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Fourier Analysis of SCHB (Schwab U.S. Broad Market ETF)


SCHB (Schwab U.S. Broad Market ETF) appears to have interesting cyclic behaviour every 32 weeks (1.3982*sine), 39 weeks (1.0966*sine), and 35 weeks (.9436*sine).

SCHB (Schwab U.S. Broad Market ETF) has an average price of 37.74 (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 11/3/2009 to 3/20/2017 for SCHB (Schwab U.S. Broad Market ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
037.74056   0 
1-.0637 -12.28465 (1*2π)/386386 weeks
2-.04078 -3.32099 (2*2π)/386193 weeks
3.45283 -3.40029 (3*2π)/386129 weeks
4.57972 -3.14544 (4*2π)/38697 weeks
5.2602 -2.79271 (5*2π)/38677 weeks
6.23436 -1.5538 (6*2π)/38664 weeks
7-.16647 -.82141 (7*2π)/38655 weeks
8-.2765 -1.28141 (8*2π)/38648 weeks
9.00472 -1.36389 (9*2π)/38643 weeks
10.07831 -1.09658 (10*2π)/38639 weeks
11.01873 -.9436 (11*2π)/38635 weeks
12-.2113 -1.39819 (12*2π)/38632 weeks
13.04793 -1.0658 (13*2π)/38630 weeks
14-.20977 -.86971 (14*2π)/38628 weeks
15-.09434 -.70533 (15*2π)/38626 weeks
16.21892 -.5849 (16*2π)/38624 weeks
17-.10985 -.88496 (17*2π)/38623 weeks
18-.07787 -.84795 (18*2π)/38621 weeks
19-.23872 -.34746 (19*2π)/38620 weeks
20-.30191 -.34264 (20*2π)/38619 weeks
21-.05113 -.27147 (21*2π)/38618 weeks
22.2049 -.43204 (22*2π)/38618 weeks
23.00263 -.52894 (23*2π)/38617 weeks
24-.23266 -.45844 (24*2π)/38616 weeks
25-.19658 -.49875 (25*2π)/38615 weeks
26-.05789 -.35199 (26*2π)/38615 weeks
27-.14135 -.44965 (27*2π)/38614 weeks
28-.17411 -.35151 (28*2π)/38614 weeks
29-.11821 -.58452 (29*2π)/38613 weeks
30-.06614 -.50697 (30*2π)/38613 weeks
31-.04296 -.26877 (31*2π)/38612 weeks
32-.09173 -.42804 (32*2π)/38612 weeks
33-.26889 -.5019 (33*2π)/38612 weeks
34-.05272 -.18926 (34*2π)/38611 weeks
35-.02699 -.37831 (35*2π)/38611 weeks
36-.0651 -.3083 (36*2π)/38611 weeks
37-.20889 -.36064 (37*2π)/38610 weeks
38-.169 -.33778 (38*2π)/38610 weeks
39-.17394 -.32581 (39*2π)/38610 weeks
40-.04699 -.13015 (40*2π)/38610 weeks
41-.06386 -.23943 (41*2π)/3869 weeks
42-.13615 -.1824 (42*2π)/3869 weeks
43-.11138 -.24948 (43*2π)/3869 weeks
44-.00213 -.30531 (44*2π)/3869 weeks
45-.12334 -.16911 (45*2π)/3869 weeks
46.01644 -.19253 (46*2π)/3868 weeks
47-.17621 -.36861 (47*2π)/3868 weeks
48.00779 -.23248 (48*2π)/3868 weeks
49-.06924 -.15692 (49*2π)/3868 weeks
50-.08486 -.22451 (50*2π)/3868 weeks
51-.18434 -.23164 (51*2π)/3868 weeks
52-.03101 -.13564 (52*2π)/3867 weeks
53-.00309 -.13156 (53*2π)/3867 weeks
54-.2127 -.08391 (54*2π)/3867 weeks
55-.18081 -.18161 (55*2π)/3867 weeks
56-.0929 -.24664 (56*2π)/3867 weeks
57-.10181 -.16539 (57*2π)/3867 weeks
58-.18225 -.15033 (58*2π)/3867 weeks
59-.11109 -.20582 (59*2π)/3867 weeks
60-.06856 -.15511 (60*2π)/3866 weeks
61-.12134 -.10306 (61*2π)/3866 weeks
62-.01235 -.11102 (62*2π)/3866 weeks
63-.02824 -.17492 (63*2π)/3866 weeks
64-.08281 -.18917 (64*2π)/3866 weeks
65-.09583 -.16228 (65*2π)/3866 weeks
66-.15251 -.16253 (66*2π)/3866 weeks
67-.12416 -.21985 (67*2π)/3866 weeks
68-.12387 -.12442 (68*2π)/3866 weeks
69-.11704 -.12214 (69*2π)/3866 weeks
70-.10113 -.07573 (70*2π)/3866 weeks
71-.01654 -.13398 (71*2π)/3865 weeks
72-.07436 -.17583 (72*2π)/3865 weeks
73-.09828 -.12513 (73*2π)/3865 weeks
74-.10529 -.20141 (74*2π)/3865 weeks
75-.1067 -.05335 (75*2π)/3865 weeks
76-.07378 -.06888 (76*2π)/3865 weeks
77-.04519 -.15562 (77*2π)/3865 weeks
78-.119 -.16024 (78*2π)/3865 weeks
79-.1336 -.138 (79*2π)/3865 weeks
80-.06878 -.14481 (80*2π)/3865 weeks
81-.0722 -.05995 (81*2π)/3865 weeks
82-.01119 -.08099 (82*2π)/3865 weeks
83-.05761 -.12597 (83*2π)/3865 weeks
84-.08369 -.18743 (84*2π)/3865 weeks
85-.14108 -.09325 (85*2π)/3865 weeks
86-.08218 -.10157 (86*2π)/3864 weeks
87-.13349 -.03352 (87*2π)/3864 weeks
88-.03333 -.08749 (88*2π)/3864 weeks
89-.07133 -.13743 (89*2π)/3864 weeks
90-.13478 -.10646 (90*2π)/3864 weeks
91-.10361 -.07902 (91*2π)/3864 weeks
92-.14977 -.13192 (92*2π)/3864 weeks
93-.16871 -.06854 (93*2π)/3864 weeks
94-.08143 -.0509 (94*2π)/3864 weeks
95-.00173 -.12808 (95*2π)/3864 weeks
96-.09301 -.11156 (96*2π)/3864 weeks
97-.15159 -.04862 (97*2π)/3864 weeks
98-.13314 -.05537 (98*2π)/3864 weeks
99-.02016 -.04199 (99*2π)/3864 weeks
100-.04997 -.01569 (100*2π)/3864 weeks
101-.03535 -.07032 (101*2π)/3864 weeks
102-.10987 -.15052 (102*2π)/3864 weeks
103-.13058 -.09955 (103*2π)/3864 weeks
104-.07861 -.04898 (104*2π)/3864 weeks
105-.09441 -.10751 (105*2π)/3864 weeks
106-.08999 -.14744 (106*2π)/3864 weeks
107-.06096 -.09656 (107*2π)/3864 weeks
108-.11787 -.093 (108*2π)/3864 weeks
109-.11822 -.10593 (109*2π)/3864 weeks
110-.11717 -.0695 (110*2π)/3864 weeks
111-.03679 -.04952 (111*2π)/3863 weeks
112-.10604 -.01684 (112*2π)/3863 weeks
113-.10458 -.0526 (113*2π)/3863 weeks
114-.12196 -.07333 (114*2π)/3863 weeks
115-.1243 -.01589 (115*2π)/3863 weeks
116-.08572 -.08882 (116*2π)/3863 weeks
117-.07326 -.03017 (117*2π)/3863 weeks
118-.08819 -.04992 (118*2π)/3863 weeks
119-.09277 -.06431 (119*2π)/3863 weeks
120-.08043 -.02539 (120*2π)/3863 weeks
121-.06033 -.08933 (121*2π)/3863 weeks
122-.10467 -.06089 (122*2π)/3863 weeks
123-.11784 -.05909 (123*2π)/3863 weeks
124-.10024 -.04012 (124*2π)/3863 weeks
125-.06123 -.05402 (125*2π)/3863 weeks
126-.08289 -.03866 (126*2π)/3863 weeks
127-.08925 -.0537 (127*2π)/3863 weeks
128-.08263 -.07674 (128*2π)/3863 weeks
129-.10726 -.01281 (129*2π)/3863 weeks
130-.0888 -.04116 (130*2π)/3863 weeks
131-.04179 -.04116 (131*2π)/3863 weeks
132-.0926 -.05312 (132*2π)/3863 weeks
133-.12458 -.02029 (133*2π)/3863 weeks
134-.0789 -.0397 (134*2π)/3863 weeks
135-.0637 -.04277 (135*2π)/3863 weeks
136-.11303 -.01892 (136*2π)/3863 weeks
137-.17257 -.02774 (137*2π)/3863 weeks
138-.06393 -.06217 (138*2π)/3863 weeks
139-.08609 -.02275 (139*2π)/3863 weeks
140-.06957 -.02212 (140*2π)/3863 weeks
141-.1329 -.07486 (141*2π)/3863 weeks
142-.04689 -.09556 (142*2π)/3863 weeks
143-.05666 -.03711 (143*2π)/3863 weeks
144-.13141 -.04435 (144*2π)/3863 weeks
145-.12366 .0038 (145*2π)/3863 weeks
146-.08988 -.04315 (146*2π)/3863 weeks
147-.10124 -.03325 (147*2π)/3863 weeks
148-.12485 .00481 (148*2π)/3863 weeks
149-.0915 -.01783 (149*2π)/3863 weeks
150-.09204 -.10003 (150*2π)/3863 weeks
151-.1141 -.01515 (151*2π)/3863 weeks
152-.10416 -.01894 (152*2π)/3863 weeks
153-.08791 -.04165 (153*2π)/3863 weeks
154-.09276 -.06282 (154*2π)/3863 weeks
155-.09659 -.0446 (155*2π)/3862 weeks
156-.04499 -.02385 (156*2π)/3862 weeks
157-.06118 -.00832 (157*2π)/3862 weeks
158-.10119 .00166 (158*2π)/3862 weeks
159-.06927 -.05898 (159*2π)/3862 weeks
160-.06304 -.03725 (160*2π)/3862 weeks
161-.13153 -.01948 (161*2π)/3862 weeks
162-.13655 .02265 (162*2π)/3862 weeks
163-.07676 .00689 (163*2π)/3862 weeks
164-.07963 -.01658 (164*2π)/3862 weeks
165-.0945 -.00895 (165*2π)/3862 weeks
166-.09497 -.00517 (166*2π)/3862 weeks
167-.12312 -.01742 (167*2π)/3862 weeks
168-.01659 .00924 (168*2π)/3862 weeks
169-.08866 -.00073 (169*2π)/3862 weeks
170-.08678 -.05922 (170*2π)/3862 weeks
171-.06256 -.01176 (171*2π)/3862 weeks
172-.06384 .00934 (172*2π)/3862 weeks
173-.05588 -.02032 (173*2π)/3862 weeks
174-.13266 -.06798 (174*2π)/3862 weeks
175-.0905 .00749 (175*2π)/3862 weeks
176-.06024 -.02425 (176*2π)/3862 weeks
177-.10398 -.01149 (177*2π)/3862 weeks
178-.06661 .02719 (178*2π)/3862 weeks
179-.07007 -.04952 (179*2π)/3862 weeks
180-.08628 .00596 (180*2π)/3862 weeks
181-.11864 .00346 (181*2π)/3862 weeks
182-.1358 -.02946 (182*2π)/3862 weeks
183-.10485 -.02108 (183*2π)/3862 weeks
184-.13936 .00323 (184*2π)/3862 weeks
185-.04999 .02384 (185*2π)/3862 weeks
186-.05638 .00815 (186*2π)/3862 weeks
187-.0706 -.0431 (187*2π)/3862 weeks
188-.09979 .02195 (188*2π)/3862 weeks
189-.10685 .06896 (189*2π)/3862 weeks
190-.07187 .05805 (190*2π)/3862 weeks
191-.03606 -.01662 (191*2π)/3862 weeks
192-.08851 .01188 (192*2π)/3862 weeks
193-.13572   (193*2π)/3862 weeks
194-.08851 -.01188 (194*2π)/3862 weeks
195-.03606 .01662 (195*2π)/3862 weeks
196-.07187 -.05805 (196*2π)/3862 weeks
197-.10685 -.06896 (197*2π)/3862 weeks
198-.09979 -.02195 (198*2π)/3862 weeks
199-.0706 .0431 (199*2π)/3862 weeks
200-.05638 -.00815 (200*2π)/3862 weeks
201-.04999 -.02384 (201*2π)/3862 weeks
202-.13936 -.00323 (202*2π)/3862 weeks
203-.10485 .02108 (203*2π)/3862 weeks
204-.1358 .02946 (204*2π)/3862 weeks
205-.11864 -.00346 (205*2π)/3862 weeks
206-.08628 -.00596 (206*2π)/3862 weeks
207-.07007 .04952 (207*2π)/3862 weeks
208-.06661 -.02719 (208*2π)/3862 weeks
209-.10398 .01149 (209*2π)/3862 weeks
210-.06024 .02425 (210*2π)/3862 weeks
211-.0905 -.00749 (211*2π)/3862 weeks
212-.13266 .06798 (212*2π)/3862 weeks
213-.05588 .02032 (213*2π)/3862 weeks
214-.06384 -.00934 (214*2π)/3862 weeks
215-.06256 .01176 (215*2π)/3862 weeks
216-.08678 .05922 (216*2π)/3862 weeks
217-.08866 .00073 (217*2π)/3862 weeks
218-.01659 -.00924 (218*2π)/3862 weeks
219-.12312 .01742 (219*2π)/3862 weeks
220-.09497 .00517 (220*2π)/3862 weeks
221-.0945 .00895 (221*2π)/3862 weeks
222-.07963 .01658 (222*2π)/3862 weeks
223-.07676 -.00689 (223*2π)/3862 weeks
224-.13655 -.02265 (224*2π)/3862 weeks
225-.13153 .01948 (225*2π)/3862 weeks
226-.06304 .03725 (226*2π)/3862 weeks
227-.06927 .05898 (227*2π)/3862 weeks
228-.10119 -.00166 (228*2π)/3862 weeks
229-.06118 .00832 (229*2π)/3862 weeks
230-.04499 .02385 (230*2π)/3862 weeks
231-.09659 .0446 (231*2π)/3862 weeks
232-.09276 .06282 (232*2π)/3862 weeks
233-.08791 .04165 (233*2π)/3862 weeks
234-.10416 .01894 (234*2π)/3862 weeks
235-.1141 .01515 (235*2π)/3862 weeks
236-.09204 .10003 (236*2π)/3862 weeks
237-.0915 .01783 (237*2π)/3862 weeks
238-.12485 -.00481 (238*2π)/3862 weeks
239-.10124 .03325 (239*2π)/3862 weeks
240-.08988 .04315 (240*2π)/3862 weeks
241-.12366 -.0038 (241*2π)/3862 weeks
242-.13141 .04435 (242*2π)/3862 weeks
243-.05666 .03711 (243*2π)/3862 weeks
244-.04689 .09556 (244*2π)/3862 weeks
245-.1329 .07486 (245*2π)/3862 weeks
246-.06957 .02212 (246*2π)/3862 weeks
247-.08609 .02275 (247*2π)/3862 weeks
248-.06393 .06217 (248*2π)/3862 weeks
249-.17257 .02774 (249*2π)/3862 weeks
250-.11303 .01892 (250*2π)/3862 weeks
251-.0637 .04277 (251*2π)/3862 weeks
252-.0789 .0397 (252*2π)/3862 weeks
253-.12458 .02029 (253*2π)/3862 weeks
254-.0926 .05312 (254*2π)/3862 weeks
255-.04179 .04116 (255*2π)/3862 weeks
256-.0888 .04116 (256*2π)/3862 weeks
257-.10726 .01281 (257*2π)/3862 weeks
258-.08263 .07674 (258*2π)/3861 weeks
259-.08925 .0537 (259*2π)/3861 weeks
260-.08289 .03866 (260*2π)/3861 weeks
261-.06123 .05402 (261*2π)/3861 weeks
262-.10024 .04012 (262*2π)/3861 weeks
263-.11784 .05909 (263*2π)/3861 weeks
264-.10467 .06089 (264*2π)/3861 weeks
265-.06033 .08933 (265*2π)/3861 weeks
266-.08043 .02539 (266*2π)/3861 weeks
267-.09277 .06431 (267*2π)/3861 weeks
268-.08819 .04992 (268*2π)/3861 weeks
269-.07326 .03017 (269*2π)/3861 weeks
270-.08572 .08882 (270*2π)/3861 weeks
271-.1243 .01589 (271*2π)/3861 weeks
272-.12196 .07333 (272*2π)/3861 weeks
273-.10458 .0526 (273*2π)/3861 weeks
274-.10604 .01684 (274*2π)/3861 weeks
275-.03679 .04952 (275*2π)/3861 weeks
276-.11717 .0695 (276*2π)/3861 weeks
277-.11822 .10593 (277*2π)/3861 weeks
278-.11787 .093 (278*2π)/3861 weeks
279-.06096 .09656 (279*2π)/3861 weeks
280-.08999 .14744 (280*2π)/3861 weeks
281-.09441 .10751 (281*2π)/3861 weeks
282-.07861 .04898 (282*2π)/3861 weeks
283-.13058 .09955 (283*2π)/3861 weeks
284-.10987 .15052 (284*2π)/3861 weeks
285-.03535 .07032 (285*2π)/3861 weeks
286-.04997 .01569 (286*2π)/3861 weeks
287-.02016 .04199 (287*2π)/3861 weeks
288-.13314 .05537 (288*2π)/3861 weeks
289-.15159 .04862 (289*2π)/3861 weeks
290-.09301 .11156 (290*2π)/3861 weeks
291-.00173 .12808 (291*2π)/3861 weeks
292-.08143 .0509 (292*2π)/3861 weeks
293-.16871 .06854 (293*2π)/3861 weeks
294-.14977 .13192 (294*2π)/3861 weeks
295-.10361 .07902 (295*2π)/3861 weeks
296-.13478 .10646 (296*2π)/3861 weeks
297-.07133 .13743 (297*2π)/3861 weeks
298-.03333 .08749 (298*2π)/3861 weeks
299-.13349 .03352 (299*2π)/3861 weeks
300-.08218 .10157 (300*2π)/3861 weeks
301-.14108 .09325 (301*2π)/3861 weeks
302-.08369 .18743 (302*2π)/3861 weeks
303-.05761 .12597 (303*2π)/3861 weeks
304-.01119 .08099 (304*2π)/3861 weeks
305-.0722 .05995 (305*2π)/3861 weeks
306-.06878 .14481 (306*2π)/3861 weeks
307-.1336 .138 (307*2π)/3861 weeks
308-.119 .16024 (308*2π)/3861 weeks
309-.04519 .15562 (309*2π)/3861 weeks
310-.07378 .06888 (310*2π)/3861 weeks
311-.1067 .05335 (311*2π)/3861 weeks
312-.10529 .20141 (312*2π)/3861 weeks
313-.09828 .12513 (313*2π)/3861 weeks
314-.07436 .17583 (314*2π)/3861 weeks
315-.01654 .13398 (315*2π)/3861 weeks
316-.10113 .07573 (316*2π)/3861 weeks
317-.11704 .12214 (317*2π)/3861 weeks
318-.12387 .12442 (318*2π)/3861 weeks
319-.12416 .21985 (319*2π)/3861 weeks
320-.15251 .16253 (320*2π)/3861 weeks
321-.09583 .16228 (321*2π)/3861 weeks
322-.08281 .18917 (322*2π)/3861 weeks
323-.02824 .17492 (323*2π)/3861 weeks
324-.01235 .11102 (324*2π)/3861 weeks
325-.12134 .10306 (325*2π)/3861 weeks
326-.06856 .15511 (326*2π)/3861 weeks
327-.11109 .20582 (327*2π)/3861 weeks
328-.18225 .15033 (328*2π)/3861 weeks
329-.10181 .16539 (329*2π)/3861 weeks
330-.0929 .24664 (330*2π)/3861 weeks
331-.18081 .18161 (331*2π)/3861 weeks
332-.2127 .08391 (332*2π)/3861 weeks
333-.00309 .13156 (333*2π)/3861 weeks
334-.03101 .13564 (334*2π)/3861 weeks
335-.18434 .23164 (335*2π)/3861 weeks
336-.08486 .22451 (336*2π)/3861 weeks
337-.06924 .15692 (337*2π)/3861 weeks
338.00779 .23248 (338*2π)/3861 weeks
339-.17621 .36861 (339*2π)/3861 weeks
340.01644 .19253 (340*2π)/3861 weeks
341-.12334 .16911 (341*2π)/3861 weeks
342-.00213 .30531 (342*2π)/3861 weeks
343-.11138 .24948 (343*2π)/3861 weeks
344-.13615 .1824 (344*2π)/3861 weeks
345-.06386 .23943 (345*2π)/3861 weeks
346-.04699 .13015 (346*2π)/3861 weeks
347-.17394 .32581 (347*2π)/3861 weeks
348-.169 .33778 (348*2π)/3861 weeks
349-.20889 .36064 (349*2π)/3861 weeks
350-.0651 .3083 (350*2π)/3861 weeks
351-.02699 .37831 (351*2π)/3861 weeks
352-.05272 .18926 (352*2π)/3861 weeks
353-.26889 .5019 (353*2π)/3861 weeks
354-.09173 .42804 (354*2π)/3861 weeks
355-.04296 .26877 (355*2π)/3861 weeks
356-.06614 .50697 (356*2π)/3861 weeks
357-.11821 .58452 (357*2π)/3861 weeks
358-.17411 .35151 (358*2π)/3861 weeks
359-.14135 .44965 (359*2π)/3861 weeks
360-.05789 .35199 (360*2π)/3861 weeks
361-.19658 .49875 (361*2π)/3861 weeks
362-.23266 .45844 (362*2π)/3861 weeks
363.00263 .52894 (363*2π)/3861 weeks
364.2049 .43204 (364*2π)/3861 weeks
365-.05113 .27147 (365*2π)/3861 weeks
366-.30191 .34264 (366*2π)/3861 weeks
367-.23872 .34746 (367*2π)/3861 weeks
368-.07787 .84795 (368*2π)/3861 weeks
369-.10985 .88496 (369*2π)/3861 weeks
370.21892 .5849 (370*2π)/3861 weeks
371-.09434 .70533 (371*2π)/3861 weeks
372-.20977 .86971 (372*2π)/3861 weeks
373.04793 1.0658 (373*2π)/3861 weeks
374-.2113 1.39819 (374*2π)/3861 weeks
375.01873 .9436 (375*2π)/3861 weeks
376.07831 1.09658 (376*2π)/3861 weeks
377.00472 1.36389 (377*2π)/3861 weeks
378-.2765 1.28141 (378*2π)/3861 weeks
379-.16647 .82141 (379*2π)/3861 weeks
380.23436 1.5538 (380*2π)/3861 weeks
381.2602 2.79271 (381*2π)/3861 weeks
382.57972 3.14544 (382*2π)/3861 weeks
383.45283 3.40029 (383*2π)/3861 weeks
384-.04078 3.32099 (384*2π)/3861 weeks

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