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# Fourier Analysis of EXM (Excel Maritime Carriers Ltd.)

EXM (Excel Maritime Carriers Ltd.) appears to have interesting cyclic behaviour every 10 weeks (38.8133*sine), 10 weeks (37.3201*sine), and 10 weeks (36.8996*cosine).

EXM (Excel Maritime Carriers Ltd.) has an average price of 56.97 (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.

## Fourier Analysis

Using data from 1/29/1988 to 1/9/2017 for EXM (Excel Maritime Carriers Ltd.), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
056.96664   0
1-6.14756 -2.089 (1*2π)/952952 weeks
2-17.02605 45.32421 (2*2π)/952476 weeks
332.66933 34.18665 (3*2π)/952317 weeks
4-1.70636 -35.46052 (4*2π)/952238 weeks
5-37.03265 26.48567 (5*2π)/952190 weeks
618.44621 16.22279 (6*2π)/952159 weeks
718.93856 -27.19122 (7*2π)/952136 weeks
8-37.02279 -3.81978 (8*2π)/952119 weeks
921.66581 13.80138 (9*2π)/952106 weeks
1025.28038 -13.66195 (10*2π)/95295 weeks
11-8.18612 -18.06117 (11*2π)/95287 weeks
1211.93122 32.04277 (12*2π)/95279 weeks
1318.02439 -7.05845 (13*2π)/95273 weeks
145.88151 -5.07161 (14*2π)/95268 weeks
15-5.35455 13.97349 (15*2π)/95263 weeks
1625.10386 9.93188 (16*2π)/95260 weeks
17-5.29998 4.11138 (17*2π)/95256 weeks
18.25449 -1.14449 (18*2π)/95253 weeks
194.46624 20.05792 (19*2π)/95250 weeks
201.24305 -8.4369 (20*2π)/95248 weeks
212.83384 6.67252 (21*2π)/95245 weeks
22-6.7237 1.9537 (22*2π)/95243 weeks
2315.03314 .96193 (23*2π)/95241 weeks
24-7.93653 2.10677 (24*2π)/95240 weeks
258.82321 -2.95101 (25*2π)/95238 weeks
265.61153 7.0575 (26*2π)/95237 weeks
271.46508 -4.95161 (27*2π)/95235 weeks
288.79388 16.10663 (28*2π)/95234 weeks
29-1.72388 -9.55965 (29*2π)/95233 weeks
308.35036 5.41039 (30*2π)/95232 weeks
31-1.19552 15.57009 (31*2π)/95231 weeks
3212.6989 -8.06922 (32*2π)/95230 weeks
33-15.42917 6.1782 (33*2π)/95229 weeks
349.61577 5.62701 (34*2π)/95228 weeks
3513.18833 2.09651 (35*2π)/95227 weeks
36-15.98977 -10.39844 (36*2π)/95226 weeks
3711.24743 21.32582 (37*2π)/95226 weeks
388.51111 -7.10748 (38*2π)/95225 weeks
39-2.02317 -9.09199 (39*2π)/95224 weeks
40-4.32221 24.61724 (40*2π)/95224 weeks
4122.72845 -9.88728 (41*2π)/95223 weeks
42-10.10811 2.21054 (42*2π)/95223 weeks
43-4.26187 11.19748 (43*2π)/95222 weeks
4422.28811 5.82471 (44*2π)/95222 weeks
45-18.22185 -10.62779 (45*2π)/95221 weeks
465.49757 17.47055 (46*2π)/95221 weeks
475.87447 -1.26604 (47*2π)/95220 weeks
48-1.88003 -16.06923 (48*2π)/95220 weeks
49-1.74289 24.34816 (49*2π)/95219 weeks
5017.92112 -11.5983 (50*2π)/95219 weeks
51-5.27334 -.19262 (51*2π)/95219 weeks
52-5.051 14.92038 (52*2π)/95218 weeks
5327.12892 1.60462 (53*2π)/95218 weeks
54-20.33409 -8.31861 (54*2π)/95218 weeks
555.46097 17.03882 (55*2π)/95217 weeks
5615.16946 9.10307 (56*2π)/95217 weeks
57-9.05937 -19.71085 (57*2π)/95217 weeks
58-8.56125 27.68025 (58*2π)/95216 weeks
5914.32152 -3.06047 (59*2π)/95216 weeks
602.32916 -11.57997 (60*2π)/95216 weeks
61-20.70687 11.60089 (61*2π)/95216 weeks
6225.9318 7.0197 (62*2π)/95215 weeks
63-2.63895 -8.54862 (63*2π)/95215 weeks
64-8.20519 -.14566 (64*2π)/95215 weeks
659.33826 22.9183 (65*2π)/95215 weeks
666.38699 -15.86102 (66*2π)/95214 weeks
67-4.66427 6.78464 (67*2π)/95214 weeks
68-6.56181 9.5428 (68*2π)/95214 weeks
6920.40853 .33618 (69*2π)/95214 weeks
70-13.47271 -1.33762 (70*2π)/95214 weeks
71.94559 3.01834 (71*2π)/95213 weeks
726.44593 13.82166 (72*2π)/95213 weeks
73.99135 -15.16818 (73*2π)/95213 weeks
74-3.38353 12.39515 (74*2π)/95213 weeks
75.17434 2.9489 (75*2π)/95213 weeks
7613.74106 -2.19801 (76*2π)/95213 weeks
77-14.45612 3.50267 (77*2π)/95212 weeks
7812.32223 5.52728 (78*2π)/95212 weeks
79-.54093 3.78994 (79*2π)/95212 weeks
80-3.70957 -3.71894 (80*2π)/95212 weeks
816.32138 17.0535 (81*2π)/95212 weeks
82-3.15964 -12.93978 (82*2π)/95212 weeks
83-1.70619 11.98291 (83*2π)/95211 weeks
841.5694 6.90336 (84*2π)/95211 weeks
859.44763 -14.24287 (85*2π)/95211 weeks
86-21.65551 14.80063 (86*2π)/95211 weeks
8719.95642 6.15357 (87*2π)/95211 weeks
883.82894 -10.65481 (88*2π)/95211 weeks
89-26.00415 -1.93267 (89*2π)/95211 weeks
9024.60479 29.58602 (90*2π)/95211 weeks
918.06438 -26.1909 (91*2π)/95210 weeks
92-22.31165 2.32177 (92*2π)/95210 weeks
932.24282 37.3201 (93*2π)/95210 weeks
9431.8892 -27.85636 (94*2π)/95210 weeks
95-36.03428 -3.80721 (95*2π)/95210 weeks
96-.37767 31.45462 (96*2π)/95210 weeks
9736.89957 -4.34853 (97*2π)/95210 weeks
98-33.21264 -30.65712 (98*2π)/95210 weeks
99-5.66489 38.81329 (99*2π)/95210 weeks
10028.52083 2.3402 (100*2π)/95210 weeks
101-5.84419 -34.34841 (101*2π)/9529 weeks
102-30.45118 32.03299 (102*2π)/9529 weeks
10333.08463 6.29345 (103*2π)/9529 weeks
1044.0752 -19.54141 (104*2π)/9529 weeks
105-32.22877 4.11249 (105*2π)/9529 weeks
10623.15448 29.14904 (106*2π)/9529 weeks
1074.45386 -20.64697 (107*2π)/9529 weeks
108-14.38926 -6.02242 (108*2π)/9529 weeks
109-6.11658 28.57108 (109*2π)/9529 weeks
11022.38574 -13.59838 (110*2π)/9529 weeks
111-12.5696 -5.00305 (111*2π)/9529 weeks
112-12.2894 7.06563 (112*2π)/9529 weeks
11322.49463 13.65429 (113*2π)/9528 weeks
114-6.78914 -18.45942 (114*2π)/9528 weeks
115-6.25348 6.80075 (115*2π)/9528 weeks
1162.1872 17.85168 (116*2π)/9528 weeks
11715.50533 -15.05942 (117*2π)/9528 weeks
118-18.03114 7.44357 (118*2π)/9528 weeks
119.63074 8.62599 (119*2π)/9528 weeks
12012.80998 3.58187 (120*2π)/9528 weeks
121-18.2996 -12.43139 (121*2π)/9528 weeks
1224.9646 14.39954 (122*2π)/9528 weeks
123.98564 -1.76301 (123*2π)/9528 weeks
1241.378 -9.45989 (124*2π)/9528 weeks
125-7.89263 15.22153 (125*2π)/9528 weeks
1268.96186 -10.65609 (126*2π)/9528 weeks
127-3.19874 5.78883 (127*2π)/9527 weeks
128-1.45538 -.30995 (128*2π)/9527 weeks
12913.27824 3.46882 (129*2π)/9527 weeks
130-16.32995 1.63987 (130*2π)/9527 weeks
13111.98987 7.94377 (131*2π)/9527 weeks
132-4.15501 -.6279 (132*2π)/9527 weeks
133-7.64884 -4.65498 (133*2π)/9527 weeks
1343.22162 19.2406 (134*2π)/9527 weeks
1351.92832 -18.01551 (135*2π)/9527 weeks
136-8.84144 7.33463 (136*2π)/9527 weeks
137-1.8665 7.58051 (137*2π)/9527 weeks
13815.14655 -10.31585 (138*2π)/9527 weeks
139-22.4531 1.5979 (139*2π)/9527 weeks
14013.63583 6.55551 (140*2π)/9527 weeks
1415.49341 -2.70362 (141*2π)/9527 weeks
142-12.91197 -7.87385 (142*2π)/9527 weeks
14310.14088 23.57601 (143*2π)/9527 weeks
144.69012 -16.10551 (144*2π)/9527 weeks
145-7.52603 3.83941 (145*2π)/9527 weeks
146-2.37715 16.01761 (146*2π)/9527 weeks
14715.46398 -16.02499 (147*2π)/9526 weeks
148-23.31739 6.27954 (148*2π)/9526 weeks
1497.89673 8.46276 (149*2π)/9526 weeks
15012.15119 -5.39437 (150*2π)/9526 weeks
151-22.23779 -11.28026 (151*2π)/9526 weeks
15210.45571 25.24102 (152*2π)/9526 weeks
1536.05253 -12.96601 (153*2π)/9526 weeks
154-8.27948 -11.74978 (154*2π)/9526 weeks
155-8.50255 25.6066 (155*2π)/9526 weeks
15623.73049 -11.13302 (156*2π)/9526 weeks
157-14.07104 -4.90523 (157*2π)/9526 weeks
158-12.1589 9.0253 (158*2π)/9526 weeks
15922.25646 11.72602 (159*2π)/9526 weeks
160-11.64303 -21.60866 (160*2π)/9526 weeks
161-7.37786 9.04245 (161*2π)/9526 weeks
1624.00488 15.17175 (162*2π)/9526 weeks
16314.24019 -20.31356 (163*2π)/9526 weeks
164-20.29807 5.7571 (164*2π)/9526 weeks
1651.935 10.06385 (165*2π)/9526 weeks
16618.56365 1.2051 (166*2π)/9526 weeks
167-19.06078 -19.39678 (167*2π)/9526 weeks
168-.11928 20.49231 (168*2π)/9526 weeks
16910.89315 5.04273 (169*2π)/9526 weeks
1702.3671 -21.54288 (170*2π)/9526 weeks
171-24.10846 17.83227 (171*2π)/9526 weeks
17219.77 4.17787 (172*2π)/9526 weeks
1734.22943 -10.41746 (173*2π)/9526 weeks
174-25.07393 -3.49403 (174*2π)/9525 weeks
17518.31463 21.27773 (175*2π)/9525 weeks
1761.175 -17.59705 (176*2π)/9525 weeks
177-9.16032 -2.07232 (177*2π)/9525 weeks
178-1.02764 21.26763 (178*2π)/9525 weeks
17914.35318 -17.93331 (179*2π)/9525 weeks
180-16.08653 7.87252 (180*2π)/9525 weeks
1811.96474 4.11212 (181*2π)/9525 weeks
18211.29967 -2.54346 (182*2π)/9525 weeks
183-20.27125 -2.22504 (183*2π)/9525 weeks
18415.10903 11.03229 (184*2π)/9525 weeks
185-6.35991 -10.60496 (185*2π)/9525 weeks
186-7.27011 -1.34608 (186*2π)/9525 weeks
1878.74329 19.18344 (187*2π)/9525 weeks
1883.28771 -25.78453 (188*2π)/9525 weeks
189-15.83609 13.82271 (189*2π)/9525 weeks
1907.49142 10.81664 (190*2π)/9525 weeks
19116.71206 -17.43187 (191*2π)/9525 weeks
192-32.81083 1.75478 (192*2π)/9525 weeks
19318.20695 21.02288 (193*2π)/9525 weeks
1948.96367 -11.60072 (194*2π)/9525 weeks
195-24.4152 -16.3732 (195*2π)/9525 weeks
1961.83659 34.27712 (196*2π)/9525 weeks
19717.73307 -19.81137 (197*2π)/9525 weeks
198-12.70773 -12.13753 (198*2π)/9525 weeks
199-17.28688 20.29789 (199*2π)/9525 weeks
20032.14951 -1.47286 (200*2π)/9525 weeks
201-14.66798 -16.44875 (201*2π)/9525 weeks
202-12.00213 6.55289 (202*2π)/9525 weeks
20314.42676 20.5281 (203*2π)/9525 weeks
2043.60982 -27.08716 (204*2π)/9525 weeks
205-14.1855 7.79705 (205*2π)/9525 weeks
206-3.6204 13.9585 (206*2π)/9525 weeks
20722.46238 -8.22053 (207*2π)/9525 weeks
208-23.37833 -10.28206 (208*2π)/9525 weeks
209-2.23406 10.40027 (209*2π)/9525 weeks
21014.48293 8.86732 (210*2π)/9525 weeks
211-3.73658 -27.83505 (211*2π)/9525 weeks
212-13.80827 17.72709 (212*2π)/9524 weeks
2138.70982 5.21469 (213*2π)/9524 weeks
21413.78885 -16.53523 (214*2π)/9524 weeks
215-26.65075 .65858 (215*2π)/9524 weeks
21617.67257 13.99646 (216*2π)/9524 weeks
2175.30168 -5.9312 (217*2π)/9524 weeks
218-14.11408 -12.30405 (218*2π)/9524 weeks
2191.12859 23.95849 (219*2π)/9524 weeks
2206.97393 -15.99164 (220*2π)/9524 weeks
221-3.85332 -1.91455 (221*2π)/9524 weeks
222-9.61586 8.12169 (222*2π)/9524 weeks
22316.01521 -5.43247 (223*2π)/9524 weeks
224-13.66683 -.2306 (224*2π)/9524 weeks
2255.43313 -2.88725 (225*2π)/9524 weeks
2261.6639 4.88022 (226*2π)/9524 weeks
227-6.30202 -8.79155 (227*2π)/9524 weeks
22810.14244 8.8867 (228*2π)/9524 weeks
229-7.09637 -10.91491 (229*2π)/9524 weeks
2303.67193 6.7286 (230*2π)/9524 weeks
231-.3923 5.13489 (231*2π)/9524 weeks
2324.69691 -15.54553 (232*2π)/9524 weeks
233-11.67337 14.65971 (233*2π)/9524 weeks
23411.51304 -4.3978 (234*2π)/9524 weeks
2351.27659 -4.14807 (235*2π)/9524 weeks
236-16.24259 1.03255 (236*2π)/9524 weeks
23719.72593 8.87505 (237*2π)/9524 weeks
238-9.44269 -13.74886 (238*2π)/9524 weeks
239-3.34988 3.37116 (239*2π)/9524 weeks
2405.93965 12.82489 (240*2π)/9524 weeks
2412.71415 -23.46931 (241*2π)/9524 weeks
242-10.85103 14.57274 (242*2π)/9524 weeks
2439.82717 -.20926 (243*2π)/9524 weeks
2448.14139 -9.55572 (244*2π)/9524 weeks
245-20.98979 4.15778 (245*2π)/9524 weeks
24621.59101 9.18381 (246*2π)/9524 weeks
247-4.44814 -10.97241 (247*2π)/9524 weeks
248-10.2703 -3.86477 (248*2π)/9524 weeks
24910.24344 21.29056 (249*2π)/9524 weeks
2507.11609 -21.99908 (250*2π)/9524 weeks
251-11.88257 7.67578 (251*2π)/9524 weeks
252-3.26295 11.52567 (252*2π)/9524 weeks
25321.12019 -9.61757 (253*2π)/9524 weeks
254-21.96177 -6.22365 (254*2π)/9524 weeks
2553.8687 10.7949 (255*2π)/9524 weeks
25611.75821 6.29036 (256*2π)/9524 weeks
257-6.22297 -23.86821 (257*2π)/9524 weeks
258-9.70941 18.46039 (258*2π)/9524 weeks
2599.55827 2.61564 (259*2π)/9524 weeks
26013.61546 -13.67992 (260*2π)/9524 weeks
261-28.01578 .75497 (261*2π)/9524 weeks
26215.9014 15.63993 (262*2π)/9524 weeks
26312.65721 -7.00004 (263*2π)/9524 weeks
264-16.45158 -18.56061 (264*2π)/9524 weeks
265-5.39415 34.34158 (265*2π)/9524 weeks
26621.7431 -12.11395 (266*2π)/9524 weeks
267-7.55414 -16.87512 (267*2π)/9524 weeks
268-26.23772 20.32901 (268*2π)/9524 weeks
26935.47113 6.8971 (269*2π)/9524 weeks
270-12.02806 -24.44247 (270*2π)/9524 weeks
271-20.70581 6.11964 (271*2π)/9524 weeks
27220.62213 25.0794 (272*2π)/9524 weeks
2736.04526 -35.83491 (273*2π)/9523 weeks
274-20.70697 11.33919 (274*2π)/9523 weeks
2755.88084 16.60086 (275*2π)/9523 weeks
27621.8554 -17.68748 (276*2π)/9523 weeks
277-28.4616 -1.28073 (277*2π)/9523 weeks
27811.18766 14.09242 (278*2π)/9523 weeks
2797.22686 -2.15208 (279*2π)/9523 weeks
280-12.38786 -14.8878 (280*2π)/9523 weeks
2812.95074 18.80248 (281*2π)/9523 weeks
282.98048 -11.00222 (282*2π)/9523 weeks
2831.66296 1.11973 (283*2π)/9523 weeks
284-7.40591 3.6469 (284*2π)/9523 weeks
2857.45543 -8.65851 (285*2π)/9523 weeks
286-9.32382 8.04749 (286*2π)/9523 weeks
28711.35975 -7.69373 (287*2π)/9523 weeks
288-1.98781 1.55683 (288*2π)/9523 weeks
289-10.29922 .46825 (289*2π)/9523 weeks
29016.65871 8.55525 (290*2π)/9523 weeks
291-10.49203 -14.64191 (291*2π)/9523 weeks
292-1.82796 5.62494 (292*2π)/9523 weeks
2932.13276 11.94021 (293*2π)/9523 weeks
2947.69366 -19.98255 (294*2π)/9523 weeks
295-14.23402 9.35296 (295*2π)/9523 weeks
2963.13169 2.07042 (296*2π)/9523 weeks
29711.99046 -1.07581 (297*2π)/9523 weeks
298-16.61088 -11.44606 (298*2π)/9523 weeks
2996.27126 9.84173 (299*2π)/9523 weeks
3001.18769 1.98137 (300*2π)/9523 weeks
3016.27592 -14.85231 (301*2π)/9523 weeks
302-13.48353 9.86025 (302*2π)/9523 weeks
3036.57095 -.28837 (303*2π)/9523 weeks
30411.48646 .19694 (304*2π)/9523 weeks
305-16.91638 -13.07247 (305*2π)/9523 weeks
3065.11753 17.22381 (306*2π)/9523 weeks
3076.16619 -3.24266 (307*2π)/9523 weeks
3081.11907 -17.83838 (308*2π)/9523 weeks
309-16.76445 19.1335 (309*2π)/9523 weeks
31019.16864 -2.37711 (310*2π)/9523 weeks
311-1.08771 -9.71372 (311*2π)/9523 weeks
312-19.21691 -.34045 (312*2π)/9523 weeks
31318.72573 17.04621 (313*2π)/9523 weeks
314-4.49815 -19.72444 (314*2π)/9523 weeks
315-6.81824 -.98379 (315*2π)/9523 weeks
316.47762 15.08154 (316*2π)/9523 weeks
31713.17026 -17.96317 (317*2π)/9523 weeks
318-12.9111 5.73009 (318*2π)/9523 weeks
3191.62173 -.84802 (319*2π)/9523 weeks
32010.53813 1.00962 (320*2π)/9523 weeks
321-11.22667 -7.43042 (321*2π)/9523 weeks
32211.48064 4.95912 (322*2π)/9523 weeks
323-7.85291 -.71717 (323*2π)/9523 weeks
3246.41963 -3.31548 (324*2π)/9523 weeks
3251.07997 6.21023 (325*2π)/9523 weeks
326-3.74975 -10.64072 (326*2π)/9523 weeks
327.86011 15.74953 (327*2π)/9523 weeks
3281.42597 -11.48651 (328*2π)/9523 weeks
329.4738 -3.70893 (329*2π)/9523 weeks
330-10.44452 9.71775 (330*2π)/9523 weeks
33119.36887 -6.61129 (331*2π)/9523 weeks
332-15.12002 -4.27589 (332*2π)/9523 weeks
333-.56565 1.60801 (333*2π)/9523 weeks
33413.98326 5.68099 (334*2π)/9523 weeks
335-9.27025 -19.05749 (335*2π)/9523 weeks
3361.72464 16.12265 (336*2π)/9523 weeks
3375.15237 -3.59434 (337*2π)/9523 weeks
3384.36662 -11.29884 (338*2π)/9523 weeks
339-12.78481 14.33941 (339*2π)/9523 weeks
34017.09945 -6.02114 (340*2π)/9523 weeks
341-7.17454 -2.06243 (341*2π)/9523 weeks
342-6.80285 .04509 (342*2π)/9523 weeks
34315.96989 8.66281 (343*2π)/9523 weeks
344-11.08762 -15.40547 (344*2π)/9523 weeks
3451.17281 9.0621 (345*2π)/9523 weeks
3462.15126 3.69152 (346*2π)/9523 weeks
3477.01603 -16.2704 (347*2π)/9523 weeks
348-12.57652 12.55315 (348*2π)/9523 weeks
3498.8133 -2.33968 (349*2π)/9523 weeks
3506.25952 -1.64773 (350*2π)/9523 weeks
351-14.78448 -8.32697 (351*2π)/9523 weeks
35210.68808 12.58208 (352*2π)/9523 weeks
3531.58705 -5.13554 (353*2π)/9523 weeks
3541.68993 -11.2796 (354*2π)/9523 weeks
355-13.29872 15.05621 (355*2π)/9523 weeks
35616.6284 -4.80472 (356*2π)/9523 weeks
3571.89503 -7.39724 (357*2π)/9523 weeks
358-18.40182 -3.55958 (358*2π)/9523 weeks
35918.37635 20.9863 (359*2π)/9523 weeks
3604.95408 -20.18907 (360*2π)/9523 weeks
361-12.94919 -5.92854 (361*2π)/9523 weeks
362-3.63185 28.94763 (362*2π)/9523 weeks
36329.06239 -19.71228 (363*2π)/9523 weeks
364-24.25842 -9.05666 (364*2π)/9523 weeks
365-9.03413 18.88503 (365*2π)/9523 weeks
36634.1554 5.00783 (366*2π)/9523 weeks
367-22.28775 -33.23601 (367*2π)/9523 weeks
368-10.64769 23.34301 (368*2π)/9523 weeks
36921.49463 9.94992 (369*2π)/9523 weeks
3705.81313 -35.19044 (370*2π)/9523 weeks
371-29.80408 18.99772 (371*2π)/9523 weeks
37222.72624 8.83457 (372*2π)/9523 weeks
37312.19935 -16.77729 (373*2π)/9523 weeks
374-27.82191 -7.7909 (374*2π)/9523 weeks
37518.13936 23.53768 (375*2π)/9523 weeks
3767.87102 -12.16367 (376*2π)/9523 weeks
377-6.26074 -10.29796 (377*2π)/9523 weeks
378-10.12582 19.52685 (378*2π)/9523 weeks
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