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# Fourier Analysis of ROYT (Pacific Coast Oil Trust)

ROYT (Pacific Coast Oil Trust) appears to have interesting cyclic behaviour every 31 weeks (.3964*sine), 21 weeks (.2664*sine), and 28 weeks (.255*sine).

ROYT (Pacific Coast Oil Trust) has an average price of 5.9 (topmost row, frequency = 0).

Click on the checkboxes shown on the right to see how the various frequencies contribute to the graph. Look for large magnitude coefficients (sine or cosine), as these are associated with frequencies which contribute most to the associated stock plot. If you find a large magnitude coefficient which dramatically changes the graph, look at the associated "Period" in weeks, as you may have found a significant recurring cycle for the stock of interest.

Right click on the graph above to see the menu of operations (download, full screen, etc.)

## Fourier Analysis

Using data from 5/3/2012 to 4/16/2018 for ROYT (Pacific Coast Oil Trust), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
05.89987   0
11.5379 5.80576 (1*2π)/312312 weeks
2-.58756 1.23459 (2*2π)/312156 weeks
3.15793 1.21999 (3*2π)/312104 weeks
4-.15275 .60246 (4*2π)/31278 weeks
5.21243 .3764 (5*2π)/31262 weeks
6.19124 .83543 (6*2π)/31252 weeks
7-.02052 .34384 (7*2π)/31245 weeks
8-.07624 .28375 (8*2π)/31239 weeks
9.00705 .28626 (9*2π)/31235 weeks
10.02279 .39639 (10*2π)/31231 weeks
11-.12604 .25495 (11*2π)/31228 weeks
12.04076 .11975 (12*2π)/31226 weeks
13-.00642 .14675 (13*2π)/31224 weeks
14.04969 .20432 (14*2π)/31222 weeks
15.07883 .26644 (15*2π)/31221 weeks
16-.05861 .13132 (16*2π)/31220 weeks
17.15336 .17833 (17*2π)/31218 weeks
18-.07151 .24988 (18*2π)/31217 weeks
19.0456 .1009 (19*2π)/31216 weeks
20.02813 .16249 (20*2π)/31216 weeks
21.0259 .06259 (21*2π)/31215 weeks
22.04384 .13142 (22*2π)/31214 weeks
23.11639 .08831 (23*2π)/31214 weeks
24.05477 .19061 (24*2π)/31213 weeks
25-.01868 .06522 (25*2π)/31212 weeks
26.10989 .0863 (26*2π)/31212 weeks
27-.00696 .05271 (27*2π)/31212 weeks
28.12015 .10587 (28*2π)/31211 weeks
29-.05017 .15312 (29*2π)/31211 weeks
30.06893 -.0058 (30*2π)/31210 weeks
31.04716 .11917 (31*2π)/31210 weeks
32.01397 .03926 (32*2π)/31210 weeks
33.06176 .04972 (33*2π)/3129 weeks
34.04468 .12444 (34*2π)/3129 weeks
35.02279 .03337 (35*2π)/3129 weeks
36.1036 .1014 (36*2π)/3129 weeks
37-.00649 .06454 (37*2π)/3128 weeks
38.09134 .07927 (38*2π)/3128 weeks
39.03938 .13408 (39*2π)/3128 weeks
40.07884 .02498 (40*2π)/3128 weeks
41.08345 .1024 (41*2π)/3128 weeks
42.04356 .06648 (42*2π)/3127 weeks
43.05217 .09034 (43*2π)/3127 weeks
44.04214 .06038 (44*2π)/3127 weeks
45.05285 .10279 (45*2π)/3127 weeks
46.03165 .04763 (46*2π)/3127 weeks
47.0765 .07106 (47*2π)/3127 weeks
48.00491 .02578 (48*2π)/3127 weeks
49.073 .02924 (49*2π)/3126 weeks
50.03425 .10613 (50*2π)/3126 weeks
51.04454 .0261 (51*2π)/3126 weeks
52.06124 .0258 (52*2π)/3126 weeks
53.0446 .04958 (53*2π)/3126 weeks
54.06119 .07923 (54*2π)/3126 weeks
55.01201 .07334 (55*2π)/3126 weeks
56.01156 .04857 (56*2π)/3126 weeks
57.07538 .02948 (57*2π)/3125 weeks
58.0276 .08631 (58*2π)/3125 weeks
59.03261 .05686 (59*2π)/3125 weeks
60.03773 .03914 (60*2π)/3125 weeks
61.02932 .04708 (61*2π)/3125 weeks
62.05535 .06422 (62*2π)/3125 weeks
63.03049 .0698 (63*2π)/3125 weeks
64.0427 .05918 (64*2π)/3125 weeks
65.00296 .0438 (65*2π)/3125 weeks
66.04063 .03751 (66*2π)/3125 weeks
67.03877 .06815 (67*2π)/3125 weeks
68.03191 .03489 (68*2π)/3125 weeks
69.00727 .04307 (69*2π)/3125 weeks
70.02673 .0262 (70*2π)/3124 weeks
71.03926 .03495 (71*2π)/3124 weeks
72.04892 .03816 (72*2π)/3124 weeks
73.02853 .04592 (73*2π)/3124 weeks
74.03027 .01265 (74*2π)/3124 weeks
75.06048 .04 (75*2π)/3124 weeks
76.01535 .03275 (76*2π)/3124 weeks
77.05389 .02896 (77*2π)/3124 weeks
78.01744 .03692 (78*2π)/3124 weeks
79.03341 .01495 (79*2π)/3124 weeks
80.02886 .05375 (80*2π)/3124 weeks
81-.00873 .00463 (81*2π)/3124 weeks
82.04527 .01758 (82*2π)/3124 weeks
83.02786 .02349 (83*2π)/3124 weeks
84.04026 .00345 (84*2π)/3124 weeks
85.05127 .02328 (85*2π)/3124 weeks
86.02011 .03253 (86*2π)/3124 weeks
87.04337 .03666 (87*2π)/3124 weeks
88.04091 .03734 (88*2π)/3124 weeks
89.03392 .01845 (89*2π)/3124 weeks
90.02224 .03435 (90*2π)/3123 weeks
91.01118 .0134 (91*2π)/3123 weeks
92.04946 .00805 (92*2π)/3123 weeks
93.03995 .01771 (93*2π)/3123 weeks
94.03369 .02829 (94*2π)/3123 weeks
95.03395 .00822 (95*2π)/3123 weeks
96.04509 .01033 (96*2π)/3123 weeks
97.05072 .01223 (97*2π)/3123 weeks
98.05304 .02022 (98*2π)/3123 weeks
99.03957 .03681 (99*2π)/3123 weeks
100.03285 .00558 (100*2π)/3123 weeks
101.04982 .03529 (101*2π)/3123 weeks
102.02452 -.00288 (102*2π)/3123 weeks
103.05599 .02121 (103*2π)/3123 weeks
104.03614 .0091 (104*2π)/3123 weeks
105.04812 .00846 (105*2π)/3123 weeks
106.04405 .00887 (106*2π)/3123 weeks
107.06042 .02536 (107*2π)/3123 weeks
108.04374 .02253 (108*2π)/3123 weeks
109.05394 .02106 (109*2π)/3123 weeks
110.03019 .0401 (110*2π)/3123 weeks
111.02677 .00922 (111*2π)/3123 weeks
112.04494 .02108 (112*2π)/3123 weeks
113.04228 .00565 (113*2π)/3123 weeks
114.04166 .02477 (114*2π)/3123 weeks
115.03789 .02813 (115*2π)/3123 weeks
116.03207 -.00149 (116*2π)/3123 weeks
117.06792 .02865 (117*2π)/3123 weeks
118.04318 .0345 (118*2π)/3123 weeks
119.03882 .02174 (119*2π)/3123 weeks
120.03118 .03364 (120*2π)/3123 weeks
121.03335 .00396 (121*2π)/3123 weeks
122.04548 .03559 (122*2π)/3123 weeks
123.04093 .01336 (123*2π)/3123 weeks
124.04802 .03212 (124*2π)/3123 weeks
125.02594 .0095 (125*2π)/3122 weeks
126.04635 .01849 (126*2π)/3122 weeks
127.02573 .02231 (127*2π)/3122 weeks
128.05787 .01966 (128*2π)/3122 weeks
129.0383 .02427 (129*2π)/3122 weeks
130.02484 .02833 (130*2π)/3122 weeks
131.03104 .01723 (131*2π)/3122 weeks
132.01755 .01647 (132*2π)/3122 weeks
133.02979 .01836 (133*2π)/3122 weeks
134.01875 .02352 (134*2π)/3122 weeks
135.0057 .01415 (135*2π)/3122 weeks
136.04192 -.00898 (136*2π)/3122 weeks
137.02837 .01775 (137*2π)/3122 weeks
138.0214 .00349 (138*2π)/3122 weeks
139.02975 .01847 (139*2π)/3122 weeks
140.03457 .00965 (140*2π)/3122 weeks
141.04461 .02411 (141*2π)/3122 weeks
142.01698 .01922 (142*2π)/3122 weeks
143.02261 .0123 (143*2π)/3122 weeks
144.03073 .00041 (144*2π)/3122 weeks
145.02211 .01696 (145*2π)/3122 weeks
146.03202 -.00303 (146*2π)/3122 weeks
147.03386 -.00069 (147*2π)/3122 weeks
148.03614 .01428 (148*2π)/3122 weeks
149.03247 -.0018 (149*2π)/3122 weeks
150.02568 .02222 (150*2π)/3122 weeks
151.01615 -.01989 (151*2π)/3122 weeks
152.04146 .00346 (152*2π)/3122 weeks
153.03472 .00455 (153*2π)/3122 weeks
154.02586 .00746 (154*2π)/3122 weeks
155.02054 .02206 (155*2π)/3122 weeks
156.01799   (156*2π)/3122 weeks
157.02054 -.02206 (157*2π)/3122 weeks
158.02586 -.00746 (158*2π)/3122 weeks
159.03472 -.00455 (159*2π)/3122 weeks
160.04146 -.00346 (160*2π)/3122 weeks
161.01615 .01989 (161*2π)/3122 weeks
162.02568 -.02222 (162*2π)/3122 weeks
163.03247 .0018 (163*2π)/3122 weeks
164.03614 -.01428 (164*2π)/3122 weeks
165.03386 .00069 (165*2π)/3122 weeks
166.03202 .00303 (166*2π)/3122 weeks
167.02211 -.01696 (167*2π)/3122 weeks
168.03073 -.00041 (168*2π)/3122 weeks
169.02261 -.0123 (169*2π)/3122 weeks
170.01698 -.01922 (170*2π)/3122 weeks
171.04461 -.02411 (171*2π)/3122 weeks
172.03457 -.00965 (172*2π)/3122 weeks
173.02975 -.01847 (173*2π)/3122 weeks
174.0214 -.00349 (174*2π)/3122 weeks
175.02837 -.01775 (175*2π)/3122 weeks
176.04192 .00898 (176*2π)/3122 weeks
177.0057 -.01415 (177*2π)/3122 weeks
178.01875 -.02352 (178*2π)/3122 weeks
179.02979 -.01836 (179*2π)/3122 weeks
180.01755 -.01647 (180*2π)/3122 weeks
181.03104 -.01723 (181*2π)/3122 weeks
182.02484 -.02833 (182*2π)/3122 weeks
183.0383 -.02427 (183*2π)/3122 weeks
184.05787 -.01966 (184*2π)/3122 weeks
185.02573 -.02231 (185*2π)/3122 weeks
186.04635 -.01849 (186*2π)/3122 weeks
187.02594 -.0095 (187*2π)/3122 weeks
188.04802 -.03212 (188*2π)/3122 weeks
189.04093 -.01336 (189*2π)/3122 weeks
190.04548 -.03559 (190*2π)/3122 weeks
191.03335 -.00396 (191*2π)/3122 weeks
192.03118 -.03364 (192*2π)/3122 weeks
193.03882 -.02174 (193*2π)/3122 weeks
194.04318 -.0345 (194*2π)/3122 weeks
195.06792 -.02865 (195*2π)/3122 weeks
196.03207 .00149 (196*2π)/3122 weeks
197.03789 -.02813 (197*2π)/3122 weeks
198.04166 -.02477 (198*2π)/3122 weeks
199.04228 -.00565 (199*2π)/3122 weeks
200.04494 -.02108 (200*2π)/3122 weeks
201.02677 -.00922 (201*2π)/3122 weeks
202.03019 -.0401 (202*2π)/3122 weeks
203.05394 -.02106 (203*2π)/3122 weeks
204.04374 -.02253 (204*2π)/3122 weeks
205.06042 -.02536 (205*2π)/3122 weeks
206.04405 -.00887 (206*2π)/3122 weeks
207.04812 -.00846 (207*2π)/3122 weeks
208.03614 -.0091 (208*2π)/3122 weeks
209.05599 -.02121 (209*2π)/3121 weeks
210.02452 .00288 (210*2π)/3121 weeks
211.04982 -.03529 (211*2π)/3121 weeks
212.03285 -.00558 (212*2π)/3121 weeks
213.03957 -.03681 (213*2π)/3121 weeks
214.05304 -.02022 (214*2π)/3121 weeks
215.05072 -.01223 (215*2π)/3121 weeks
216.04509 -.01033 (216*2π)/3121 weeks
217.03395 -.00822 (217*2π)/3121 weeks
218.03369 -.02829 (218*2π)/3121 weeks
219.03995 -.01771 (219*2π)/3121 weeks
220.04946 -.00805 (220*2π)/3121 weeks
221.01118 -.0134 (221*2π)/3121 weeks
222.02224 -.03435 (222*2π)/3121 weeks
223.03392 -.01845 (223*2π)/3121 weeks
224.04091 -.03734 (224*2π)/3121 weeks
225.04337 -.03666 (225*2π)/3121 weeks
226.02011 -.03253 (226*2π)/3121 weeks
227.05127 -.02328 (227*2π)/3121 weeks
228.04026 -.00345 (228*2π)/3121 weeks
229.02786 -.02349 (229*2π)/3121 weeks
230.04527 -.01758 (230*2π)/3121 weeks
231-.00873 -.00463 (231*2π)/3121 weeks
232.02886 -.05375 (232*2π)/3121 weeks
233.03341 -.01495 (233*2π)/3121 weeks
234.01744 -.03692 (234*2π)/3121 weeks
235.05389 -.02896 (235*2π)/3121 weeks
236.01535 -.03275 (236*2π)/3121 weeks
237.06048 -.04 (237*2π)/3121 weeks
238.03027 -.01265 (238*2π)/3121 weeks
239.02853 -.04592 (239*2π)/3121 weeks
240.04892 -.03816 (240*2π)/3121 weeks
241.03926 -.03495 (241*2π)/3121 weeks
242.02673 -.0262 (242*2π)/3121 weeks
243.00727 -.04307 (243*2π)/3121 weeks
244.03191 -.03489 (244*2π)/3121 weeks
245.03877 -.06815 (245*2π)/3121 weeks
246.04063 -.03751 (246*2π)/3121 weeks
247.00296 -.0438 (247*2π)/3121 weeks
248.0427 -.05918 (248*2π)/3121 weeks
249.03049 -.0698 (249*2π)/3121 weeks
250.05535 -.06422 (250*2π)/3121 weeks
251.02932 -.04708 (251*2π)/3121 weeks
252.03773 -.03914 (252*2π)/3121 weeks
253.03261 -.05686 (253*2π)/3121 weeks
254.0276 -.08631 (254*2π)/3121 weeks
255.07538 -.02948 (255*2π)/3121 weeks
256.01156 -.04857 (256*2π)/3121 weeks
257.01201 -.07334 (257*2π)/3121 weeks
258.06119 -.07923 (258*2π)/3121 weeks
259.0446 -.04958 (259*2π)/3121 weeks
260.06124 -.0258 (260*2π)/3121 weeks
261.04454 -.0261 (261*2π)/3121 weeks
262.03425 -.10613 (262*2π)/3121 weeks
263.073 -.02924 (263*2π)/3121 weeks
264.00491 -.02578 (264*2π)/3121 weeks
265.0765 -.07106 (265*2π)/3121 weeks
266.03165 -.04763 (266*2π)/3121 weeks
267.05285 -.10279 (267*2π)/3121 weeks
268.04214 -.06038 (268*2π)/3121 weeks
269.05217 -.09034 (269*2π)/3121 weeks
270.04356 -.06648 (270*2π)/3121 weeks
271.08345 -.1024 (271*2π)/3121 weeks
272.07884 -.02498 (272*2π)/3121 weeks
273.03938 -.13408 (273*2π)/3121 weeks
274.09134 -.07927 (274*2π)/3121 weeks
275-.00649 -.06454 (275*2π)/3121 weeks
276.1036 -.1014 (276*2π)/3121 weeks
277.02279 -.03337 (277*2π)/3121 weeks
278.04468 -.12444 (278*2π)/3121 weeks
279.06176 -.04972 (279*2π)/3121 weeks
280.01397 -.03926 (280*2π)/3121 weeks
281.04716 -.11917 (281*2π)/3121 weeks
282.06893 .0058 (282*2π)/3121 weeks
283-.05017 -.15312 (283*2π)/3121 weeks
284.12015 -.10587 (284*2π)/3121 weeks
285-.00696 -.05271 (285*2π)/3121 weeks
286.10989 -.0863 (286*2π)/3121 weeks
287-.01868 -.06522 (287*2π)/3121 weeks
288.05477 -.19061 (288*2π)/3121 weeks
289.11639 -.08831 (289*2π)/3121 weeks
290.04384 -.13142 (290*2π)/3121 weeks
291.0259 -.06259 (291*2π)/3121 weeks
292.02813 -.16249 (292*2π)/3121 weeks
293.0456 -.1009 (293*2π)/3121 weeks
294-.07151 -.24988 (294*2π)/3121 weeks
295.15336 -.17833 (295*2π)/3121 weeks
296-.05861 -.13132 (296*2π)/3121 weeks
297.07883 -.26644 (297*2π)/3121 weeks
298.04969 -.20432 (298*2π)/3121 weeks
299-.00642 -.14675 (299*2π)/3121 weeks
300.04076 -.11975 (300*2π)/3121 weeks
301-.12604 -.25495 (301*2π)/3121 weeks
302.02279 -.39639 (302*2π)/3121 weeks
303.00705 -.28626 (303*2π)/3121 weeks
304-.07624 -.28375 (304*2π)/3121 weeks
305-.02052 -.34384 (305*2π)/3121 weeks
306.19124 -.83543 (306*2π)/3121 weeks
307.21243 -.3764 (307*2π)/3121 weeks
308-.15275 -.60246 (308*2π)/3121 weeks
309.15793 -1.21999 (309*2π)/3121 weeks
310-.58756 -1.23459 (310*2π)/3121 weeks