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Fourier Analysis of SEA (Guggenheim Shipping ETF)


SEA (Guggenheim Shipping ETF) appears to have interesting cyclic behaviour every 27 weeks (.3577*sine), 24 weeks (.2655*cosine), and 21 weeks (.1909*cosine).

SEA (Guggenheim Shipping ETF) has an average price of 15.16 (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 6/11/2010 to 3/20/2017 for SEA (Guggenheim Shipping ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
015.16305   0 
1-.36947 .02464 (1*2π)/355355 weeks
21.45307 3.36719 (2*2π)/355178 weeks
3.44391 1.56499 (3*2π)/355118 weeks
4.07707 1.27989 (4*2π)/35589 weeks
5-.46181 .18326 (5*2π)/35571 weeks
6-.64116 .11034 (6*2π)/35559 weeks
7.34593 .25248 (7*2π)/35551 weeks
8.48003 .33272 (8*2π)/35544 weeks
9-.17461 .41929 (9*2π)/35539 weeks
10.0208 .18758 (10*2π)/35536 weeks
11-.01273 -.06873 (11*2π)/35532 weeks
12-.0379 .11309 (12*2π)/35530 weeks
13.06334 .35773 (13*2π)/35527 weeks
14.04241 .12317 (14*2π)/35525 weeks
15.26547 .03272 (15*2π)/35524 weeks
16.00795 .08957 (16*2π)/35522 weeks
17-.19092 .13934 (17*2π)/35521 weeks
18-.06974 .06124 (18*2π)/35520 weeks
19.0839 .1941 (19*2π)/35519 weeks
20.04918 .14952 (20*2π)/35518 weeks
21.0058 .21561 (21*2π)/35517 weeks
22-.10117 .05364 (22*2π)/35516 weeks
23-.01779 .11241 (23*2π)/35515 weeks
24.06735 .11511 (24*2π)/35515 weeks
25.02848 .08823 (25*2π)/35514 weeks
26.04399 .15992 (26*2π)/35514 weeks
27-.04383 .14247 (27*2π)/35513 weeks
28-.09746 .05819 (28*2π)/35513 weeks
29.07897 .00613 (29*2π)/35512 weeks
30-.00193 -.03123 (30*2π)/35512 weeks
31.01551 .11676 (31*2π)/35511 weeks
32.09631 -.00848 (32*2π)/35511 weeks
33-.00878 .06593 (33*2π)/35511 weeks
34.03238 .05454 (34*2π)/35510 weeks
35-.02407 .02067 (35*2π)/35510 weeks
36-.0242 .01586 (36*2π)/35510 weeks
37.09921 .04847 (37*2π)/35510 weeks
38.00906 .03094 (38*2π)/3559 weeks
39.06462 .07895 (39*2π)/3559 weeks
40.03807 .0701 (40*2π)/3559 weeks
41-.05822 .04236 (41*2π)/3559 weeks
42.06337 .07746 (42*2π)/3558 weeks
43.05736 -.0595 (43*2π)/3558 weeks
44.10426 .03486 (44*2π)/3558 weeks
45.07339 .10211 (45*2π)/3558 weeks
46.04181 .01268 (46*2π)/3558 weeks
47-.01787 .012 (47*2π)/3558 weeks
48.05446 -.00243 (48*2π)/3557 weeks
49.08927 -.01506 (49*2π)/3557 weeks
50.0934 .13348 (50*2π)/3557 weeks
51.06248 .10725 (51*2π)/3557 weeks
52-.01659 .05303 (52*2π)/3557 weeks
53-.01773 -.02775 (53*2π)/3557 weeks
54.01212 .04911 (54*2π)/3557 weeks
55.01342 .0837 (55*2π)/3556 weeks
56-.00222 .07253 (56*2π)/3556 weeks
57.05048 .07194 (57*2π)/3556 weeks
58.05089 .04709 (58*2π)/3556 weeks
59.0746 .05495 (59*2π)/3556 weeks
60.06199 .05515 (60*2π)/3556 weeks
61.01255 .0889 (61*2π)/3556 weeks
62-.01819 .04714 (62*2π)/3556 weeks
63-.01851 .07345 (63*2π)/3556 weeks
64.02518 .08888 (64*2π)/3556 weeks
65.08124 .03652 (65*2π)/3555 weeks
66.06379 .01267 (66*2π)/3555 weeks
67-.00373 .02565 (67*2π)/3555 weeks
68.00004 -.00688 (68*2π)/3555 weeks
69.01066 .11109 (69*2π)/3555 weeks
70.02699 .09621 (70*2π)/3555 weeks
71.04517 .01925 (71*2π)/3555 weeks
72.01389 .0455 (72*2π)/3555 weeks
73.00118 .05428 (73*2π)/3555 weeks
74-.04761 .03067 (74*2π)/3555 weeks
75.01621 .04263 (75*2π)/3555 weeks
76.0131 .01196 (76*2π)/3555 weeks
77-.00811 .01649 (77*2π)/3555 weeks
78-.01041 .00656 (78*2π)/3555 weeks
79.03078 .00849 (79*2π)/3554 weeks
80-.01031 .04865 (80*2π)/3554 weeks
81.05448 .03659 (81*2π)/3554 weeks
82.01359 -.00387 (82*2π)/3554 weeks
83.02823 .01602 (83*2π)/3554 weeks
84.04186 .03255 (84*2π)/3554 weeks
85-.01247 .03295 (85*2π)/3554 weeks
86.00223 .10508 (86*2π)/3554 weeks
87.04727 .07095 (87*2π)/3554 weeks
88.00578 .01491 (88*2π)/3554 weeks
89-.02722 -.0217 (89*2π)/3554 weeks
90-.00471 .00958 (90*2π)/3554 weeks
91.01692 .06604 (91*2π)/3554 weeks
92.03545 .0504 (92*2π)/3554 weeks
93.02603 .02301 (93*2π)/3554 weeks
94.0024 -.01427 (94*2π)/3554 weeks
95-.01526 .01635 (95*2π)/3554 weeks
96.0459 .01111 (96*2π)/3554 weeks
97.04042 .0534 (97*2π)/3554 weeks
98.01964 .03332 (98*2π)/3554 weeks
99.00826 -.00773 (99*2π)/3554 weeks
100.0091 .01254 (100*2π)/3554 weeks
101.00967 .01967 (101*2π)/3554 weeks
102.02984 .01816 (102*2π)/3553 weeks
103-.01692 .03385 (103*2π)/3553 weeks
104.01263 .03132 (104*2π)/3553 weeks
105.00687 .01691 (105*2π)/3553 weeks
106-.01006 .08809 (106*2π)/3553 weeks
107-.00639 .01156 (107*2π)/3553 weeks
108.02407 .02775 (108*2π)/3553 weeks
109.03343 .01322 (109*2π)/3553 weeks
110.00663 .01776 (110*2π)/3553 weeks
111.04517 .00529 (111*2π)/3553 weeks
112.00693 .01091 (112*2π)/3553 weeks
113.00537 .01175 (113*2π)/3553 weeks
114-.00176 .02284 (114*2π)/3553 weeks
115.03506 .00193 (115*2π)/3553 weeks
116.01827 .0299 (116*2π)/3553 weeks
117.03254 .00265 (117*2π)/3553 weeks
118-.01595 .00888 (118*2π)/3553 weeks
119.0305 .03303 (119*2π)/3553 weeks
120.0224 .03868 (120*2π)/3553 weeks
121.00075 -.00559 (121*2π)/3553 weeks
122-.01017 .00047 (122*2π)/3553 weeks
123.00947 .0311 (123*2π)/3553 weeks
124.03637 .01081 (124*2π)/3553 weeks
125.0023 .01254 (125*2π)/3553 weeks
126-.01191 .00478 (126*2π)/3553 weeks
127.02081 -.01714 (127*2π)/3553 weeks
128.03143 .01992 (128*2π)/3553 weeks
129.02147 .02786 (129*2π)/3553 weeks
130-.01195 .03959 (130*2π)/3553 weeks
131-.01446 -.00954 (131*2π)/3553 weeks
132.0219 -.00873 (132*2π)/3553 weeks
133.00039 .0353 (133*2π)/3553 weeks
134.01706 -.00771 (134*2π)/3553 weeks
135-.00046 -.01137 (135*2π)/3553 weeks
136-.00562 .00216 (136*2π)/3553 weeks
137.01028 -.00562 (137*2π)/3553 weeks
138.03386 -.0285 (138*2π)/3553 weeks
139.02605 .01739 (139*2π)/3553 weeks
140.00305 .03135 (140*2π)/3553 weeks
141.01668 .0207 (141*2π)/3553 weeks
142.01501 .0127 (142*2π)/3553 weeks
143.02077 .01459 (143*2π)/3552 weeks
144-.01416 .00792 (144*2π)/3552 weeks
145.00844 -.00495 (145*2π)/3552 weeks
146.03751 -.01927 (146*2π)/3552 weeks
147.05047 -.00093 (147*2π)/3552 weeks
148-.00748 .00101 (148*2π)/3552 weeks
149-.012 .01611 (149*2π)/3552 weeks
150.02377 .00627 (150*2π)/3552 weeks
151.02159 .00343 (151*2π)/3552 weeks
152.034 .00446 (152*2π)/3552 weeks
153.03833 -.01024 (153*2π)/3552 weeks
154-.00748 .01604 (154*2π)/3552 weeks
155.0191 -.00126 (155*2π)/3552 weeks
156.03406 -.0115 (156*2π)/3552 weeks
157.02456 .02101 (157*2π)/3552 weeks
158.01429 .02858 (158*2π)/3552 weeks
159.01485 -.00464 (159*2π)/3552 weeks
160-.02872 -.03451 (160*2π)/3552 weeks
161.0324 -.02139 (161*2π)/3552 weeks
162.01915 -.02618 (162*2π)/3552 weeks
163.00047 .00711 (163*2π)/3552 weeks
164.02046 -.01194 (164*2π)/3552 weeks
165-.0021 -.03284 (165*2π)/3552 weeks
166.04216 -.02601 (166*2π)/3552 weeks
167.05954 -.02485 (167*2π)/3552 weeks
168.02924 -.00256 (168*2π)/3552 weeks
169.00459 -.00299 (169*2π)/3552 weeks
170.04516 .01638 (170*2π)/3552 weeks
171.04805 .01683 (171*2π)/3552 weeks
172.04469 -.03315 (172*2π)/3552 weeks
173.0544 -.01103 (173*2π)/3552 weeks
174.03843 .01464 (174*2π)/3552 weeks
175.02837 .02439 (175*2π)/3552 weeks
176.0229 -.0216 (176*2π)/3552 weeks
177.05704 -.00975 (177*2π)/3552 weeks
178.05704 .00975 (178*2π)/3552 weeks
179.0229 .0216 (179*2π)/3552 weeks
180.02837 -.02439 (180*2π)/3552 weeks
181.03843 -.01464 (181*2π)/3552 weeks
182.0544 .01103 (182*2π)/3552 weeks
183.04469 .03315 (183*2π)/3552 weeks
184.04805 -.01683 (184*2π)/3552 weeks
185.04516 -.01638 (185*2π)/3552 weeks
186.00459 .00299 (186*2π)/3552 weeks
187.02924 .00256 (187*2π)/3552 weeks
188.05954 .02485 (188*2π)/3552 weeks
189.04216 .02601 (189*2π)/3552 weeks
190-.0021 .03284 (190*2π)/3552 weeks
191.02046 .01194 (191*2π)/3552 weeks
192.00047 -.00711 (192*2π)/3552 weeks
193.01915 .02618 (193*2π)/3552 weeks
194.0324 .02139 (194*2π)/3552 weeks
195-.02872 .03451 (195*2π)/3552 weeks
196.01485 .00464 (196*2π)/3552 weeks
197.01429 -.02858 (197*2π)/3552 weeks
198.02456 -.02101 (198*2π)/3552 weeks
199.03406 .0115 (199*2π)/3552 weeks
200.0191 .00126 (200*2π)/3552 weeks
201-.00748 -.01604 (201*2π)/3552 weeks
202.03833 .01024 (202*2π)/3552 weeks
203.034 -.00446 (203*2π)/3552 weeks
204.02159 -.00343 (204*2π)/3552 weeks
205.02377 -.00627 (205*2π)/3552 weeks
206-.012 -.01611 (206*2π)/3552 weeks
207-.00748 -.00101 (207*2π)/3552 weeks
208.05047 .00093 (208*2π)/3552 weeks
209.03751 .01927 (209*2π)/3552 weeks
210.00844 .00495 (210*2π)/3552 weeks
211-.01416 -.00792 (211*2π)/3552 weeks
212.02077 -.01459 (212*2π)/3552 weeks
213.01501 -.0127 (213*2π)/3552 weeks
214.01668 -.0207 (214*2π)/3552 weeks
215.00305 -.03135 (215*2π)/3552 weeks
216.02605 -.01739 (216*2π)/3552 weeks
217.03386 .0285 (217*2π)/3552 weeks
218.01028 .00562 (218*2π)/3552 weeks
219-.00562 -.00216 (219*2π)/3552 weeks
220-.00046 .01137 (220*2π)/3552 weeks
221.01706 .00771 (221*2π)/3552 weeks
222.00039 -.0353 (222*2π)/3552 weeks
223.0219 .00873 (223*2π)/3552 weeks
224-.01446 .00954 (224*2π)/3552 weeks
225-.01195 -.03959 (225*2π)/3552 weeks
226.02147 -.02786 (226*2π)/3552 weeks
227.03143 -.01992 (227*2π)/3552 weeks
228.02081 .01714 (228*2π)/3552 weeks
229-.01191 -.00478 (229*2π)/3552 weeks
230.0023 -.01254 (230*2π)/3552 weeks
231.03637 -.01081 (231*2π)/3552 weeks
232.00947 -.0311 (232*2π)/3552 weeks
233-.01017 -.00047 (233*2π)/3552 weeks
234.00075 .00559 (234*2π)/3552 weeks
235.0224 -.03868 (235*2π)/3552 weeks
236.0305 -.03303 (236*2π)/3552 weeks
237-.01595 -.00888 (237*2π)/3551 weeks
238.03254 -.00265 (238*2π)/3551 weeks
239.01827 -.0299 (239*2π)/3551 weeks
240.03506 -.00193 (240*2π)/3551 weeks
241-.00176 -.02284 (241*2π)/3551 weeks
242.00537 -.01175 (242*2π)/3551 weeks
243.00693 -.01091 (243*2π)/3551 weeks
244.04517 -.00529 (244*2π)/3551 weeks
245.00663 -.01776 (245*2π)/3551 weeks
246.03343 -.01322 (246*2π)/3551 weeks
247.02407 -.02775 (247*2π)/3551 weeks
248-.00639 -.01156 (248*2π)/3551 weeks
249-.01006 -.08809 (249*2π)/3551 weeks
250.00687 -.01691 (250*2π)/3551 weeks
251.01263 -.03132 (251*2π)/3551 weeks
252-.01692 -.03385 (252*2π)/3551 weeks
253.02984 -.01816 (253*2π)/3551 weeks
254.00967 -.01967 (254*2π)/3551 weeks
255.0091 -.01254 (255*2π)/3551 weeks
256.00826 .00773 (256*2π)/3551 weeks
257.01964 -.03332 (257*2π)/3551 weeks
258.04042 -.0534 (258*2π)/3551 weeks
259.0459 -.01111 (259*2π)/3551 weeks
260-.01526 -.01635 (260*2π)/3551 weeks
261.0024 .01427 (261*2π)/3551 weeks
262.02603 -.02301 (262*2π)/3551 weeks
263.03545 -.0504 (263*2π)/3551 weeks
264.01692 -.06604 (264*2π)/3551 weeks
265-.00471 -.00958 (265*2π)/3551 weeks
266-.02722 .0217 (266*2π)/3551 weeks
267.00578 -.01491 (267*2π)/3551 weeks
268.04727 -.07095 (268*2π)/3551 weeks
269.00223 -.10508 (269*2π)/3551 weeks
270-.01247 -.03295 (270*2π)/3551 weeks
271.04186 -.03255 (271*2π)/3551 weeks
272.02823 -.01602 (272*2π)/3551 weeks
273.01359 .00387 (273*2π)/3551 weeks
274.05448 -.03659 (274*2π)/3551 weeks
275-.01031 -.04865 (275*2π)/3551 weeks
276.03078 -.00849 (276*2π)/3551 weeks
277-.01041 -.00656 (277*2π)/3551 weeks
278-.00811 -.01649 (278*2π)/3551 weeks
279.0131 -.01196 (279*2π)/3551 weeks
280.01621 -.04263 (280*2π)/3551 weeks
281-.04761 -.03067 (281*2π)/3551 weeks
282.00118 -.05428 (282*2π)/3551 weeks
283.01389 -.0455 (283*2π)/3551 weeks
284.04517 -.01925 (284*2π)/3551 weeks
285.02699 -.09621 (285*2π)/3551 weeks
286.01066 -.11109 (286*2π)/3551 weeks
287.00004 .00688 (287*2π)/3551 weeks
288-.00373 -.02565 (288*2π)/3551 weeks
289.06379 -.01267 (289*2π)/3551 weeks
290.08124 -.03652 (290*2π)/3551 weeks
291.02518 -.08888 (291*2π)/3551 weeks
292-.01851 -.07345 (292*2π)/3551 weeks
293-.01819 -.04714 (293*2π)/3551 weeks
294.01255 -.0889 (294*2π)/3551 weeks
295.06199 -.05515 (295*2π)/3551 weeks
296.0746 -.05495 (296*2π)/3551 weeks
297.05089 -.04709 (297*2π)/3551 weeks
298.05048 -.07194 (298*2π)/3551 weeks
299-.00222 -.07253 (299*2π)/3551 weeks
300.01342 -.0837 (300*2π)/3551 weeks
301.01212 -.04911 (301*2π)/3551 weeks
302-.01773 .02775 (302*2π)/3551 weeks
303-.01659 -.05303 (303*2π)/3551 weeks
304.06248 -.10725 (304*2π)/3551 weeks
305.0934 -.13348 (305*2π)/3551 weeks
306.08927 .01506 (306*2π)/3551 weeks
307.05446 .00243 (307*2π)/3551 weeks
308-.01787 -.012 (308*2π)/3551 weeks
309.04181 -.01268 (309*2π)/3551 weeks
310.07339 -.10211 (310*2π)/3551 weeks
311.10426 -.03486 (311*2π)/3551 weeks
312.05736 .0595 (312*2π)/3551 weeks
313.06337 -.07746 (313*2π)/3551 weeks
314-.05822 -.04236 (314*2π)/3551 weeks
315.03807 -.0701 (315*2π)/3551 weeks
316.06462 -.07895 (316*2π)/3551 weeks
317.00906 -.03094 (317*2π)/3551 weeks
318.09921 -.04847 (318*2π)/3551 weeks
319-.0242 -.01586 (319*2π)/3551 weeks
320-.02407 -.02067 (320*2π)/3551 weeks
321.03238 -.05454 (321*2π)/3551 weeks
322-.00878 -.06593 (322*2π)/3551 weeks
323.09631 .00848 (323*2π)/3551 weeks
324.01551 -.11676 (324*2π)/3551 weeks
325-.00193 .03123 (325*2π)/3551 weeks
326.07897 -.00613 (326*2π)/3551 weeks
327-.09746 -.05819 (327*2π)/3551 weeks
328-.04383 -.14247 (328*2π)/3551 weeks
329.04399 -.15992 (329*2π)/3551 weeks
330.02848 -.08823 (330*2π)/3551 weeks
331.06735 -.11511 (331*2π)/3551 weeks
332-.01779 -.11241 (332*2π)/3551 weeks
333-.10117 -.05364 (333*2π)/3551 weeks
334.0058 -.21561 (334*2π)/3551 weeks
335.04918 -.14952 (335*2π)/3551 weeks
336.0839 -.1941 (336*2π)/3551 weeks
337-.06974 -.06124 (337*2π)/3551 weeks
338-.19092 -.13934 (338*2π)/3551 weeks
339.00795 -.08957 (339*2π)/3551 weeks
340.26547 -.03272 (340*2π)/3551 weeks
341.04241 -.12317 (341*2π)/3551 weeks
342.06334 -.35773 (342*2π)/3551 weeks
343-.0379 -.11309 (343*2π)/3551 weeks
344-.01273 .06873 (344*2π)/3551 weeks
345.0208 -.18758 (345*2π)/3551 weeks
346-.17461 -.41929 (346*2π)/3551 weeks
347.48003 -.33272 (347*2π)/3551 weeks
348.34593 -.25248 (348*2π)/3551 weeks
349-.64116 -.11034 (349*2π)/3551 weeks
350-.46181 -.18326 (350*2π)/3551 weeks
351.07707 -1.27989 (351*2π)/3551 weeks
352.44391 -1.56499 (352*2π)/3551 weeks
3531.45307 -3.36719 (353*2π)/3551 weeks

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