[ROW][C]0.1042 (9.6)[/C][C]854.106417[/C][/ROW]
[ROW][C]0.1111 (9)[/C][C]454.283437[/C][/ROW]
[ROW][C]0.1181 (8.4706)[/C][C]125.530203[/C][/ROW]
[ROW][C]0.125 (8)[/C][C]30.347246[/C][/ROW]
[ROW][C]0.1319 (7.5789)[/C][C]70.029431[/C][/ROW]
[ROW][C]0.1389 (7.2)[/C][C]204.158401[/C][/ROW]
[ROW][C]0.1458 (6.8571)[/C][C]203.994506[/C][/ROW]
[ROW][C]0.1528 (6.5455)[/C][C]348.864801[/C][/ROW]
[ROW][C]0.1597 (6.2609)[/C][C]1597.138661[/C][/ROW]
[ROW][C]0.1667 (6)[/C][C]18608.352793[/C][/ROW]
[ROW][C]0.1736 (5.76)[/C][C]2154.647278[/C][/ROW]
[ROW][C]0.1806 (5.5385)[/C][C]608.650096[/C][/ROW]
[ROW][C]0.1875 (5.3333)[/C][C]615.202265[/C][/ROW]
[ROW][C]0.1944 (5.1429)[/C][C]120.078527[/C][/ROW]
[ROW][C]0.2014 (4.9655)[/C][C]130.147126[/C][/ROW]
[ROW][C]0.2083 (4.8)[/C][C]121.85189[/C][/ROW]
[ROW][C]0.2153 (4.6452)[/C][C]40.141534[/C][/ROW]
[ROW][C]0.2222 (4.5)[/C][C]217.826943[/C][/ROW]
[ROW][C]0.2292 (4.3636)[/C][C]68.288003[/C][/ROW]
[ROW][C]0.2361 (4.2353)[/C][C]214.055484[/C][/ROW]
[ROW][C]0.2431 (4.1143)[/C][C]331.595519[/C][/ROW]
[ROW][C]0.25 (4)[/C][C]3179.724197[/C][/ROW]
[ROW][C]0.2569 (3.8919)[/C][C]203.863339[/C][/ROW]
[ROW][C]0.2639 (3.7895)[/C][C]64.50686[/C][/ROW]
[ROW][C]0.2708 (3.6923)[/C][C]3.43721[/C][/ROW]
[ROW][C]0.2778 (3.6)[/C][C]31.782121[/C][/ROW]
[ROW][C]0.2847 (3.5122)[/C][C]6.688219[/C][/ROW]
[ROW][C]0.2917 (3.4286)[/C][C]16.986738[/C][/ROW]
[ROW][C]0.2986 (3.3488)[/C][C]42.173804[/C][/ROW]
[ROW][C]0.3056 (3.2727)[/C][C]29.803217[/C][/ROW]
[ROW][C]0.3125 (3.2)[/C][C]33.804933[/C][/ROW]
[ROW][C]0.3194 (3.1304)[/C][C]60.212446[/C][/ROW]
[ROW][C]0.3264 (3.0638)[/C][C]379.911387[/C][/ROW]
[ROW][C]0.3333 (3)[/C][C]2005.72132[/C][/ROW]
[ROW][C]0.3403 (2.9388)[/C][C]75.434588[/C][/ROW]
[ROW][C]0.3472 (2.88)[/C][C]140.072127[/C][/ROW]
[ROW][C]0.3542 (2.8235)[/C][C]9.294066[/C][/ROW]
[ROW][C]0.3611 (2.7692)[/C][C]15.430795[/C][/ROW]
[ROW][C]0.3681 (2.717)[/C][C]10.698128[/C][/ROW]
[ROW][C]0.375 (2.6667)[/C][C]4.21834[/C][/ROW]
[ROW][C]0.3819 (2.6182)[/C][C]35.411804[/C][/ROW]
[ROW][C]0.3889 (2.5714)[/C][C]16.11576[/C][/ROW]
[ROW][C]0.3958 (2.5263)[/C][C]11.881808[/C][/ROW]
[ROW][C]0.4028 (2.4828)[/C][C]183.988521[/C][/ROW]
[ROW][C]0.4097 (2.4407)[/C][C]159.788028[/C][/ROW]
[ROW][C]0.4167 (2.4)[/C][C]1276.34537[/C][/ROW]
[ROW][C]0.4236 (2.3607)[/C][C]113.356981[/C][/ROW]
[ROW][C]0.4306 (2.3226)[/C][C]208.3604[/C][/ROW]
[ROW][C]0.4375 (2.2857)[/C][C]105.674799[/C][/ROW]
[ROW][C]0.4444 (2.25)[/C][C]48.09594[/C][/ROW]
[ROW][C]0.4514 (2.2154)[/C][C]10.461349[/C][/ROW]
[ROW][C]0.4583 (2.1818)[/C][C]50.391079[/C][/ROW]
[ROW][C]0.4653 (2.1493)[/C][C]26.292831[/C][/ROW]
[ROW][C]0.4722 (2.1176)[/C][C]29.647284[/C][/ROW]
[ROW][C]0.4792 (2.087)[/C][C]24.120557[/C][/ROW]
[ROW][C]0.4861 (2.0571)[/C][C]8.778387[/C][/ROW]
[ROW][C]0.4931 (2.0282)[/C][C]8.689016[/C][/ROW]
[ROW][C]0.5 (2)[/C][C]25.907638[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27738&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27738&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
0.0069 (144)	3792.028873
0.0139 (72)	1238.009494
0.0208 (48)	1826.626686
0.0278 (36)	201.90456
0.0347 (28.8)	331.907846
0.0417 (24)	695.956872
0.0486 (20.5714)	189.838038
0.0556 (18)	632.668292
0.0625 (16)	287.593613
0.0694 (14.4)	1791.509224
0.0764 (13.0909)	9958.986159
0.0833 (12)	68001.700911
0.0903 (11.0769)	6339.30519
0.0972 (10.2857)	1529.925619
0.1042 (9.6)	854.106417
0.1111 (9)	454.283437
0.1181 (8.4706)	125.530203
0.125 (8)	30.347246
0.1319 (7.5789)	70.029431
0.1389 (7.2)	204.158401
0.1458 (6.8571)	203.994506
0.1528 (6.5455)	348.864801
0.1597 (6.2609)	1597.138661
0.1667 (6)	18608.352793
0.1736 (5.76)	2154.647278
0.1806 (5.5385)	608.650096
0.1875 (5.3333)	615.202265
0.1944 (5.1429)	120.078527
0.2014 (4.9655)	130.147126
0.2083 (4.8)	121.85189
0.2153 (4.6452)	40.141534
0.2222 (4.5)	217.826943
0.2292 (4.3636)	68.288003
0.2361 (4.2353)	214.055484
0.2431 (4.1143)	331.595519
0.25 (4)	3179.724197
0.2569 (3.8919)	203.863339
0.2639 (3.7895)	64.50686
0.2708 (3.6923)	3.43721
0.2778 (3.6)	31.782121
0.2847 (3.5122)	6.688219
0.2917 (3.4286)	16.986738
0.2986 (3.3488)	42.173804
0.3056 (3.2727)	29.803217
0.3125 (3.2)	33.804933
0.3194 (3.1304)	60.212446
0.3264 (3.0638)	379.911387
0.3333 (3)	2005.72132
0.3403 (2.9388)	75.434588
0.3472 (2.88)	140.072127
0.3542 (2.8235)	9.294066
0.3611 (2.7692)	15.430795
0.3681 (2.717)	10.698128
0.375 (2.6667)	4.21834
0.3819 (2.6182)	35.411804
0.3889 (2.5714)	16.11576
0.3958 (2.5263)	11.881808
0.4028 (2.4828)	183.988521
0.4097 (2.4407)	159.788028
0.4167 (2.4)	1276.34537
0.4236 (2.3607)	113.356981
0.4306 (2.3226)	208.3604
0.4375 (2.2857)	105.674799
0.4444 (2.25)	48.09594
0.4514 (2.2154)	10.461349
0.4583 (2.1818)	50.391079
0.4653 (2.1493)	26.292831
0.4722 (2.1176)	29.647284
0.4792 (2.087)	24.120557
0.4861 (2.0571)	8.778387
0.4931 (2.0282)	8.689016
0.5 (2)	25.907638

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