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Fourier Analysis of BBRC (Columbia Beyond BRICs ETF)


BBRC (Columbia Beyond BRICs ETF) appears to have interesting cyclic behaviour every 26 weeks (.2233*cosine), 26 weeks (.1675*sine), and 11 weeks (.1652*cosine).

BBRC (Columbia Beyond BRICs ETF) has an average price of 17.65 (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 8/17/2012 to 7/17/2017 for BBRC (Columbia Beyond BRICs ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
017.65361   0 
1-.43011 2.53515 (1*2π)/258258 weeks
2.93633 -.05451 (2*2π)/258129 weeks
3-.23328 .66107 (3*2π)/25886 weeks
4-.1707 .37219 (4*2π)/25865 weeks
5.36388 -.29329 (5*2π)/25852 weeks
6-.24843 -.01047 (6*2π)/25843 weeks
7.10961 -.2595 (7*2π)/25837 weeks
8.05954 .08755 (8*2π)/25832 weeks
9.09967 .02929 (9*2π)/25829 weeks
10-.2233 .16749 (10*2π)/25826 weeks
11.14261 .02648 (11*2π)/25823 weeks
12.12585 -.12783 (12*2π)/25822 weeks
13-.09728 .00295 (13*2π)/25820 weeks
14.02774 .11934 (14*2π)/25818 weeks
15.05552 .00214 (15*2π)/25817 weeks
16-.10923 .06444 (16*2π)/25816 weeks
17-.0083 .05538 (17*2π)/25815 weeks
18-.07236 .03256 (18*2π)/25814 weeks
19-.06474 -.00878 (19*2π)/25814 weeks
20.09947 -.09818 (20*2π)/25813 weeks
21-.02378 -.00183 (21*2π)/25812 weeks
22.10574 .06648 (22*2π)/25812 weeks
23-.16515 .02121 (23*2π)/25811 weeks
24-.00876 .01827 (24*2π)/25811 weeks
25.01183 -.05137 (25*2π)/25810 weeks
26.10091 -.02994 (26*2π)/25810 weeks
27.04323 .07193 (27*2π)/25810 weeks
28-.02823 .0172 (28*2π)/2589 weeks
29-.03254 .03047 (29*2π)/2589 weeks
30-.02301 -.01201 (30*2π)/2589 weeks
31.08291 -.01806 (31*2π)/2588 weeks
32-.01034 .0052 (32*2π)/2588 weeks
33.02338 -.01541 (33*2π)/2588 weeks
34-.02799 .02077 (34*2π)/2588 weeks
35-.02349 -.06683 (35*2π)/2587 weeks
36.02844 .04066 (36*2π)/2587 weeks
37-.01931 .00348 (37*2π)/2587 weeks
38-.01353 .00178 (38*2π)/2587 weeks
39.02238 -.03524 (39*2π)/2587 weeks
40.00764 .02922 (40*2π)/2586 weeks
41.01188 -.05167 (41*2π)/2586 weeks
42.00781 .0563 (42*2π)/2586 weeks
43.00756 -.02497 (43*2π)/2586 weeks
44-.00336 -.03102 (44*2π)/2586 weeks
45.00535 -.06913 (45*2π)/2586 weeks
46.01964 .0685 (46*2π)/2586 weeks
47.06567 .03581 (47*2π)/2585 weeks
48-.02242 -.08867 (48*2π)/2585 weeks
49-.04925 .00502 (49*2π)/2585 weeks
50.04747 .00469 (50*2π)/2585 weeks
51-.02727 .00238 (51*2π)/2585 weeks
52-.00129 .04775 (52*2π)/2585 weeks
53-.00424 -.01405 (53*2π)/2585 weeks
54.03193 -.06677 (54*2π)/2585 weeks
55.02582 .04268 (55*2π)/2585 weeks
56.02045 -.00787 (56*2π)/2585 weeks
57-.03291 .0009 (57*2π)/2585 weeks
58-.04815 -.02529 (58*2π)/2584 weeks
59.032 -.00509 (59*2π)/2584 weeks
60.02973 -.0106 (60*2π)/2584 weeks
61.00442 -.00243 (61*2π)/2584 weeks
62-.03301 .00249 (62*2π)/2584 weeks
63.05232 -.01657 (63*2π)/2584 weeks
64-.02881 -.01622 (64*2π)/2584 weeks
65.0211 .01011 (65*2π)/2584 weeks
66.00833 -.00088 (66*2π)/2584 weeks
67.00711 -.02068 (67*2π)/2584 weeks
68.00871 .02231 (68*2π)/2584 weeks
69.01074 -.0172 (69*2π)/2584 weeks
70.01555 .02184 (70*2π)/2584 weeks
71-.00317 .00615 (71*2π)/2584 weeks
72.02909 -.00896 (72*2π)/2584 weeks
73-.00054 -.0311 (73*2π)/2584 weeks
74.01605 .02435 (74*2π)/2583 weeks
75-.00916 .00057 (75*2π)/2583 weeks
76-.03301 .00523 (76*2π)/2583 weeks
77-.00667 .03013 (77*2π)/2583 weeks
78-.0093 .0047 (78*2π)/2583 weeks
79.00804 -.01186 (79*2π)/2583 weeks
80.00871 .0158 (80*2π)/2583 weeks
81-.0117 .00646 (81*2π)/2583 weeks
82.00632 .03692 (82*2π)/2583 weeks
83.00668 -.00613 (83*2π)/2583 weeks
84-.01906 .00598 (84*2π)/2583 weeks
85.00293 .00681 (85*2π)/2583 weeks
86.00731 -.01266 (86*2π)/2583 weeks
87-.00231 .01342 (87*2π)/2583 weeks
88.00103 .00115 (88*2π)/2583 weeks
89-.02792 -.02466 (89*2π)/2583 weeks
90.02344 -.00511 (90*2π)/2583 weeks
91-.01854 -.00743 (91*2π)/2583 weeks
92.01838 .04604 (92*2π)/2583 weeks
93-.00837 .0333 (93*2π)/2583 weeks
94-.02094 -.01392 (94*2π)/2583 weeks
95-.00991 .01252 (95*2π)/2583 weeks
96.0188 -.00227 (96*2π)/2583 weeks
97-.00854 -.00072 (97*2π)/2583 weeks
98.00212 .02315 (98*2π)/2583 weeks
99-.00138 -.00507 (99*2π)/2583 weeks
100-.02533 .01793 (100*2π)/2583 weeks
101-.00983 -.03475 (101*2π)/2583 weeks
102-.00847 .00622 (102*2π)/2583 weeks
103.00392 -.03181 (103*2π)/2583 weeks
104.00641 .00799 (104*2π)/2582 weeks
105-.00795 .00598 (105*2π)/2582 weeks
106-.00733 .00838 (106*2π)/2582 weeks
107-.00086 -.01296 (107*2π)/2582 weeks
108-.00829 .02151 (108*2π)/2582 weeks
109.02573 .00134 (109*2π)/2582 weeks
110.0018 .0185 (110*2π)/2582 weeks
111.00335 -.00047 (111*2π)/2582 weeks
112-.0094 -.03036 (112*2π)/2582 weeks
113.00251 -.003 (113*2π)/2582 weeks
114.0266 .02322 (114*2π)/2582 weeks
115.00083 .00986 (115*2π)/2582 weeks
116.02035 .04361 (116*2π)/2582 weeks
117-.023 -.01217 (117*2π)/2582 weeks
118-.00374 -.01096 (118*2π)/2582 weeks
119.00561 .03188 (119*2π)/2582 weeks
120.03465 -.01023 (120*2π)/2582 weeks
121-.00074 -.00947 (121*2π)/2582 weeks
122-.01355 .01454 (122*2π)/2582 weeks
123.00075 .03392 (123*2π)/2582 weeks
124.00533 -.01735 (124*2π)/2582 weeks
125-.03627 -.02737 (125*2π)/2582 weeks
126.02756 .00215 (126*2π)/2582 weeks
127.00452 -.03196 (127*2π)/2582 weeks
128.00923 .02889 (128*2π)/2582 weeks
129.0061   (129*2π)/2582 weeks
130.00923 -.02889 (130*2π)/2582 weeks
131.00452 .03196 (131*2π)/2582 weeks
132.02756 -.00215 (132*2π)/2582 weeks
133-.03627 .02737 (133*2π)/2582 weeks
134.00533 .01735 (134*2π)/2582 weeks
135.00075 -.03392 (135*2π)/2582 weeks
136-.01355 -.01454 (136*2π)/2582 weeks
137-.00074 .00947 (137*2π)/2582 weeks
138.03465 .01023 (138*2π)/2582 weeks
139.00561 -.03188 (139*2π)/2582 weeks
140-.00374 .01096 (140*2π)/2582 weeks
141-.023 .01217 (141*2π)/2582 weeks
142.02035 -.04361 (142*2π)/2582 weeks
143.00083 -.00986 (143*2π)/2582 weeks
144.0266 -.02322 (144*2π)/2582 weeks
145.00251 .003 (145*2π)/2582 weeks
146-.0094 .03036 (146*2π)/2582 weeks
147.00335 .00047 (147*2π)/2582 weeks
148.0018 -.0185 (148*2π)/2582 weeks
149.02573 -.00134 (149*2π)/2582 weeks
150-.00829 -.02151 (150*2π)/2582 weeks
151-.00086 .01296 (151*2π)/2582 weeks
152-.00733 -.00838 (152*2π)/2582 weeks
153-.00795 -.00598 (153*2π)/2582 weeks
154.00641 -.00799 (154*2π)/2582 weeks
155.00392 .03181 (155*2π)/2582 weeks
156-.00847 -.00622 (156*2π)/2582 weeks
157-.00983 .03475 (157*2π)/2582 weeks
158-.02533 -.01793 (158*2π)/2582 weeks
159-.00138 .00507 (159*2π)/2582 weeks
160.00212 -.02315 (160*2π)/2582 weeks
161-.00854 .00072 (161*2π)/2582 weeks
162.0188 .00227 (162*2π)/2582 weeks
163-.00991 -.01252 (163*2π)/2582 weeks
164-.02094 .01392 (164*2π)/2582 weeks
165-.00837 -.0333 (165*2π)/2582 weeks
166.01838 -.04604 (166*2π)/2582 weeks
167-.01854 .00743 (167*2π)/2582 weeks
168.02344 .00511 (168*2π)/2582 weeks
169-.02792 .02466 (169*2π)/2582 weeks
170.00103 -.00115 (170*2π)/2582 weeks
171-.00231 -.01342 (171*2π)/2582 weeks
172.00731 .01266 (172*2π)/2582 weeks
173.00293 -.00681 (173*2π)/2581 weeks
174-.01906 -.00598 (174*2π)/2581 weeks
175.00668 .00613 (175*2π)/2581 weeks
176.00632 -.03692 (176*2π)/2581 weeks
177-.0117 -.00646 (177*2π)/2581 weeks
178.00871 -.0158 (178*2π)/2581 weeks
179.00804 .01186 (179*2π)/2581 weeks
180-.0093 -.0047 (180*2π)/2581 weeks
181-.00667 -.03013 (181*2π)/2581 weeks
182-.03301 -.00523 (182*2π)/2581 weeks
183-.00916 -.00057 (183*2π)/2581 weeks
184.01605 -.02435 (184*2π)/2581 weeks
185-.00054 .0311 (185*2π)/2581 weeks
186.02909 .00896 (186*2π)/2581 weeks
187-.00317 -.00615 (187*2π)/2581 weeks
188.01555 -.02184 (188*2π)/2581 weeks
189.01074 .0172 (189*2π)/2581 weeks
190.00871 -.02231 (190*2π)/2581 weeks
191.00711 .02068 (191*2π)/2581 weeks
192.00833 .00088 (192*2π)/2581 weeks
193.0211 -.01011 (193*2π)/2581 weeks
194-.02881 .01622 (194*2π)/2581 weeks
195.05232 .01657 (195*2π)/2581 weeks
196-.03301 -.00249 (196*2π)/2581 weeks
197.00442 .00243 (197*2π)/2581 weeks
198.02973 .0106 (198*2π)/2581 weeks
199.032 .00509 (199*2π)/2581 weeks
200-.04815 .02529 (200*2π)/2581 weeks
201-.03291 -.0009 (201*2π)/2581 weeks
202.02045 .00787 (202*2π)/2581 weeks
203.02582 -.04268 (203*2π)/2581 weeks
204.03193 .06677 (204*2π)/2581 weeks
205-.00424 .01405 (205*2π)/2581 weeks
206-.00129 -.04775 (206*2π)/2581 weeks
207-.02727 -.00238 (207*2π)/2581 weeks
208.04747 -.00469 (208*2π)/2581 weeks
209-.04925 -.00502 (209*2π)/2581 weeks
210-.02242 .08867 (210*2π)/2581 weeks
211.06567 -.03581 (211*2π)/2581 weeks
212.01964 -.0685 (212*2π)/2581 weeks
213.00535 .06913 (213*2π)/2581 weeks
214-.00336 .03102 (214*2π)/2581 weeks
215.00756 .02497 (215*2π)/2581 weeks
216.00781 -.0563 (216*2π)/2581 weeks
217.01188 .05167 (217*2π)/2581 weeks
218.00764 -.02922 (218*2π)/2581 weeks
219.02238 .03524 (219*2π)/2581 weeks
220-.01353 -.00178 (220*2π)/2581 weeks
221-.01931 -.00348 (221*2π)/2581 weeks
222.02844 -.04066 (222*2π)/2581 weeks
223-.02349 .06683 (223*2π)/2581 weeks
224-.02799 -.02077 (224*2π)/2581 weeks
225.02338 .01541 (225*2π)/2581 weeks
226-.01034 -.0052 (226*2π)/2581 weeks
227.08291 .01806 (227*2π)/2581 weeks
228-.02301 .01201 (228*2π)/2581 weeks
229-.03254 -.03047 (229*2π)/2581 weeks
230-.02823 -.0172 (230*2π)/2581 weeks
231.04323 -.07193 (231*2π)/2581 weeks
232.10091 .02994 (232*2π)/2581 weeks
233.01183 .05137 (233*2π)/2581 weeks
234-.00876 -.01827 (234*2π)/2581 weeks
235-.16515 -.02121 (235*2π)/2581 weeks
236.10574 -.06648 (236*2π)/2581 weeks
237-.02378 .00183 (237*2π)/2581 weeks
238.09947 .09818 (238*2π)/2581 weeks
239-.06474 .00878 (239*2π)/2581 weeks
240-.07236 -.03256 (240*2π)/2581 weeks
241-.0083 -.05538 (241*2π)/2581 weeks
242-.10923 -.06444 (242*2π)/2581 weeks
243.05552 -.00214 (243*2π)/2581 weeks
244.02774 -.11934 (244*2π)/2581 weeks
245-.09728 -.00295 (245*2π)/2581 weeks
246.12585 .12783 (246*2π)/2581 weeks
247.14261 -.02648 (247*2π)/2581 weeks
248-.2233 -.16749 (248*2π)/2581 weeks
249.09967 -.02929 (249*2π)/2581 weeks
250.05954 -.08755 (250*2π)/2581 weeks
251.10961 .2595 (251*2π)/2581 weeks
252-.24843 .01047 (252*2π)/2581 weeks
253.36388 .29329 (253*2π)/2581 weeks
254-.1707 -.37219 (254*2π)/2581 weeks
255-.23328 -.66107 (255*2π)/2581 weeks
256.93633 .05451 (256*2π)/2581 weeks



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