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Fourier Analysis of YYY (YieldShares High Income ETF)


YYY (YieldShares High Income ETF) appears to have interesting cyclic behaviour every 23 weeks (.3418*sine), 21 weeks (.2651*sine), and 21 weeks (.1771*cosine).

YYY (YieldShares High Income ETF) has an average price of 16.97 (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.

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

Fourier Analysis

Using data from 6/12/2012 to 3/13/2017 for YYY (YieldShares High Income ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
016.97038   0 
1-.7142 -.07276 (1*2π)/249249 weeks
2.58292 -.90241 (2*2π)/249125 weeks
3-.34628 -.60082 (3*2π)/24983 weeks
4-.43789 -.56608 (4*2π)/24962 weeks
5.04402 -.12558 (5*2π)/24950 weeks
6.09145 -.30118 (6*2π)/24942 weeks
7.15419 -.12731 (7*2π)/24936 weeks
8-.00824 -.21825 (8*2π)/24931 weeks
9-.15411 -.16416 (9*2π)/24928 weeks
10-.00902 -.1042 (10*2π)/24925 weeks
11-.06784 -.34177 (11*2π)/24923 weeks
12-.17707 -.26512 (12*2π)/24921 weeks
13-.12951 -.20425 (13*2π)/24919 weeks
14.02919 -.12232 (14*2π)/24918 weeks
15.02458 -.166 (15*2π)/24917 weeks
16-.02737 -.10614 (16*2π)/24916 weeks
17-.01193 -.11745 (17*2π)/24915 weeks
18-.03173 -.0517 (18*2π)/24914 weeks
19-.0148 -.10963 (19*2π)/24913 weeks
20.00081 -.04565 (20*2π)/24912 weeks
21-.01287 -.1422 (21*2π)/24912 weeks
22-.06311 .00618 (22*2π)/24911 weeks
23-.02037 -.10909 (23*2π)/24911 weeks
24-.02724 -.13408 (24*2π)/24910 weeks
25-.02 -.12387 (25*2π)/24910 weeks
26-.05297 .00324 (26*2π)/24910 weeks
27-.05499 -.04586 (27*2π)/2499 weeks
28-.04746 -.06303 (28*2π)/2499 weeks
29-.08929 -.08566 (29*2π)/2499 weeks
30.04204 -.0633 (30*2π)/2498 weeks
31.01107 -.00844 (31*2π)/2498 weeks
32-.01813 -.02521 (32*2π)/2498 weeks
33-.06914 -.0574 (33*2π)/2498 weeks
34-.01706 -.07562 (34*2π)/2497 weeks
35-.05183 -.07691 (35*2π)/2497 weeks
36-.00715 -.07986 (36*2π)/2497 weeks
37.01159 -.04899 (37*2π)/2497 weeks
38-.0153 -.0489 (38*2π)/2497 weeks
39-.03801 -.0364 (39*2π)/2496 weeks
40-.04341 -.0001 (40*2π)/2496 weeks
41-.02668 -.01721 (41*2π)/2496 weeks
42-.00379 -.03338 (42*2π)/2496 weeks
43-.0119 -.0436 (43*2π)/2496 weeks
44-.038 -.04413 (44*2π)/2496 weeks
45-.04636 -.03307 (45*2π)/2496 weeks
46-.00943 .00799 (46*2π)/2495 weeks
47-.00851 -.03783 (47*2π)/2495 weeks
48-.02689 -.06698 (48*2π)/2495 weeks
49-.0465 -.02506 (49*2π)/2495 weeks
50-.00085 -.03592 (50*2π)/2495 weeks
51-.01927 -.06011 (51*2π)/2495 weeks
52-.04511 -.06333 (52*2π)/2495 weeks
53-.00916 -.0039 (53*2π)/2495 weeks
54.00215 -.0272 (54*2π)/2495 weeks
55-.02056 -.01455 (55*2π)/2495 weeks
56-.03696 -.03856 (56*2π)/2494 weeks
57-.01628 .0238 (57*2π)/2494 weeks
58-.01261 -.02527 (58*2π)/2494 weeks
59.01223 -.00933 (59*2π)/2494 weeks
60-.02584 -.03591 (60*2π)/2494 weeks
61-.04874 .00907 (61*2π)/2494 weeks
62-.02263 -.02993 (62*2π)/2494 weeks
63-.02739 -.03363 (63*2π)/2494 weeks
64-.03788 -.01899 (64*2π)/2494 weeks
65-.04597 .00109 (65*2π)/2494 weeks
66-.01556 -.00868 (66*2π)/2494 weeks
67-.04729 .00296 (67*2π)/2494 weeks
68-.0274 -.0257 (68*2π)/2494 weeks
69-.04183 -.01579 (69*2π)/2494 weeks
70-.01861 -.03965 (70*2π)/2494 weeks
71-.03592 -.04974 (71*2π)/2494 weeks
72-.00169 -.04182 (72*2π)/2493 weeks
73-.01098 -.04983 (73*2π)/2493 weeks
74-.01104 -.04718 (74*2π)/2493 weeks
75-.00877 -.02093 (75*2π)/2493 weeks
76-.01992 -.0154 (76*2π)/2493 weeks
77-.03157 -.04184 (77*2π)/2493 weeks
78-.02197 .00346 (78*2π)/2493 weeks
79.00297 -.02966 (79*2π)/2493 weeks
80-.01858 -.03968 (80*2π)/2493 weeks
81-.01491 -.03036 (81*2π)/2493 weeks
82-.01732 -.00217 (82*2π)/2493 weeks
83-.0004 -.02273 (83*2π)/2493 weeks
84-.01111 -.02113 (84*2π)/2493 weeks
85-.00866 -.00365 (85*2π)/2493 weeks
86-.02028 -.00764 (86*2π)/2493 weeks
87-.01312 -.00005 (87*2π)/2493 weeks
88-.01144 -.01709 (88*2π)/2493 weeks
89-.03115 -.02321 (89*2π)/2493 weeks
90-.04757 -.0316 (90*2π)/2493 weeks
91-.01157 -.02545 (91*2π)/2493 weeks
92-.00516 -.02541 (92*2π)/2493 weeks
93-.00011 -.0029 (93*2π)/2493 weeks
94-.03319 .01938 (94*2π)/2493 weeks
95-.01369 .00461 (95*2π)/2493 weeks
96-.04494 -.03005 (96*2π)/2493 weeks
97-.01155 -.01574 (97*2π)/2493 weeks
98-.00907 -.00463 (98*2π)/2493 weeks
99-.00069 -.00639 (99*2π)/2493 weeks
100-.02216 .00072 (100*2π)/2492 weeks
101-.03381 .01209 (101*2π)/2492 weeks
102-.03595 -.00112 (102*2π)/2492 weeks
103-.03309 -.02399 (103*2π)/2492 weeks
104-.01404 -.01299 (104*2π)/2492 weeks
105-.02847 -.01506 (105*2π)/2492 weeks
106-.02894 -.01024 (106*2π)/2492 weeks
107-.04071 -.01216 (107*2π)/2492 weeks
108-.02163 -.03218 (108*2π)/2492 weeks
109-.01895 -.02133 (109*2π)/2492 weeks
110-.00141 .00004 (110*2π)/2492 weeks
111-.01975 -.00196 (111*2π)/2492 weeks
112-.03107 .01646 (112*2π)/2492 weeks
113-.03051 -.00725 (113*2π)/2492 weeks
114-.01188 -.01322 (114*2π)/2492 weeks
115-.01772 -.00853 (115*2π)/2492 weeks
116-.01844 .01996 (116*2π)/2492 weeks
117-.0251 .00939 (117*2π)/2492 weeks
118-.01891 -.00725 (118*2π)/2492 weeks
119-.02981 -.03664 (119*2π)/2492 weeks
120-.02534 -.00386 (120*2π)/2492 weeks
121-.00706 .02113 (121*2π)/2492 weeks
122-.00944 -.0051 (122*2π)/2492 weeks
123-.03796 -.0051 (123*2π)/2492 weeks
124-.02094 -.00047 (124*2π)/2492 weeks
125-.02094 .00047 (125*2π)/2492 weeks
126-.03796 .0051 (126*2π)/2492 weeks
127-.00944 .0051 (127*2π)/2492 weeks
128-.00706 -.02113 (128*2π)/2492 weeks
129-.02534 .00386 (129*2π)/2492 weeks
130-.02981 .03664 (130*2π)/2492 weeks
131-.01891 .00725 (131*2π)/2492 weeks
132-.0251 -.00939 (132*2π)/2492 weeks
133-.01844 -.01996 (133*2π)/2492 weeks
134-.01772 .00853 (134*2π)/2492 weeks
135-.01188 .01322 (135*2π)/2492 weeks
136-.03051 .00725 (136*2π)/2492 weeks
137-.03107 -.01646 (137*2π)/2492 weeks
138-.01975 .00196 (138*2π)/2492 weeks
139-.00141 -.00004 (139*2π)/2492 weeks
140-.01895 .02133 (140*2π)/2492 weeks
141-.02163 .03218 (141*2π)/2492 weeks
142-.04071 .01216 (142*2π)/2492 weeks
143-.02894 .01024 (143*2π)/2492 weeks
144-.02847 .01506 (144*2π)/2492 weeks
145-.01404 .01299 (145*2π)/2492 weeks
146-.03309 .02399 (146*2π)/2492 weeks
147-.03595 .00112 (147*2π)/2492 weeks
148-.03381 -.01209 (148*2π)/2492 weeks
149-.02216 -.00072 (149*2π)/2492 weeks
150-.00069 .00639 (150*2π)/2492 weeks
151-.00907 .00463 (151*2π)/2492 weeks
152-.01155 .01574 (152*2π)/2492 weeks
153-.04494 .03005 (153*2π)/2492 weeks
154-.01369 -.00461 (154*2π)/2492 weeks
155-.03319 -.01938 (155*2π)/2492 weeks
156-.00011 .0029 (156*2π)/2492 weeks
157-.00516 .02541 (157*2π)/2492 weeks
158-.01157 .02545 (158*2π)/2492 weeks
159-.04757 .0316 (159*2π)/2492 weeks
160-.03115 .02321 (160*2π)/2492 weeks
161-.01144 .01709 (161*2π)/2492 weeks
162-.01312 .00005 (162*2π)/2492 weeks
163-.02028 .00764 (163*2π)/2492 weeks
164-.00866 .00365 (164*2π)/2492 weeks
165-.01111 .02113 (165*2π)/2492 weeks
166-.0004 .02273 (166*2π)/2492 weeks
167-.01732 .00217 (167*2π)/2491 weeks
168-.01491 .03036 (168*2π)/2491 weeks
169-.01858 .03968 (169*2π)/2491 weeks
170.00297 .02966 (170*2π)/2491 weeks
171-.02197 -.00346 (171*2π)/2491 weeks
172-.03157 .04184 (172*2π)/2491 weeks
173-.01992 .0154 (173*2π)/2491 weeks
174-.00877 .02093 (174*2π)/2491 weeks
175-.01104 .04718 (175*2π)/2491 weeks
176-.01098 .04983 (176*2π)/2491 weeks
177-.00169 .04182 (177*2π)/2491 weeks
178-.03592 .04974 (178*2π)/2491 weeks
179-.01861 .03965 (179*2π)/2491 weeks
180-.04183 .01579 (180*2π)/2491 weeks
181-.0274 .0257 (181*2π)/2491 weeks
182-.04729 -.00296 (182*2π)/2491 weeks
183-.01556 .00868 (183*2π)/2491 weeks
184-.04597 -.00109 (184*2π)/2491 weeks
185-.03788 .01899 (185*2π)/2491 weeks
186-.02739 .03363 (186*2π)/2491 weeks
187-.02263 .02993 (187*2π)/2491 weeks
188-.04874 -.00907 (188*2π)/2491 weeks
189-.02584 .03591 (189*2π)/2491 weeks
190.01223 .00933 (190*2π)/2491 weeks
191-.01261 .02527 (191*2π)/2491 weeks
192-.01628 -.0238 (192*2π)/2491 weeks
193-.03696 .03856 (193*2π)/2491 weeks
194-.02056 .01455 (194*2π)/2491 weeks
195.00215 .0272 (195*2π)/2491 weeks
196-.00916 .0039 (196*2π)/2491 weeks
197-.04511 .06333 (197*2π)/2491 weeks
198-.01927 .06011 (198*2π)/2491 weeks
199-.00085 .03592 (199*2π)/2491 weeks
200-.0465 .02506 (200*2π)/2491 weeks
201-.02689 .06698 (201*2π)/2491 weeks
202-.00851 .03783 (202*2π)/2491 weeks
203-.00943 -.00799 (203*2π)/2491 weeks
204-.04636 .03307 (204*2π)/2491 weeks
205-.038 .04413 (205*2π)/2491 weeks
206-.0119 .0436 (206*2π)/2491 weeks
207-.00379 .03338 (207*2π)/2491 weeks
208-.02668 .01721 (208*2π)/2491 weeks
209-.04341 .0001 (209*2π)/2491 weeks
210-.03801 .0364 (210*2π)/2491 weeks
211-.0153 .0489 (211*2π)/2491 weeks
212.01159 .04899 (212*2π)/2491 weeks
213-.00715 .07986 (213*2π)/2491 weeks
214-.05183 .07691 (214*2π)/2491 weeks
215-.01706 .07562 (215*2π)/2491 weeks
216-.06914 .0574 (216*2π)/2491 weeks
217-.01813 .02521 (217*2π)/2491 weeks
218.01107 .00844 (218*2π)/2491 weeks
219.04204 .0633 (219*2π)/2491 weeks
220-.08929 .08566 (220*2π)/2491 weeks
221-.04746 .06303 (221*2π)/2491 weeks
222-.05499 .04586 (222*2π)/2491 weeks
223-.05297 -.00324 (223*2π)/2491 weeks
224-.02 .12387 (224*2π)/2491 weeks
225-.02724 .13408 (225*2π)/2491 weeks
226-.02037 .10909 (226*2π)/2491 weeks
227-.06311 -.00618 (227*2π)/2491 weeks
228-.01287 .1422 (228*2π)/2491 weeks
229.00081 .04565 (229*2π)/2491 weeks
230-.0148 .10963 (230*2π)/2491 weeks
231-.03173 .0517 (231*2π)/2491 weeks
232-.01193 .11745 (232*2π)/2491 weeks
233-.02737 .10614 (233*2π)/2491 weeks
234.02458 .166 (234*2π)/2491 weeks
235.02919 .12232 (235*2π)/2491 weeks
236-.12951 .20425 (236*2π)/2491 weeks
237-.17707 .26512 (237*2π)/2491 weeks
238-.06784 .34177 (238*2π)/2491 weeks
239-.00902 .1042 (239*2π)/2491 weeks
240-.15411 .16416 (240*2π)/2491 weeks
241-.00824 .21825 (241*2π)/2491 weeks
242.15419 .12731 (242*2π)/2491 weeks
243.09145 .30118 (243*2π)/2491 weeks
244.04402 .12558 (244*2π)/2491 weeks
245-.43789 .56608 (245*2π)/2491 weeks
246-.34628 .60082 (246*2π)/2491 weeks
247.58292 .90241 (247*2π)/2491 weeks

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