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# Fourier Analysis of HDV (iShares Core High Dividend ETF)

HDV (iShares Core High Dividend ETF) appears to have interesting cyclic behaviour every 37 weeks (1.4051*sine), 28 weeks (1.3335*sine), and 31 weeks (.9551*sine).

HDV (iShares Core High Dividend ETF) has an average price of 63.81 (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 3/31/2011 to 4/16/2018 for HDV (iShares Core High Dividend ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
063.81009   0
1-.98608 -14.46518 (1*2π)/369369 weeks
2.77644 -8.97749 (2*2π)/369185 weeks
3-.90909 -5.18212 (3*2π)/369123 weeks
4.83423 -3.60948 (4*2π)/36992 weeks
5-.30277 -4.13681 (5*2π)/36974 weeks
6-.0843 -2.67335 (6*2π)/36962 weeks
7.36774 -1.78413 (7*2π)/36953 weeks
8-.33624 -2.29106 (8*2π)/36946 weeks
9-.44476 -1.98707 (9*2π)/36941 weeks
10-.34851 -1.40506 (10*2π)/36937 weeks
11-.09134 -.62928 (11*2π)/36934 weeks
12-.43516 -.95511 (12*2π)/36931 weeks
13-.36243 -1.33351 (13*2π)/36928 weeks
14-.31964 -.59507 (14*2π)/36926 weeks
15-.30795 -.98253 (15*2π)/36925 weeks
16-.31339 -.43638 (16*2π)/36923 weeks
17-.0229 -.60314 (17*2π)/36922 weeks
18-.31549 -.98305 (18*2π)/36921 weeks
19-.31289 -.45827 (19*2π)/36919 weeks
20-.01262 -.53223 (20*2π)/36918 weeks
21.05596 -.80801 (21*2π)/36918 weeks
22-.23943 -.4394 (22*2π)/36917 weeks
23.05552 -.4999 (23*2π)/36916 weeks
24.09127 -.60329 (24*2π)/36915 weeks
25-.07793 -.40632 (25*2π)/36915 weeks
26.09862 -.73362 (26*2π)/36914 weeks
27.08341 -.70836 (27*2π)/36914 weeks
28-.00077 -.45252 (28*2π)/36913 weeks
29-.24861 -.5754 (29*2π)/36913 weeks
30-.27427 -.32754 (30*2π)/36912 weeks
31.08481 -.3489 (31*2π)/36912 weeks
32-.33029 -.61456 (32*2π)/36912 weeks
33-.05455 -.41544 (33*2π)/36911 weeks
34-.33542 -.49519 (34*2π)/36911 weeks
35-.29318 -.26011 (35*2π)/36911 weeks
36-.13846 -.38041 (36*2π)/36910 weeks
37.02888 -.43857 (37*2π)/36910 weeks
38-.23519 -.33976 (38*2π)/36910 weeks
39-.04628 -.26941 (39*2π)/3699 weeks
40-.17714 -.38447 (40*2π)/3699 weeks
41-.14831 -.33614 (41*2π)/3699 weeks
42-.17325 -.36964 (42*2π)/3699 weeks
43-.16658 -.46436 (43*2π)/3699 weeks
44-.28258 -.20222 (44*2π)/3698 weeks
45-.11753 -.50726 (45*2π)/3698 weeks
46-.11489 -.2845 (46*2π)/3698 weeks
47-.02206 -.15231 (47*2π)/3698 weeks
48-.04276 -.29423 (48*2π)/3698 weeks
49.04193 -.25136 (49*2π)/3698 weeks
50-.09187 -.25294 (50*2π)/3697 weeks
51.08284 -.2732 (51*2π)/3697 weeks
52-.09359 -.21023 (52*2π)/3697 weeks
53-.07664 -.17762 (53*2π)/3697 weeks
54-.06267 -.24603 (54*2π)/3697 weeks
55-.03975 -.15003 (55*2π)/3697 weeks
56-.05974 -.31498 (56*2π)/3697 weeks
57-.06783 -.30574 (57*2π)/3696 weeks
58-.01758 -.35969 (58*2π)/3696 weeks
59-.05119 -.22438 (59*2π)/3696 weeks
60-.074 -.33696 (60*2π)/3696 weeks
61-.2097 -.33919 (61*2π)/3696 weeks
62-.17397 -.29023 (62*2π)/3696 weeks
63-.08629 -.27211 (63*2π)/3696 weeks
64-.0836 -.25077 (64*2π)/3696 weeks
65-.22426 -.28627 (65*2π)/3696 weeks
66-.19859 -.21152 (66*2π)/3696 weeks
67-.07396 -.16893 (67*2π)/3696 weeks
68-.17774 -.34407 (68*2π)/3695 weeks
69-.2037 -.18665 (69*2π)/3695 weeks
70-.19209 -.19518 (70*2π)/3695 weeks
71-.12232 -.2328 (71*2π)/3695 weeks
72-.18995 -.10596 (72*2π)/3695 weeks
73-.09173 -.12293 (73*2π)/3695 weeks
74-.22115 -.22927 (74*2π)/3695 weeks
75-.14338 -.11006 (75*2π)/3695 weeks
76-.13114 -.19237 (76*2π)/3695 weeks
77-.14268 -.17945 (77*2π)/3695 weeks
78-.1848 -.05198 (78*2π)/3695 weeks
79-.06542 -.1747 (79*2π)/3695 weeks
80-.13602 -.22198 (80*2π)/3695 weeks
81-.13335 -.04563 (81*2π)/3695 weeks
82-.13388 -.14797 (82*2π)/3695 weeks
83-.09751 -.19634 (83*2π)/3694 weeks
84-.12404 -.0588 (84*2π)/3694 weeks
85-.05123 -.20595 (85*2π)/3694 weeks
86-.1344 -.14165 (86*2π)/3694 weeks
87-.09738 -.18503 (87*2π)/3694 weeks
88-.13836 -.13974 (88*2π)/3694 weeks
89-.06314 -.18737 (89*2π)/3694 weeks
90-.16973 -.15822 (90*2π)/3694 weeks
91-.06935 -.1362 (91*2π)/3694 weeks
92-.19427 -.21409 (92*2π)/3694 weeks
93-.12176 -.05374 (93*2π)/3694 weeks
94-.05652 -.12296 (94*2π)/3694 weeks
95-.16786 -.1487 (95*2π)/3694 weeks
96-.21337 -.12716 (96*2π)/3694 weeks
97-.12755 -.0367 (97*2π)/3694 weeks
98-.20705 -.17916 (98*2π)/3694 weeks
99-.16835 -.05937 (99*2π)/3694 weeks
100-.13346 -.13533 (100*2π)/3694 weeks
101-.22168 -.06651 (101*2π)/3694 weeks
102-.18832 -.1292 (102*2π)/3694 weeks
103-.0841 -.05763 (103*2π)/3694 weeks
104-.10843 -.06823 (104*2π)/3694 weeks
105-.16174 -.06713 (105*2π)/3694 weeks
106-.03 -.01943 (106*2π)/3693 weeks
107-.0954 .0019 (107*2π)/3693 weeks
108-.06917 -.05016 (108*2π)/3693 weeks
109-.06895 -.05459 (109*2π)/3693 weeks
110-.15171 -.11701 (110*2π)/3693 weeks
111-.11677 -.11759 (111*2π)/3693 weeks
112-.04497 -.05738 (112*2π)/3693 weeks
113-.10674 -.05644 (113*2π)/3693 weeks
114-.04246 -.03843 (114*2π)/3693 weeks
115-.10057 -.12614 (115*2π)/3693 weeks
116-.02324 -.01381 (116*2π)/3693 weeks
117-.08803 -.12146 (117*2π)/3693 weeks
118-.11817 -.10149 (118*2π)/3693 weeks
119-.07982 -.08129 (119*2π)/3693 weeks
120-.1137 -.11541 (120*2π)/3693 weeks
121-.10774 -.13215 (121*2π)/3693 weeks
122-.17337 -.15008 (122*2π)/3693 weeks
123-.07554 -.13911 (123*2π)/3693 weeks
124-.10609 -.10843 (124*2π)/3693 weeks
125-.08435 -.11003 (125*2π)/3693 weeks
126-.14413 -.15104 (126*2π)/3693 weeks
127-.1558 -.05924 (127*2π)/3693 weeks
128-.16905 -.11356 (128*2π)/3693 weeks
129-.17516 -.07866 (129*2π)/3693 weeks
130-.18336 -.12383 (130*2π)/3693 weeks
131-.28447 -.12522 (131*2π)/3693 weeks
132-.14935 -.09506 (132*2π)/3693 weeks
133-.16932 -.05653 (133*2π)/3693 weeks
134-.18614 -.12737 (134*2π)/3693 weeks
135-.14725 -.05764 (135*2π)/3693 weeks
136-.11052 -.02161 (136*2π)/3693 weeks
137-.12412 -.02365 (137*2π)/3693 weeks
138-.18729 -.04025 (138*2π)/3693 weeks
139-.08007 .01459 (139*2π)/3693 weeks
140-.13703 -.0367 (140*2π)/3693 weeks
141-.11118 -.01304 (141*2π)/3693 weeks
142-.15653 -.07749 (142*2π)/3693 weeks
143-.14926 .03283 (143*2π)/3693 weeks
144-.18297 -.07606 (144*2π)/3693 weeks
145-.13209 -.00644 (145*2π)/3693 weeks
146-.13953 -.04873 (146*2π)/3693 weeks
147-.16375 -.01902 (147*2π)/3693 weeks
148-.11203 -.02874 (148*2π)/3692 weeks
149-.16236 -.02576 (149*2π)/3692 weeks
150-.14728 -.01166 (150*2π)/3692 weeks
151-.14752 -.01683 (151*2π)/3692 weeks
152-.11695 -.09636 (152*2π)/3692 weeks
153-.16534 -.07104 (153*2π)/3692 weeks
154-.12465 .01194 (154*2π)/3692 weeks
155-.10358 -.07715 (155*2π)/3692 weeks
156-.15701 -.02097 (156*2π)/3692 weeks
157-.1436 -.02922 (157*2π)/3692 weeks
158-.12884 -.03641 (158*2π)/3692 weeks
159-.11806 -.01038 (159*2π)/3692 weeks
160-.08464 -.00911 (160*2π)/3692 weeks
161-.15915 .0007 (161*2π)/3692 weeks
162-.17376 .00214 (162*2π)/3692 weeks
163-.11744 -.05892 (163*2π)/3692 weeks
164-.15008 -.02449 (164*2π)/3692 weeks
165-.07782 -.02591 (165*2π)/3692 weeks
166-.20916 -.0494 (166*2π)/3692 weeks
167-.08194 -.01975 (167*2π)/3692 weeks
168-.13616 -.0182 (168*2π)/3692 weeks
169-.11416 .01865 (169*2π)/3692 weeks
170-.12836 .03123 (170*2π)/3692 weeks
171-.08339 -.02382 (171*2π)/3692 weeks
172-.12435 .01636 (172*2π)/3692 weeks
173-.10446 .02915 (173*2π)/3692 weeks
174-.10788 .04259 (174*2π)/3692 weeks
175-.09762 .00804 (175*2π)/3692 weeks
176-.14271 -.06768 (176*2π)/3692 weeks
177-.09585 .04786 (177*2π)/3692 weeks
178-.10551 .01943 (178*2π)/3692 weeks
179-.14975 .00221 (179*2π)/3692 weeks
180-.06916 .00028 (180*2π)/3692 weeks
181-.10967 -.09238 (181*2π)/3692 weeks
182-.16733 -.00214 (182*2π)/3692 weeks
183-.06056 .03192 (183*2π)/3692 weeks
184-.10283 -.01942 (184*2π)/3692 weeks
185-.10283 .01942 (185*2π)/3692 weeks
186-.06056 -.03192 (186*2π)/3692 weeks
187-.16733 .00214 (187*2π)/3692 weeks
188-.10967 .09238 (188*2π)/3692 weeks
189-.06916 -.00028 (189*2π)/3692 weeks
190-.14975 -.00221 (190*2π)/3692 weeks
191-.10551 -.01943 (191*2π)/3692 weeks
192-.09585 -.04786 (192*2π)/3692 weeks
193-.14271 .06768 (193*2π)/3692 weeks
194-.09762 -.00804 (194*2π)/3692 weeks
195-.10788 -.04259 (195*2π)/3692 weeks
196-.10446 -.02915 (196*2π)/3692 weeks
197-.12435 -.01636 (197*2π)/3692 weeks
198-.08339 .02382 (198*2π)/3692 weeks
199-.12836 -.03123 (199*2π)/3692 weeks
200-.11416 -.01865 (200*2π)/3692 weeks
201-.13616 .0182 (201*2π)/3692 weeks
202-.08194 .01975 (202*2π)/3692 weeks
203-.20916 .0494 (203*2π)/3692 weeks
204-.07782 .02591 (204*2π)/3692 weeks
205-.15008 .02449 (205*2π)/3692 weeks
206-.11744 .05892 (206*2π)/3692 weeks
207-.17376 -.00214 (207*2π)/3692 weeks
208-.15915 -.0007 (208*2π)/3692 weeks
209-.08464 .00911 (209*2π)/3692 weeks
210-.11806 .01038 (210*2π)/3692 weeks
211-.12884 .03641 (211*2π)/3692 weeks
212-.1436 .02922 (212*2π)/3692 weeks
213-.15701 .02097 (213*2π)/3692 weeks
214-.10358 .07715 (214*2π)/3692 weeks
215-.12465 -.01194 (215*2π)/3692 weeks
216-.16534 .07104 (216*2π)/3692 weeks
217-.11695 .09636 (217*2π)/3692 weeks
218-.14752 .01683 (218*2π)/3692 weeks
219-.14728 .01166 (219*2π)/3692 weeks
220-.16236 .02576 (220*2π)/3692 weeks
221-.11203 .02874 (221*2π)/3692 weeks
222-.16375 .01902 (222*2π)/3692 weeks
223-.13953 .04873 (223*2π)/3692 weeks
224-.13209 .00644 (224*2π)/3692 weeks
225-.18297 .07606 (225*2π)/3692 weeks
226-.14926 -.03283 (226*2π)/3692 weeks
227-.15653 .07749 (227*2π)/3692 weeks
228-.11118 .01304 (228*2π)/3692 weeks
229-.13703 .0367 (229*2π)/3692 weeks
230-.08007 -.01459 (230*2π)/3692 weeks
231-.18729 .04025 (231*2π)/3692 weeks
232-.12412 .02365 (232*2π)/3692 weeks
233-.11052 .02161 (233*2π)/3692 weeks
234-.14725 .05764 (234*2π)/3692 weeks
235-.18614 .12737 (235*2π)/3692 weeks
236-.16932 .05653 (236*2π)/3692 weeks
237-.14935 .09506 (237*2π)/3692 weeks
238-.28447 .12522 (238*2π)/3692 weeks
239-.18336 .12383 (239*2π)/3692 weeks
240-.17516 .07866 (240*2π)/3692 weeks
241-.16905 .11356 (241*2π)/3692 weeks
242-.1558 .05924 (242*2π)/3692 weeks
243-.14413 .15104 (243*2π)/3692 weeks
244-.08435 .11003 (244*2π)/3692 weeks
245-.10609 .10843 (245*2π)/3692 weeks
246-.07554 .13911 (246*2π)/3692 weeks
247-.17337 .15008 (247*2π)/3691 weeks
248-.10774 .13215 (248*2π)/3691 weeks
249-.1137 .11541 (249*2π)/3691 weeks
250-.07982 .08129 (250*2π)/3691 weeks
251-.11817 .10149 (251*2π)/3691 weeks
252-.08803 .12146 (252*2π)/3691 weeks
253-.02324 .01381 (253*2π)/3691 weeks
254-.10057 .12614 (254*2π)/3691 weeks
255-.04246 .03843 (255*2π)/3691 weeks
256-.10674 .05644 (256*2π)/3691 weeks
257-.04497 .05738 (257*2π)/3691 weeks
258-.11677 .11759 (258*2π)/3691 weeks
259-.15171 .11701 (259*2π)/3691 weeks
260-.06895 .05459 (260*2π)/3691 weeks
261-.06917 .05016 (261*2π)/3691 weeks
262-.0954 -.0019 (262*2π)/3691 weeks
263-.03 .01943 (263*2π)/3691 weeks
264-.16174 .06713 (264*2π)/3691 weeks
265-.10843 .06823 (265*2π)/3691 weeks
266-.0841 .05763 (266*2π)/3691 weeks
267-.18832 .1292 (267*2π)/3691 weeks
268-.22168 .06651 (268*2π)/3691 weeks
269-.13346 .13533 (269*2π)/3691 weeks
270-.16835 .05937 (270*2π)/3691 weeks
271-.20705 .17916 (271*2π)/3691 weeks
272-.12755 .0367 (272*2π)/3691 weeks
273-.21337 .12716 (273*2π)/3691 weeks
274-.16786 .1487 (274*2π)/3691 weeks
275-.05652 .12296 (275*2π)/3691 weeks
276-.12176 .05374 (276*2π)/3691 weeks
277-.19427 .21409 (277*2π)/3691 weeks
278-.06935 .1362 (278*2π)/3691 weeks
279-.16973 .15822 (279*2π)/3691 weeks
280-.06314 .18737 (280*2π)/3691 weeks
281-.13836 .13974 (281*2π)/3691 weeks
282-.09738 .18503 (282*2π)/3691 weeks
283-.1344 .14165 (283*2π)/3691 weeks
284-.05123 .20595 (284*2π)/3691 weeks
285-.12404 .0588 (285*2π)/3691 weeks
286-.09751 .19634 (286*2π)/3691 weeks
287-.13388 .14797 (287*2π)/3691 weeks
288-.13335 .04563 (288*2π)/3691 weeks
289-.13602 .22198 (289*2π)/3691 weeks
290-.06542 .1747 (290*2π)/3691 weeks
291-.1848 .05198 (291*2π)/3691 weeks
292-.14268 .17945 (292*2π)/3691 weeks
293-.13114 .19237 (293*2π)/3691 weeks
294-.14338 .11006 (294*2π)/3691 weeks
295-.22115 .22927 (295*2π)/3691 weeks
296-.09173 .12293 (296*2π)/3691 weeks
297-.18995 .10596 (297*2π)/3691 weeks
298-.12232 .2328 (298*2π)/3691 weeks
299-.19209 .19518 (299*2π)/3691 weeks
300-.2037 .18665 (300*2π)/3691 weeks
301-.17774 .34407 (301*2π)/3691 weeks
302-.07396 .16893 (302*2π)/3691 weeks
303-.19859 .21152 (303*2π)/3691 weeks
304-.22426 .28627 (304*2π)/3691 weeks
305-.0836 .25077 (305*2π)/3691 weeks
306-.08629 .27211 (306*2π)/3691 weeks
307-.17397 .29023 (307*2π)/3691 weeks
308-.2097 .33919 (308*2π)/3691 weeks
309-.074 .33696 (309*2π)/3691 weeks
310-.05119 .22438 (310*2π)/3691 weeks
311-.01758 .35969 (311*2π)/3691 weeks
312-.06783 .30574 (312*2π)/3691 weeks
313-.05974 .31498 (313*2π)/3691 weeks
314-.03975 .15003 (314*2π)/3691 weeks
315-.06267 .24603 (315*2π)/3691 weeks
316-.07664 .17762 (316*2π)/3691 weeks
317-.09359 .21023 (317*2π)/3691 weeks
318.08284 .2732 (318*2π)/3691 weeks
319-.09187 .25294 (319*2π)/3691 weeks
320.04193 .25136 (320*2π)/3691 weeks
321-.04276 .29423 (321*2π)/3691 weeks
322-.02206 .15231 (322*2π)/3691 weeks
323-.11489 .2845 (323*2π)/3691 weeks
324-.11753 .50726 (324*2π)/3691 weeks
325-.28258 .20222 (325*2π)/3691 weeks
326-.16658 .46436 (326*2π)/3691 weeks
327-.17325 .36964 (327*2π)/3691 weeks
328-.14831 .33614 (328*2π)/3691 weeks
329-.17714 .38447 (329*2π)/3691 weeks
330-.04628 .26941 (330*2π)/3691 weeks
331-.23519 .33976 (331*2π)/3691 weeks
332.02888 .43857 (332*2π)/3691 weeks
333-.13846 .38041 (333*2π)/3691 weeks
334-.29318 .26011 (334*2π)/3691 weeks
335-.33542 .49519 (335*2π)/3691 weeks
336-.05455 .41544 (336*2π)/3691 weeks
337-.33029 .61456 (337*2π)/3691 weeks
338.08481 .3489 (338*2π)/3691 weeks
339-.27427 .32754 (339*2π)/3691 weeks
340-.24861 .5754 (340*2π)/3691 weeks
341-.00077 .45252 (341*2π)/3691 weeks
342.08341 .70836 (342*2π)/3691 weeks
343.09862 .73362 (343*2π)/3691 weeks
344-.07793 .40632 (344*2π)/3691 weeks
345.09127 .60329 (345*2π)/3691 weeks
346.05552 .4999 (346*2π)/3691 weeks
347-.23943 .4394 (347*2π)/3691 weeks
348.05596 .80801 (348*2π)/3691 weeks
349-.01262 .53223 (349*2π)/3691 weeks
350-.31289 .45827 (350*2π)/3691 weeks
351-.31549 .98305 (351*2π)/3691 weeks
352-.0229 .60314 (352*2π)/3691 weeks
353-.31339 .43638 (353*2π)/3691 weeks
354-.30795 .98253 (354*2π)/3691 weeks
355-.31964 .59507 (355*2π)/3691 weeks
356-.36243 1.33351 (356*2π)/3691 weeks
357-.43516 .95511 (357*2π)/3691 weeks
358-.09134 .62928 (358*2π)/3691 weeks
359-.34851 1.40506 (359*2π)/3691 weeks
360-.44476 1.98707 (360*2π)/3691 weeks
361-.33624 2.29106 (361*2π)/3691 weeks
362.36774 1.78413 (362*2π)/3691 weeks
363-.0843 2.67335 (363*2π)/3691 weeks
364-.30277 4.13681 (364*2π)/3691 weeks
365.83423 3.60948 (365*2π)/3691 weeks
366-.90909 5.18212 (366*2π)/3691 weeks
367.77644 8.97749 (367*2π)/3691 weeks