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Fourier Analysis of SCHD (Schwab US Dividend Equity ETF)

SCHD (Schwab US Dividend Equity ETF) appears to have interesting cyclic behaviour every 28 weeks (.9414*sine), 31 weeks (.8846*sine), and 34 weeks (.6501*sine).

SCHD (Schwab US Dividend Equity ETF) has an average price of 34.75 (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 10/20/2011 to 4/16/2018 for SCHD (Schwab US Dividend Equity ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
034.75359   0
1.05145 -7.61973 (1*2π)/340340 weeks
2.88289 -5.68376 (2*2π)/340170 weeks
3-.04626 -2.98675 (3*2π)/340113 weeks
4.59292 -2.38974 (4*2π)/34085 weeks
5-.28561 -2.12441 (5*2π)/34068 weeks
6-.19982 -1.64647 (6*2π)/34057 weeks
7-.19518 -1.70795 (7*2π)/34049 weeks
8-.22986 -1.35655 (8*2π)/34043 weeks
9-.35644 -1.0886 (9*2π)/34038 weeks
10-.36189 -.65013 (10*2π)/34034 weeks
11-.31559 -.88461 (11*2π)/34031 weeks
12-.30141 -.94139 (12*2π)/34028 weeks
13-.17556 -.48033 (13*2π)/34026 weeks
14-.17924 -.7471 (14*2π)/34024 weeks
15-.03567 -.38747 (15*2π)/34023 weeks
16.12161 -.53561 (16*2π)/34021 weeks
17-.28324 -.52396 (17*2π)/34020 weeks
18-.1013 -.27011 (18*2π)/34019 weeks
19.08596 -.43633 (19*2π)/34018 weeks
20-.24926 -.45729 (20*2π)/34017 weeks
21-.03093 -.28468 (21*2π)/34016 weeks
22.01092 -.32893 (22*2π)/34015 weeks
23-.04794 -.30813 (23*2π)/34015 weeks
24.00386 -.4276 (24*2π)/34014 weeks
25.01634 -.44656 (25*2π)/34014 weeks
26-.04199 -.35152 (26*2π)/34013 weeks
27-.05712 -.35039 (27*2π)/34013 weeks
28-.06388 -.22912 (28*2π)/34012 weeks
29.04675 -.44327 (29*2π)/34012 weeks
30-.12222 -.21024 (30*2π)/34011 weeks
31-.11446 -.36325 (31*2π)/34011 weeks
32-.18604 -.25751 (32*2π)/34011 weeks
33-.03772 -.22021 (33*2π)/34010 weeks
34-.02041 -.24908 (34*2π)/34010 weeks
35-.1589 -.2571 (35*2π)/34010 weeks
36-.03234 -.22277 (36*2π)/3409 weeks
37-.0887 -.20756 (37*2π)/3409 weeks
38-.03966 -.21065 (38*2π)/3409 weeks
39-.10313 -.17315 (39*2π)/3409 weeks
40-.12455 -.26906 (40*2π)/3409 weeks
41.03483 -.11141 (41*2π)/3408 weeks
42-.11291 -.14895 (42*2π)/3408 weeks
43-.11592 -.11862 (43*2π)/3408 weeks
44-.04659 -.1986 (44*2π)/3408 weeks
45-.00435 -.12984 (45*2π)/3408 weeks
46-.07504 -.18799 (46*2π)/3407 weeks
47.02198 -.18466 (47*2π)/3407 weeks
48-.07059 -.13778 (48*2π)/3407 weeks
49-.03371 -.14138 (49*2π)/3407 weeks
50-.03218 -.15028 (50*2π)/3407 weeks
51.03323 -.14399 (51*2π)/3407 weeks
52-.02817 -.18381 (52*2π)/3407 weeks
53-.01964 -.1788 (53*2π)/3406 weeks
54-.10544 -.18023 (54*2π)/3406 weeks
55-.03084 -.2229 (55*2π)/3406 weeks
56-.12859 -.24089 (56*2π)/3406 weeks
57-.11135 -.18075 (57*2π)/3406 weeks
58-.07692 -.1699 (58*2π)/3406 weeks
59-.06348 -.16298 (59*2π)/3406 weeks
60-.14635 -.16958 (60*2π)/3406 weeks
61-.12937 -.11922 (61*2π)/3406 weeks
62-.04694 -.14143 (62*2π)/3405 weeks
63-.15258 -.1487 (63*2π)/3405 weeks
64-.10715 -.13016 (64*2π)/3405 weeks
65-.09249 -.08294 (65*2π)/3405 weeks
66-.15217 -.11086 (66*2π)/3405 weeks
67-.07124 -.09013 (67*2π)/3405 weeks
68-.12814 -.17486 (68*2π)/3405 weeks
69-.11152 -.06746 (69*2π)/3405 weeks
70-.10348 -.11293 (70*2π)/3405 weeks
71-.09873 -.12528 (71*2π)/3405 weeks
72-.08413 -.031 (72*2π)/3405 weeks
73-.05162 -.11901 (73*2π)/3405 weeks
74-.12351 -.1283 (74*2π)/3405 weeks
75-.05807 -.08109 (75*2π)/3405 weeks
76-.05918 -.08173 (76*2π)/3404 weeks
77-.13085 -.099 (77*2π)/3404 weeks
78-.02985 -.0887 (78*2π)/3404 weeks
79-.09167 -.11787 (79*2π)/3404 weeks
80-.08104 -.11557 (80*2π)/3404 weeks
81-.10865 -.07355 (81*2π)/3404 weeks
82-.05664 -.13792 (82*2π)/3404 weeks
83-.13737 -.08587 (83*2π)/3404 weeks
84-.05439 -.10521 (84*2π)/3404 weeks
85-.14606 -.11848 (85*2π)/3404 weeks
86-.08454 -.06449 (86*2π)/3404 weeks
87-.07098 -.13494 (87*2π)/3404 weeks
88-.12326 -.11383 (88*2π)/3404 weeks
89-.12578 -.03542 (89*2π)/3404 weeks
90-.08136 -.11259 (90*2π)/3404 weeks
91-.12155 -.04683 (91*2π)/3404 weeks
92-.077 -.08268 (92*2π)/3404 weeks
93-.11748 -.05458 (93*2π)/3404 weeks
94-.09724 -.07594 (94*2π)/3404 weeks
95-.06442 -.04423 (95*2π)/3404 weeks
96-.06966 -.06316 (96*2π)/3404 weeks
97-.11392 -.02419 (97*2π)/3404 weeks
98-.06342 -.05508 (98*2π)/3403 weeks
99-.02449 -.0461 (99*2π)/3403 weeks
100-.04636 -.06091 (100*2π)/3403 weeks
101-.04736 -.094 (101*2π)/3403 weeks
102-.04468 -.05016 (102*2π)/3403 weeks
103-.05914 -.00916 (103*2π)/3403 weeks
104-.05586 -.05321 (104*2π)/3403 weeks
105-.02856 -.031 (105*2π)/3403 weeks
106-.06962 -.08222 (106*2π)/3403 weeks
107-.01258 -.04081 (107*2π)/3403 weeks
108-.04774 -.08593 (108*2π)/3403 weeks
109-.05114 -.06744 (109*2π)/3403 weeks
110-.03447 -.09404 (110*2π)/3403 weeks
111-.06035 -.0847 (111*2π)/3403 weeks
112-.06749 -.09745 (112*2π)/3403 weeks
113-.06087 -.05738 (113*2π)/3403 weeks
114-.09059 -.06029 (114*2π)/3403 weeks
115-.06733 -.05719 (115*2π)/3403 weeks
116-.09596 -.09114 (116*2π)/3403 weeks
117-.09009 -.04966 (117*2π)/3403 weeks
118-.10273 -.08549 (118*2π)/3403 weeks
119-.10094 -.04963 (119*2π)/3403 weeks
120-.10351 -.07054 (120*2π)/3403 weeks
121-.14788 -.01128 (121*2π)/3403 weeks
122-.12354 -.05608 (122*2π)/3403 weeks
123-.09378 -.05322 (123*2π)/3403 weeks
124-.14043 -.01016 (124*2π)/3403 weeks
125-.12488 -.00024 (125*2π)/3403 weeks
126-.11019 -.02303 (126*2π)/3403 weeks
127-.13953 -.04876 (127*2π)/3403 weeks
128-.08597 -.00077 (128*2π)/3403 weeks
129-.10291 -.02119 (129*2π)/3403 weeks
130-.07307 -.01868 (130*2π)/3403 weeks
131-.11472 -.05038 (131*2π)/3403 weeks
132-.06806 .00117 (132*2π)/3403 weeks
133-.12779 -.01247 (133*2π)/3403 weeks
134-.09323 -.00923 (134*2π)/3403 weeks
135-.10047 -.03239 (135*2π)/3403 weeks
136-.09752 -.00286 (136*2π)/3403 weeks
137-.11432 -.03245 (137*2π)/3402 weeks
138-.10494 -.01246 (138*2π)/3402 weeks
139-.11012 -.01636 (139*2π)/3402 weeks
140-.07826 -.04142 (140*2π)/3402 weeks
141-.1111 -.02976 (141*2π)/3402 weeks
142-.07419 .01179 (142*2π)/3402 weeks
143-.09088 -.04964 (143*2π)/3402 weeks
144-.1005 -.00173 (144*2π)/3402 weeks
145-.0913 .00775 (145*2π)/3402 weeks
146-.08799 -.00335 (146*2π)/3402 weeks
147-.09529 .01018 (147*2π)/3402 weeks
148-.10068 -.05003 (148*2π)/3402 weeks
149-.10496 -.01653 (149*2π)/3402 weeks
150-.06637 -.01302 (150*2π)/3402 weeks
151-.08976 -.01249 (151*2π)/3402 weeks
152-.05008 -.00228 (152*2π)/3402 weeks
153-.12841 -.01224 (153*2π)/3402 weeks
154-.0645 -.01848 (154*2π)/3402 weeks
155-.10705 .00386 (155*2π)/3402 weeks
156-.06843 -.0031 (156*2π)/3402 weeks
157-.06921 .03141 (157*2π)/3402 weeks
158-.08935 -.01132 (158*2π)/3402 weeks
159-.08358 .00268 (159*2π)/3402 weeks
160-.08314 .01351 (160*2π)/3402 weeks
161-.05452 -.00332 (161*2π)/3402 weeks
162-.06701 -.04455 (162*2π)/3402 weeks
163-.08112 .03632 (163*2π)/3402 weeks
164-.07046 .00837 (164*2π)/3402 weeks
165-.0985 .01657 (165*2π)/3402 weeks
166-.04203 .01553 (166*2π)/3402 weeks
167-.09571 -.03908 (167*2π)/3402 weeks
168-.10511 .03786 (168*2π)/3402 weeks
169-.06482 .00526 (169*2π)/3402 weeks
170-.09303   (170*2π)/3402 weeks
171-.06482 -.00526 (171*2π)/3402 weeks
172-.10511 -.03786 (172*2π)/3402 weeks
173-.09571 .03908 (173*2π)/3402 weeks
174-.04203 -.01553 (174*2π)/3402 weeks
175-.0985 -.01657 (175*2π)/3402 weeks
176-.07046 -.00837 (176*2π)/3402 weeks
177-.08112 -.03632 (177*2π)/3402 weeks
178-.06701 .04455 (178*2π)/3402 weeks
179-.05452 .00332 (179*2π)/3402 weeks
180-.08314 -.01351 (180*2π)/3402 weeks
181-.08358 -.00268 (181*2π)/3402 weeks
182-.08935 .01132 (182*2π)/3402 weeks
183-.06921 -.03141 (183*2π)/3402 weeks
184-.06843 .0031 (184*2π)/3402 weeks
185-.10705 -.00386 (185*2π)/3402 weeks
186-.0645 .01848 (186*2π)/3402 weeks
187-.12841 .01224 (187*2π)/3402 weeks
188-.05008 .00228 (188*2π)/3402 weeks
189-.08976 .01249 (189*2π)/3402 weeks
190-.06637 .01302 (190*2π)/3402 weeks
191-.10496 .01653 (191*2π)/3402 weeks
192-.10068 .05003 (192*2π)/3402 weeks
193-.09529 -.01018 (193*2π)/3402 weeks
194-.08799 .00335 (194*2π)/3402 weeks
195-.0913 -.00775 (195*2π)/3402 weeks
196-.1005 .00173 (196*2π)/3402 weeks
197-.09088 .04964 (197*2π)/3402 weeks
198-.07419 -.01179 (198*2π)/3402 weeks
199-.1111 .02976 (199*2π)/3402 weeks
200-.07826 .04142 (200*2π)/3402 weeks
201-.11012 .01636 (201*2π)/3402 weeks
202-.10494 .01246 (202*2π)/3402 weeks
203-.11432 .03245 (203*2π)/3402 weeks
204-.09752 .00286 (204*2π)/3402 weeks
205-.10047 .03239 (205*2π)/3402 weeks
206-.09323 .00923 (206*2π)/3402 weeks
207-.12779 .01247 (207*2π)/3402 weeks
208-.06806 -.00117 (208*2π)/3402 weeks
209-.11472 .05038 (209*2π)/3402 weeks
210-.07307 .01868 (210*2π)/3402 weeks
211-.10291 .02119 (211*2π)/3402 weeks
212-.08597 .00077 (212*2π)/3402 weeks
213-.13953 .04876 (213*2π)/3402 weeks
214-.11019 .02303 (214*2π)/3402 weeks
215-.12488 .00024 (215*2π)/3402 weeks
216-.14043 .01016 (216*2π)/3402 weeks
217-.09378 .05322 (217*2π)/3402 weeks
218-.12354 .05608 (218*2π)/3402 weeks
219-.14788 .01128 (219*2π)/3402 weeks
220-.10351 .07054 (220*2π)/3402 weeks
221-.10094 .04963 (221*2π)/3402 weeks
222-.10273 .08549 (222*2π)/3402 weeks
223-.09009 .04966 (223*2π)/3402 weeks
224-.09596 .09114 (224*2π)/3402 weeks
225-.06733 .05719 (225*2π)/3402 weeks
226-.09059 .06029 (226*2π)/3402 weeks
227-.06087 .05738 (227*2π)/3401 weeks
228-.06749 .09745 (228*2π)/3401 weeks
229-.06035 .0847 (229*2π)/3401 weeks
230-.03447 .09404 (230*2π)/3401 weeks
231-.05114 .06744 (231*2π)/3401 weeks
232-.04774 .08593 (232*2π)/3401 weeks
233-.01258 .04081 (233*2π)/3401 weeks
234-.06962 .08222 (234*2π)/3401 weeks
235-.02856 .031 (235*2π)/3401 weeks
236-.05586 .05321 (236*2π)/3401 weeks
237-.05914 .00916 (237*2π)/3401 weeks
238-.04468 .05016 (238*2π)/3401 weeks
239-.04736 .094 (239*2π)/3401 weeks
240-.04636 .06091 (240*2π)/3401 weeks
241-.02449 .0461 (241*2π)/3401 weeks
242-.06342 .05508 (242*2π)/3401 weeks
243-.11392 .02419 (243*2π)/3401 weeks
244-.06966 .06316 (244*2π)/3401 weeks
245-.06442 .04423 (245*2π)/3401 weeks
246-.09724 .07594 (246*2π)/3401 weeks
247-.11748 .05458 (247*2π)/3401 weeks
248-.077 .08268 (248*2π)/3401 weeks
249-.12155 .04683 (249*2π)/3401 weeks
250-.08136 .11259 (250*2π)/3401 weeks
251-.12578 .03542 (251*2π)/3401 weeks
252-.12326 .11383 (252*2π)/3401 weeks
253-.07098 .13494 (253*2π)/3401 weeks
254-.08454 .06449 (254*2π)/3401 weeks
255-.14606 .11848 (255*2π)/3401 weeks
256-.05439 .10521 (256*2π)/3401 weeks
257-.13737 .08587 (257*2π)/3401 weeks
258-.05664 .13792 (258*2π)/3401 weeks
259-.10865 .07355 (259*2π)/3401 weeks
260-.08104 .11557 (260*2π)/3401 weeks
261-.09167 .11787 (261*2π)/3401 weeks
262-.02985 .0887 (262*2π)/3401 weeks
263-.13085 .099 (263*2π)/3401 weeks
264-.05918 .08173 (264*2π)/3401 weeks
265-.05807 .08109 (265*2π)/3401 weeks
266-.12351 .1283 (266*2π)/3401 weeks
267-.05162 .11901 (267*2π)/3401 weeks
268-.08413 .031 (268*2π)/3401 weeks
269-.09873 .12528 (269*2π)/3401 weeks
270-.10348 .11293 (270*2π)/3401 weeks
271-.11152 .06746 (271*2π)/3401 weeks
272-.12814 .17486 (272*2π)/3401 weeks
273-.07124 .09013 (273*2π)/3401 weeks
274-.15217 .11086 (274*2π)/3401 weeks
275-.09249 .08294 (275*2π)/3401 weeks
276-.10715 .13016 (276*2π)/3401 weeks
277-.15258 .1487 (277*2π)/3401 weeks
278-.04694 .14143 (278*2π)/3401 weeks
279-.12937 .11922 (279*2π)/3401 weeks
280-.14635 .16958 (280*2π)/3401 weeks
281-.06348 .16298 (281*2π)/3401 weeks
282-.07692 .1699 (282*2π)/3401 weeks
283-.11135 .18075 (283*2π)/3401 weeks
284-.12859 .24089 (284*2π)/3401 weeks
285-.03084 .2229 (285*2π)/3401 weeks
286-.10544 .18023 (286*2π)/3401 weeks
287-.01964 .1788 (287*2π)/3401 weeks
288-.02817 .18381 (288*2π)/3401 weeks
289.03323 .14399 (289*2π)/3401 weeks
290-.03218 .15028 (290*2π)/3401 weeks
291-.03371 .14138 (291*2π)/3401 weeks
292-.07059 .13778 (292*2π)/3401 weeks
293.02198 .18466 (293*2π)/3401 weeks
294-.07504 .18799 (294*2π)/3401 weeks
295-.00435 .12984 (295*2π)/3401 weeks
296-.04659 .1986 (296*2π)/3401 weeks
297-.11592 .11862 (297*2π)/3401 weeks
298-.11291 .14895 (298*2π)/3401 weeks
299.03483 .11141 (299*2π)/3401 weeks
300-.12455 .26906 (300*2π)/3401 weeks
301-.10313 .17315 (301*2π)/3401 weeks
302-.03966 .21065 (302*2π)/3401 weeks
303-.0887 .20756 (303*2π)/3401 weeks
304-.03234 .22277 (304*2π)/3401 weeks
305-.1589 .2571 (305*2π)/3401 weeks
306-.02041 .24908 (306*2π)/3401 weeks
307-.03772 .22021 (307*2π)/3401 weeks
308-.18604 .25751 (308*2π)/3401 weeks
309-.11446 .36325 (309*2π)/3401 weeks
310-.12222 .21024 (310*2π)/3401 weeks
311.04675 .44327 (311*2π)/3401 weeks
312-.06388 .22912 (312*2π)/3401 weeks
313-.05712 .35039 (313*2π)/3401 weeks
314-.04199 .35152 (314*2π)/3401 weeks
315.01634 .44656 (315*2π)/3401 weeks
316.00386 .4276 (316*2π)/3401 weeks
317-.04794 .30813 (317*2π)/3401 weeks
318.01092 .32893 (318*2π)/3401 weeks
319-.03093 .28468 (319*2π)/3401 weeks
320-.24926 .45729 (320*2π)/3401 weeks
321.08596 .43633 (321*2π)/3401 weeks
322-.1013 .27011 (322*2π)/3401 weeks
323-.28324 .52396 (323*2π)/3401 weeks
324.12161 .53561 (324*2π)/3401 weeks
325-.03567 .38747 (325*2π)/3401 weeks
326-.17924 .7471 (326*2π)/3401 weeks
327-.17556 .48033 (327*2π)/3401 weeks
328-.30141 .94139 (328*2π)/3401 weeks
329-.31559 .88461 (329*2π)/3401 weeks
330-.36189 .65013 (330*2π)/3401 weeks
331-.35644 1.0886 (331*2π)/3401 weeks
332-.22986 1.35655 (332*2π)/3401 weeks
333-.19518 1.70795 (333*2π)/3401 weeks
334-.19982 1.64647 (334*2π)/3401 weeks
335-.28561 2.12441 (335*2π)/3401 weeks
336.59292 2.38974 (336*2π)/3401 weeks
337-.04626 2.98675 (337*2π)/3401 weeks
338.88289 5.68376 (338*2π)/3401 weeks