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Fourier Analysis of BBRC (Columbia Beyond BRICs ETF)

BBRC (Columbia Beyond BRICs ETF) appears to have interesting cyclic behaviour every 25 weeks (.2289*sine), 25 weeks (.2151*cosine), and 30 weeks (.1235*sine).

BBRC (Columbia Beyond BRICs ETF) has an average price of 17.35 (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 8/17/2012 to 4/16/2018 for BBRC (Columbia Beyond BRICs ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
017.3497   0
1.98451 2.1131 (1*2π)/297297 weeks
2.51464 -.99468 (2*2π)/297149 weeks
3.32645 .35612 (3*2π)/29799 weeks
4-.17656 -.14793 (4*2π)/29774 weeks
5-.46828 -.12826 (5*2π)/29759 weeks
6.36583 -.06759 (6*2π)/29750 weeks
7-.16276 -.20155 (7*2π)/29742 weeks
8.07436 -.38513 (8*2π)/29737 weeks
9.08154 -.06684 (9*2π)/29733 weeks
10.00588 -.12348 (10*2π)/29730 weeks
11-.00427 .07381 (11*2π)/29727 weeks
12-.21514 -.22895 (12*2π)/29725 weeks
13-.0933 .04445 (13*2π)/29723 weeks
14.10121 -.04919 (14*2π)/29721 weeks
15-.12028 -.0153 (15*2π)/29720 weeks
16.03042 .09467 (16*2π)/29719 weeks
17-.00387 -.01647 (17*2π)/29717 weeks
18-.00874 .1109 (18*2π)/29717 weeks
19-.00432 -.03781 (19*2π)/29716 weeks
20-.02871 .01279 (20*2π)/29715 weeks
21-.06485 -.02488 (21*2π)/29714 weeks
22-.06243 -.04301 (22*2π)/29714 weeks
23.08559 -.1165 (23*2π)/29713 weeks
24-.00719 -.00478 (24*2π)/29712 weeks
25.08756 -.0409 (25*2π)/29712 weeks
26-.04647 .09785 (26*2π)/29711 weeks
27-.03226 -.12126 (27*2π)/29711 weeks
28-.05993 -.05681 (28*2π)/29711 weeks
29-.00767 -.07773 (29*2π)/29710 weeks
30.06841 -.04774 (30*2π)/29710 weeks
31.0201 .02905 (31*2π)/29710 weeks
32-.05303 .00807 (32*2π)/2979 weeks
33-.02867 .00911 (33*2π)/2979 weeks
34-.04858 -.02179 (34*2π)/2979 weeks
35-.03566 -.04809 (35*2π)/2978 weeks
36.04346 .03612 (36*2π)/2978 weeks
37-.00314 -.00158 (37*2π)/2978 weeks
38.02483 -.02221 (38*2π)/2978 weeks
39-.01642 .01093 (39*2π)/2978 weeks
40-.03876 -.04037 (40*2π)/2977 weeks
41.0625 -.02133 (41*2π)/2977 weeks
42-.00316 .00386 (42*2π)/2977 weeks
43-.0002 -.02794 (43*2π)/2977 weeks
44-.00962 -.03465 (44*2π)/2977 weeks
45.0299 -.0613 (45*2π)/2977 weeks
46.00712 -.01799 (46*2π)/2976 weeks
47-.02575 -.08062 (47*2π)/2976 weeks
48.01864 -.00988 (48*2π)/2976 weeks
49-.06675 -.03467 (49*2π)/2976 weeks
50-.03363 -.01015 (50*2π)/2976 weeks
51-.0151 -.02222 (51*2π)/2976 weeks
52.02082 -.07086 (52*2π)/2976 weeks
53-.00298 .04473 (53*2π)/2976 weeks
54.04352 -.00721 (54*2π)/2976 weeks
55-.0917 -.04911 (55*2π)/2975 weeks
56.00009 .02719 (56*2π)/2975 weeks
57-.00213 -.05496 (57*2π)/2975 weeks
58.00005 .02224 (58*2π)/2975 weeks
59-.02412 -.02228 (59*2π)/2975 weeks
60-.03486 .03733 (60*2π)/2975 weeks
61-.01632 -.01114 (61*2π)/2975 weeks
62-.00518 -.05621 (62*2π)/2975 weeks
63.03722 .02603 (63*2π)/2975 weeks
64-.01954 .00711 (64*2π)/2975 weeks
65.00572 .03845 (65*2π)/2975 weeks
66-.0056 -.00439 (66*2π)/2975 weeks
67-.02203 -.053 (67*2π)/2974 weeks
68.02596 -.01414 (68*2π)/2974 weeks
69.02158 -.02901 (69*2π)/2974 weeks
70-.0073 -.01294 (70*2π)/2974 weeks
71-.01623 .00563 (71*2π)/2974 weeks
72-.01118 -.05278 (72*2π)/2974 weeks
73.0097 .02442 (73*2π)/2974 weeks
74-.00503 -.03881 (74*2π)/2974 weeks
75.00516 .00017 (75*2π)/2974 weeks
76.00077 -.01312 (76*2π)/2974 weeks
77-.00921 -.02905 (77*2π)/2974 weeks
78.00673 .00056 (78*2π)/2974 weeks
79-.02501 -.01663 (79*2π)/2974 weeks
80.00406 -.00413 (80*2π)/2974 weeks
81-.01966 .0164 (81*2π)/2974 weeks
82-.02162 .00752 (82*2π)/2974 weeks
83.01672 .00792 (83*2π)/2974 weeks
84-.01017 -.01971 (84*2π)/2974 weeks
85.01495 .02442 (85*2π)/2973 weeks
86-.01419 .0208 (86*2π)/2973 weeks
87.00095 .02695 (87*2π)/2973 weeks
88.00788 -.01356 (88*2π)/2973 weeks
89-.02258 .00803 (89*2π)/2973 weeks
90-.01432 .00427 (90*2π)/2973 weeks
91.00935 -.00427 (91*2π)/2973 weeks
92.01639 .01672 (92*2π)/2973 weeks
93.0062 .01163 (93*2π)/2973 weeks
94.03362 -.00248 (94*2π)/2973 weeks
95-.01252 -.01334 (95*2π)/2973 weeks
96.00973 -.00651 (96*2π)/2973 weeks
97-.01353 -.02774 (97*2π)/2973 weeks
98-.0088 -.01406 (98*2π)/2973 weeks
99-.00542 -.03009 (99*2π)/2973 weeks
100-.01367 -.004 (100*2π)/2973 weeks
101-.02141 -.01315 (101*2π)/2973 weeks
102-.03629 .00139 (102*2π)/2973 weeks
103-.00251 -.03215 (103*2π)/2973 weeks
104.00492 .00399 (104*2π)/2973 weeks
105-.01401 -.02955 (105*2π)/2973 weeks
106-.008 .0349 (106*2π)/2973 weeks
107-.01831 .02512 (107*2π)/2973 weeks
108-.03693 -.00702 (108*2π)/2973 weeks
109-.00528 .00205 (109*2π)/2973 weeks
110-.01701 -.01856 (110*2π)/2973 weeks
111-.00843 .01223 (111*2π)/2973 weeks
112-.00953 -.00609 (112*2π)/2973 weeks
113-.01793 .01925 (113*2π)/2973 weeks
114-.01051 -.00366 (114*2π)/2973 weeks
115-.02691 .0178 (115*2π)/2973 weeks
116-.03252 -.02277 (116*2π)/2973 weeks
117.00177 .00128 (117*2π)/2973 weeks
118-.02233 -.01231 (118*2π)/2973 weeks
119.01533 -.01394 (119*2π)/2972 weeks
120-.00329 .0019 (120*2π)/2972 weeks
121-.01506 .00034 (121*2π)/2972 weeks
122-.01307 .00724 (122*2π)/2972 weeks
123-.00928 -.00899 (123*2π)/2972 weeks
124.00959 .01151 (124*2π)/2972 weeks
125-.00508 -.02423 (125*2π)/2972 weeks
126-.00177 .00819 (126*2π)/2972 weeks
127-.02086 .01003 (127*2π)/2972 weeks
128-.00833 .0076 (128*2π)/2972 weeks
129-.01056 -.02604 (129*2π)/2972 weeks
130-.00203 .0012 (130*2π)/2972 weeks
131.02629 .00734 (131*2π)/2972 weeks
132-.00273 .00929 (132*2π)/2972 weeks
133.01014 -.00238 (133*2π)/2972 weeks
134-.03313 .03336 (134*2π)/2972 weeks
135-.01495 -.01074 (135*2π)/2972 weeks
136-.00674 -.01248 (136*2π)/2972 weeks
137-.00213 .02677 (137*2π)/2972 weeks
138.01488 -.02275 (138*2π)/2972 weeks
139-.01922 .00305 (139*2π)/2972 weeks
140-.00004 .01703 (140*2π)/2972 weeks
141-.00489 -.0043 (141*2π)/2972 weeks
142-.0405 .01769 (142*2π)/2972 weeks
143.00075 .00657 (143*2π)/2972 weeks
144-.03071 -.02924 (144*2π)/2972 weeks
145.01969 -.00106 (145*2π)/2972 weeks
146-.01384 -.02096 (146*2π)/2972 weeks
147.02267 .01197 (147*2π)/2972 weeks
148-.01592 -.00275 (148*2π)/2972 weeks
149-.01592 .00275 (149*2π)/2972 weeks
150.02267 -.01197 (150*2π)/2972 weeks
151-.01384 .02096 (151*2π)/2972 weeks
152.01969 .00106 (152*2π)/2972 weeks
153-.03071 .02924 (153*2π)/2972 weeks
154.00075 -.00657 (154*2π)/2972 weeks
155-.0405 -.01769 (155*2π)/2972 weeks
156-.00489 .0043 (156*2π)/2972 weeks
157-.00004 -.01703 (157*2π)/2972 weeks
158-.01922 -.00305 (158*2π)/2972 weeks
159.01488 .02275 (159*2π)/2972 weeks
160-.00213 -.02677 (160*2π)/2972 weeks
161-.00674 .01248 (161*2π)/2972 weeks
162-.01495 .01074 (162*2π)/2972 weeks
163-.03313 -.03336 (163*2π)/2972 weeks
164.01014 .00238 (164*2π)/2972 weeks
165-.00273 -.00929 (165*2π)/2972 weeks
166.02629 -.00734 (166*2π)/2972 weeks
167-.00203 -.0012 (167*2π)/2972 weeks
168-.01056 .02604 (168*2π)/2972 weeks
169-.00833 -.0076 (169*2π)/2972 weeks
170-.02086 -.01003 (170*2π)/2972 weeks
171-.00177 -.00819 (171*2π)/2972 weeks
172-.00508 .02423 (172*2π)/2972 weeks
173.00959 -.01151 (173*2π)/2972 weeks
174-.00928 .00899 (174*2π)/2972 weeks
175-.01307 -.00724 (175*2π)/2972 weeks
176-.01506 -.00034 (176*2π)/2972 weeks
177-.00329 -.0019 (177*2π)/2972 weeks
178.01533 .01394 (178*2π)/2972 weeks
179-.02233 .01231 (179*2π)/2972 weeks
180.00177 -.00128 (180*2π)/2972 weeks
181-.03252 .02277 (181*2π)/2972 weeks
182-.02691 -.0178 (182*2π)/2972 weeks
183-.01051 .00366 (183*2π)/2972 weeks
184-.01793 -.01925 (184*2π)/2972 weeks
185-.00953 .00609 (185*2π)/2972 weeks
186-.00843 -.01223 (186*2π)/2972 weeks
187-.01701 .01856 (187*2π)/2972 weeks
188-.00528 -.00205 (188*2π)/2972 weeks
189-.03693 .00702 (189*2π)/2972 weeks
190-.01831 -.02512 (190*2π)/2972 weeks
191-.008 -.0349 (191*2π)/2972 weeks
192-.01401 .02955 (192*2π)/2972 weeks
193.00492 -.00399 (193*2π)/2972 weeks
194-.00251 .03215 (194*2π)/2972 weeks
195-.03629 -.00139 (195*2π)/2972 weeks
196-.02141 .01315 (196*2π)/2972 weeks
197-.01367 .004 (197*2π)/2972 weeks
198-.00542 .03009 (198*2π)/2972 weeks
199-.0088 .01406 (199*2π)/2971 weeks
200-.01353 .02774 (200*2π)/2971 weeks
201.00973 .00651 (201*2π)/2971 weeks
202-.01252 .01334 (202*2π)/2971 weeks
203.03362 .00248 (203*2π)/2971 weeks
204.0062 -.01163 (204*2π)/2971 weeks
205.01639 -.01672 (205*2π)/2971 weeks
206.00935 .00427 (206*2π)/2971 weeks
207-.01432 -.00427 (207*2π)/2971 weeks
208-.02258 -.00803 (208*2π)/2971 weeks
209.00788 .01356 (209*2π)/2971 weeks
210.00095 -.02695 (210*2π)/2971 weeks
211-.01419 -.0208 (211*2π)/2971 weeks
212.01495 -.02442 (212*2π)/2971 weeks
213-.01017 .01971 (213*2π)/2971 weeks
214.01672 -.00792 (214*2π)/2971 weeks
215-.02162 -.00752 (215*2π)/2971 weeks
216-.01966 -.0164 (216*2π)/2971 weeks
217.00406 .00413 (217*2π)/2971 weeks
218-.02501 .01663 (218*2π)/2971 weeks
219.00673 -.00056 (219*2π)/2971 weeks
220-.00921 .02905 (220*2π)/2971 weeks
221.00077 .01312 (221*2π)/2971 weeks
222.00516 -.00017 (222*2π)/2971 weeks
223-.00503 .03881 (223*2π)/2971 weeks
224.0097 -.02442 (224*2π)/2971 weeks
225-.01118 .05278 (225*2π)/2971 weeks
226-.01623 -.00563 (226*2π)/2971 weeks
227-.0073 .01294 (227*2π)/2971 weeks
228.02158 .02901 (228*2π)/2971 weeks
229.02596 .01414 (229*2π)/2971 weeks
230-.02203 .053 (230*2π)/2971 weeks
231-.0056 .00439 (231*2π)/2971 weeks
232.00572 -.03845 (232*2π)/2971 weeks
233-.01954 -.00711 (233*2π)/2971 weeks
234.03722 -.02603 (234*2π)/2971 weeks
235-.00518 .05621 (235*2π)/2971 weeks
236-.01632 .01114 (236*2π)/2971 weeks
237-.03486 -.03733 (237*2π)/2971 weeks
238-.02412 .02228 (238*2π)/2971 weeks
239.00005 -.02224 (239*2π)/2971 weeks
240-.00213 .05496 (240*2π)/2971 weeks
241.00009 -.02719 (241*2π)/2971 weeks
242-.0917 .04911 (242*2π)/2971 weeks
243.04352 .00721 (243*2π)/2971 weeks
244-.00298 -.04473 (244*2π)/2971 weeks
245.02082 .07086 (245*2π)/2971 weeks
246-.0151 .02222 (246*2π)/2971 weeks
247-.03363 .01015 (247*2π)/2971 weeks
248-.06675 .03467 (248*2π)/2971 weeks
249.01864 .00988 (249*2π)/2971 weeks
250-.02575 .08062 (250*2π)/2971 weeks
251.00712 .01799 (251*2π)/2971 weeks
252.0299 .0613 (252*2π)/2971 weeks
253-.00962 .03465 (253*2π)/2971 weeks
254-.0002 .02794 (254*2π)/2971 weeks
255-.00316 -.00386 (255*2π)/2971 weeks
256.0625 .02133 (256*2π)/2971 weeks
257-.03876 .04037 (257*2π)/2971 weeks
258-.01642 -.01093 (258*2π)/2971 weeks
259.02483 .02221 (259*2π)/2971 weeks
260-.00314 .00158 (260*2π)/2971 weeks
261.04346 -.03612 (261*2π)/2971 weeks
262-.03566 .04809 (262*2π)/2971 weeks
263-.04858 .02179 (263*2π)/2971 weeks
264-.02867 -.00911 (264*2π)/2971 weeks
265-.05303 -.00807 (265*2π)/2971 weeks
266.0201 -.02905 (266*2π)/2971 weeks
267.06841 .04774 (267*2π)/2971 weeks
268-.00767 .07773 (268*2π)/2971 weeks
269-.05993 .05681 (269*2π)/2971 weeks
270-.03226 .12126 (270*2π)/2971 weeks
271-.04647 -.09785 (271*2π)/2971 weeks
272.08756 .0409 (272*2π)/2971 weeks
273-.00719 .00478 (273*2π)/2971 weeks
274.08559 .1165 (274*2π)/2971 weeks
275-.06243 .04301 (275*2π)/2971 weeks
276-.06485 .02488 (276*2π)/2971 weeks
277-.02871 -.01279 (277*2π)/2971 weeks
278-.00432 .03781 (278*2π)/2971 weeks
279-.00874 -.1109 (279*2π)/2971 weeks
280-.00387 .01647 (280*2π)/2971 weeks
281.03042 -.09467 (281*2π)/2971 weeks
282-.12028 .0153 (282*2π)/2971 weeks
283.10121 .04919 (283*2π)/2971 weeks
284-.0933 -.04445 (284*2π)/2971 weeks
285-.21514 .22895 (285*2π)/2971 weeks
286-.00427 -.07381 (286*2π)/2971 weeks
287.00588 .12348 (287*2π)/2971 weeks
288.08154 .06684 (288*2π)/2971 weeks
289.07436 .38513 (289*2π)/2971 weeks
290-.16276 .20155 (290*2π)/2971 weeks
291.36583 .06759 (291*2π)/2971 weeks
292-.46828 .12826 (292*2π)/2971 weeks
293-.17656 .14793 (293*2π)/2971 weeks
294.32645 -.35612 (294*2π)/2971 weeks
295.51464 .99468 (295*2π)/2971 weeks