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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 21 weeks (1.1432*sine), 28 weeks (1.142*sine), and 22 weeks (1.0179*sine).

HDV (iShares Core High Dividend ETF) has an average price of 63.26 (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 7/17/2017 for HDV (iShares Core High Dividend ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
063.25953   0 
1-1.87856 -13.32134 (1*2π)/330330 weeks
21.2468 -7.20073 (2*2π)/330165 weeks
3-.3806 -5.84803 (3*2π)/330110 weeks
4-.76838 -2.93705 (4*2π)/33083 weeks
5.60524 -2.82002 (5*2π)/33066 weeks
6.76647 -2.31007 (6*2π)/33055 weeks
7-.40976 -2.15063 (7*2π)/33047 weeks
8-.24753 -1.92618 (8*2π)/33041 weeks
9-.10475 -1.45825 (9*2π)/33037 weeks
10-.17458 -.53863 (10*2π)/33033 weeks
11-.38828 -.92925 (11*2π)/33030 weeks
12.23339 -1.14205 (12*2π)/33028 weeks
13-.41525 -.96687 (13*2π)/33025 weeks
14.09328 -.7173 (14*2π)/33024 weeks
15-.05176 -1.01787 (15*2π)/33022 weeks
16-.47672 -1.14316 (16*2π)/33021 weeks
17-.37436 -.61882 (17*2π)/33019 weeks
18-.12771 -.6206 (18*2π)/33018 weeks
19.19461 -.77847 (19*2π)/33017 weeks
20-.24876 -.85323 (20*2π)/33017 weeks
21-.19641 -.67157 (21*2π)/33016 weeks
22-.04637 -.46395 (22*2π)/33015 weeks
23-.20671 -.81045 (23*2π)/33014 weeks
24-.08862 -.67197 (24*2π)/33014 weeks
25-.06606 -.36652 (25*2π)/33013 weeks
26-.28217 -.54822 (26*2π)/33013 weeks
27-.42165 -.4097 (27*2π)/33012 weeks
28-.20862 -.07584 (28*2π)/33012 weeks
29-.13283 -.5651 (29*2π)/33011 weeks
30-.26545 -.2062 (30*2π)/33011 weeks
31-.06544 -.29531 (31*2π)/33011 weeks
32-.13432 -.50255 (32*2π)/33010 weeks
33-.0199 -.53974 (33*2π)/33010 weeks
34-.29177 -.36758 (34*2π)/33010 weeks
35-.12098 -.23462 (35*2π)/3309 weeks
36-.18049 -.39282 (36*2π)/3309 weeks
37-.22113 -.33606 (37*2π)/3309 weeks
38-.2464 -.3527 (38*2π)/3309 weeks
39-.0538 -.2349 (39*2π)/3308 weeks
40-.24994 -.57952 (40*2π)/3308 weeks
41-.08367 -.32312 (41*2π)/3308 weeks
42-.0198 -.21002 (42*2π)/3308 weeks
43-.07036 -.3494 (43*2π)/3308 weeks
44-.00218 -.24353 (44*2π)/3308 weeks
45-.1274 -.34549 (45*2π)/3307 weeks
46-.01178 -.13079 (46*2π)/3307 weeks
47-.06712 -.21228 (47*2π)/3307 weeks
48-.13677 -.24804 (48*2π)/3307 weeks
49-.06819 -.17652 (49*2π)/3307 weeks
50-.17144 -.3021 (50*2π)/3307 weeks
51-.15163 -.2627 (51*2π)/3306 weeks
52-.05489 -.29453 (52*2π)/3306 weeks
53-.17114 -.15125 (53*2π)/3306 weeks
54-.10795 -.15131 (54*2π)/3306 weeks
55-.09635 -.26743 (55*2π)/3306 weeks
56-.0774 -.30664 (56*2π)/3306 weeks
57-.08876 -.24499 (57*2π)/3306 weeks
58-.22642 -.20132 (58*2π)/3306 weeks
59-.16514 -.16354 (59*2π)/3306 weeks
60-.05514 -.09302 (60*2π)/3306 weeks
61-.04789 -.29618 (61*2π)/3305 weeks
62-.14924 -.21523 (62*2π)/3305 weeks
63-.14967 -.23781 (63*2π)/3305 weeks
64-.0438 -.13737 (64*2π)/3305 weeks
65-.09339 -.23304 (65*2π)/3305 weeks
66-.25547 -.19868 (66*2π)/3305 weeks
67-.10647 -.12745 (67*2π)/3305 weeks
68-.1082 -.21959 (68*2π)/3305 weeks
69-.10459 -.21964 (69*2π)/3305 weeks
70-.25977 -.15456 (70*2π)/3305 weeks
71-.12945 -.10492 (71*2π)/3305 weeks
72-.00742 -.14645 (72*2π)/3305 weeks
73-.18169 -.17415 (73*2π)/3305 weeks
74-.156 -.20645 (74*2π)/3304 weeks
75-.10529 -.05753 (75*2π)/3304 weeks
76-.07227 -.22346 (76*2π)/3304 weeks
77-.16529 -.14931 (77*2π)/3304 weeks
78-.10328 -.16584 (78*2π)/3304 weeks
79-.17179 -.17058 (79*2π)/3304 weeks
80-.09255 -.08672 (80*2π)/3304 weeks
81-.09592 -.19601 (81*2π)/3304 weeks
82-.20981 -.10222 (82*2π)/3304 weeks
83-.03169 -.05555 (83*2π)/3304 weeks
84-.031 -.13981 (84*2π)/3304 weeks
85-.14174 -.14864 (85*2π)/3304 weeks
86-.18313 -.16589 (86*2π)/3304 weeks
87-.19116 -.01857 (87*2π)/3304 weeks
88-.09209 -.16957 (88*2π)/3304 weeks
89-.19418 -.14902 (89*2π)/3304 weeks
90-.14732 -.05421 (90*2π)/3304 weeks
91-.17652 -.15953 (91*2π)/3304 weeks
92-.0485 -.13588 (92*2π)/3304 weeks
93-.10134 -.13345 (93*2π)/3304 weeks
94-.17102 -.15894 (94*2π)/3304 weeks
95-.07429 -.05006 (95*2π)/3303 weeks
96-.16399 -.07046 (96*2π)/3303 weeks
97-.14515 -.07149 (97*2π)/3303 weeks
98-.20337 -.03699 (98*2π)/3303 weeks
99-.14311 -.10354 (99*2π)/3303 weeks
100-.05577 -.08881 (100*2π)/3303 weeks
101-.14324 -.06183 (101*2π)/3303 weeks
102-.09002 -.03335 (102*2π)/3303 weeks
103-.11886 -.14432 (103*2π)/3303 weeks
104-.1458 .01949 (104*2π)/3303 weeks
105-.10703 -.05537 (105*2π)/3303 weeks
106-.11433 -.09443 (106*2π)/3303 weeks
107-.16138 -.06352 (107*2π)/3303 weeks
108-.14886 -.08774 (108*2π)/3303 weeks
109-.19987 -.08328 (109*2π)/3303 weeks
110-.08409 -.09316 (110*2π)/3303 weeks
111-.12084 -.054 (111*2π)/3303 weeks
112-.09609 -.01873 (112*2π)/3303 weeks
113-.07221 -.07806 (113*2π)/3303 weeks
114-.17107 -.04954 (114*2π)/3303 weeks
115-.13263 -.05246 (115*2π)/3303 weeks
116-.18064 -.08034 (116*2π)/3303 weeks
117-.23745 -.04953 (117*2π)/3303 weeks
118-.08568 -.09026 (118*2π)/3303 weeks
119-.12086 -.04352 (119*2π)/3303 weeks
120-.10078 -.13975 (120*2π)/3303 weeks
121-.09383 -.08965 (121*2π)/3303 weeks
122-.10569 -.02949 (122*2π)/3303 weeks
123-.12555 .00239 (123*2π)/3303 weeks
124-.04676 -.07828 (124*2π)/3303 weeks
125-.14614 -.0416 (125*2π)/3303 weeks
126-.10283 -.02839 (126*2π)/3303 weeks
127-.15168 -.08653 (127*2π)/3303 weeks
128-.16534 .03576 (128*2π)/3303 weeks
129-.13881 -.09765 (129*2π)/3303 weeks
130-.16338 -.02343 (130*2π)/3303 weeks
131-.12402 -.02297 (131*2π)/3303 weeks
132-.13341 -.0664 (132*2π)/3303 weeks
133-.15773 -.01102 (133*2π)/3302 weeks
134-.14004 -.02132 (134*2π)/3302 weeks
135-.15129 -.02214 (135*2π)/3302 weeks
136-.10311 -.09699 (136*2π)/3302 weeks
137-.1372 -.10573 (137*2π)/3302 weeks
138-.18407 -.01845 (138*2π)/3302 weeks
139-.09027 -.01062 (139*2π)/3302 weeks
140-.13098 -.04221 (140*2π)/3302 weeks
141-.12598 -.05218 (141*2π)/3302 weeks
142-.10447 -.03209 (142*2π)/3302 weeks
143-.08479 -.0326 (143*2π)/3302 weeks
144-.16473 -.00728 (144*2π)/3302 weeks
145-.19337 -.01975 (145*2π)/3302 weeks
146-.10848 -.04716 (146*2π)/3302 weeks
147-.15017 -.06691 (147*2π)/3302 weeks
148-.14237 .04746 (148*2π)/3302 weeks
149-.08171 -.10137 (149*2π)/3302 weeks
150-.12927 -.01691 (150*2π)/3302 weeks
151-.09639 -.00435 (151*2π)/3302 weeks
152-.12343 .01143 (152*2π)/3302 weeks
153-.07065 -.04284 (153*2π)/3302 weeks
154-.12389 -.02288 (154*2π)/3302 weeks
155-.12367 -.00006 (155*2π)/3302 weeks
156-.16157 .00479 (156*2π)/3302 weeks
157-.18479 .01718 (157*2π)/3302 weeks
158-.04955 .01038 (158*2π)/3302 weeks
159-.12207 .0048 (159*2π)/3302 weeks
160-.16886 .00813 (160*2π)/3302 weeks
161-.08072 .00678 (161*2π)/3302 weeks
162-.07539 -.09117 (162*2π)/3302 weeks
163-.16114 -.07833 (163*2π)/3302 weeks
164-.14241 .03288 (164*2π)/3302 weeks
165-.09965   (165*2π)/3302 weeks
166-.14241 -.03288 (166*2π)/3302 weeks
167-.16114 .07833 (167*2π)/3302 weeks
168-.07539 .09117 (168*2π)/3302 weeks
169-.08072 -.00678 (169*2π)/3302 weeks
170-.16886 -.00813 (170*2π)/3302 weeks
171-.12207 -.0048 (171*2π)/3302 weeks
172-.04955 -.01038 (172*2π)/3302 weeks
173-.18479 -.01718 (173*2π)/3302 weeks
174-.16157 -.00479 (174*2π)/3302 weeks
175-.12367 .00006 (175*2π)/3302 weeks
176-.12389 .02288 (176*2π)/3302 weeks
177-.07065 .04284 (177*2π)/3302 weeks
178-.12343 -.01143 (178*2π)/3302 weeks
179-.09639 .00435 (179*2π)/3302 weeks
180-.12927 .01691 (180*2π)/3302 weeks
181-.08171 .10137 (181*2π)/3302 weeks
182-.14237 -.04746 (182*2π)/3302 weeks
183-.15017 .06691 (183*2π)/3302 weeks
184-.10848 .04716 (184*2π)/3302 weeks
185-.19337 .01975 (185*2π)/3302 weeks
186-.16473 .00728 (186*2π)/3302 weeks
187-.08479 .0326 (187*2π)/3302 weeks
188-.10447 .03209 (188*2π)/3302 weeks
189-.12598 .05218 (189*2π)/3302 weeks
190-.13098 .04221 (190*2π)/3302 weeks
191-.09027 .01062 (191*2π)/3302 weeks
192-.18407 .01845 (192*2π)/3302 weeks
193-.1372 .10573 (193*2π)/3302 weeks
194-.10311 .09699 (194*2π)/3302 weeks
195-.15129 .02214 (195*2π)/3302 weeks
196-.14004 .02132 (196*2π)/3302 weeks
197-.15773 .01102 (197*2π)/3302 weeks
198-.13341 .0664 (198*2π)/3302 weeks
199-.12402 .02297 (199*2π)/3302 weeks
200-.16338 .02343 (200*2π)/3302 weeks
201-.13881 .09765 (201*2π)/3302 weeks
202-.16534 -.03576 (202*2π)/3302 weeks
203-.15168 .08653 (203*2π)/3302 weeks
204-.10283 .02839 (204*2π)/3302 weeks
205-.14614 .0416 (205*2π)/3302 weeks
206-.04676 .07828 (206*2π)/3302 weeks
207-.12555 -.00239 (207*2π)/3302 weeks
208-.10569 .02949 (208*2π)/3302 weeks
209-.09383 .08965 (209*2π)/3302 weeks
210-.10078 .13975 (210*2π)/3302 weeks
211-.12086 .04352 (211*2π)/3302 weeks
212-.08568 .09026 (212*2π)/3302 weeks
213-.23745 .04953 (213*2π)/3302 weeks
214-.18064 .08034 (214*2π)/3302 weeks
215-.13263 .05246 (215*2π)/3302 weeks
216-.17107 .04954 (216*2π)/3302 weeks
217-.07221 .07806 (217*2π)/3302 weeks
218-.09609 .01873 (218*2π)/3302 weeks
219-.12084 .054 (219*2π)/3302 weeks
220-.08409 .09316 (220*2π)/3302 weeks
221-.19987 .08328 (221*2π)/3301 weeks
222-.14886 .08774 (222*2π)/3301 weeks
223-.16138 .06352 (223*2π)/3301 weeks
224-.11433 .09443 (224*2π)/3301 weeks
225-.10703 .05537 (225*2π)/3301 weeks
226-.1458 -.01949 (226*2π)/3301 weeks
227-.11886 .14432 (227*2π)/3301 weeks
228-.09002 .03335 (228*2π)/3301 weeks
229-.14324 .06183 (229*2π)/3301 weeks
230-.05577 .08881 (230*2π)/3301 weeks
231-.14311 .10354 (231*2π)/3301 weeks
232-.20337 .03699 (232*2π)/3301 weeks
233-.14515 .07149 (233*2π)/3301 weeks
234-.16399 .07046 (234*2π)/3301 weeks
235-.07429 .05006 (235*2π)/3301 weeks
236-.17102 .15894 (236*2π)/3301 weeks
237-.10134 .13345 (237*2π)/3301 weeks
238-.0485 .13588 (238*2π)/3301 weeks
239-.17652 .15953 (239*2π)/3301 weeks
240-.14732 .05421 (240*2π)/3301 weeks
241-.19418 .14902 (241*2π)/3301 weeks
242-.09209 .16957 (242*2π)/3301 weeks
243-.19116 .01857 (243*2π)/3301 weeks
244-.18313 .16589 (244*2π)/3301 weeks
245-.14174 .14864 (245*2π)/3301 weeks
246-.031 .13981 (246*2π)/3301 weeks
247-.03169 .05555 (247*2π)/3301 weeks
248-.20981 .10222 (248*2π)/3301 weeks
249-.09592 .19601 (249*2π)/3301 weeks
250-.09255 .08672 (250*2π)/3301 weeks
251-.17179 .17058 (251*2π)/3301 weeks
252-.10328 .16584 (252*2π)/3301 weeks
253-.16529 .14931 (253*2π)/3301 weeks
254-.07227 .22346 (254*2π)/3301 weeks
255-.10529 .05753 (255*2π)/3301 weeks
256-.156 .20645 (256*2π)/3301 weeks
257-.18169 .17415 (257*2π)/3301 weeks
258-.00742 .14645 (258*2π)/3301 weeks
259-.12945 .10492 (259*2π)/3301 weeks
260-.25977 .15456 (260*2π)/3301 weeks
261-.10459 .21964 (261*2π)/3301 weeks
262-.1082 .21959 (262*2π)/3301 weeks
263-.10647 .12745 (263*2π)/3301 weeks
264-.25547 .19868 (264*2π)/3301 weeks
265-.09339 .23304 (265*2π)/3301 weeks
266-.0438 .13737 (266*2π)/3301 weeks
267-.14967 .23781 (267*2π)/3301 weeks
268-.14924 .21523 (268*2π)/3301 weeks
269-.04789 .29618 (269*2π)/3301 weeks
270-.05514 .09302 (270*2π)/3301 weeks
271-.16514 .16354 (271*2π)/3301 weeks
272-.22642 .20132 (272*2π)/3301 weeks
273-.08876 .24499 (273*2π)/3301 weeks
274-.0774 .30664 (274*2π)/3301 weeks
275-.09635 .26743 (275*2π)/3301 weeks
276-.10795 .15131 (276*2π)/3301 weeks
277-.17114 .15125 (277*2π)/3301 weeks
278-.05489 .29453 (278*2π)/3301 weeks
279-.15163 .2627 (279*2π)/3301 weeks
280-.17144 .3021 (280*2π)/3301 weeks
281-.06819 .17652 (281*2π)/3301 weeks
282-.13677 .24804 (282*2π)/3301 weeks
283-.06712 .21228 (283*2π)/3301 weeks
284-.01178 .13079 (284*2π)/3301 weeks
285-.1274 .34549 (285*2π)/3301 weeks
286-.00218 .24353 (286*2π)/3301 weeks
287-.07036 .3494 (287*2π)/3301 weeks
288-.0198 .21002 (288*2π)/3301 weeks
289-.08367 .32312 (289*2π)/3301 weeks
290-.24994 .57952 (290*2π)/3301 weeks
291-.0538 .2349 (291*2π)/3301 weeks
292-.2464 .3527 (292*2π)/3301 weeks
293-.22113 .33606 (293*2π)/3301 weeks
294-.18049 .39282 (294*2π)/3301 weeks
295-.12098 .23462 (295*2π)/3301 weeks
296-.29177 .36758 (296*2π)/3301 weeks
297-.0199 .53974 (297*2π)/3301 weeks
298-.13432 .50255 (298*2π)/3301 weeks
299-.06544 .29531 (299*2π)/3301 weeks
300-.26545 .2062 (300*2π)/3301 weeks
301-.13283 .5651 (301*2π)/3301 weeks
302-.20862 .07584 (302*2π)/3301 weeks
303-.42165 .4097 (303*2π)/3301 weeks
304-.28217 .54822 (304*2π)/3301 weeks
305-.06606 .36652 (305*2π)/3301 weeks
306-.08862 .67197 (306*2π)/3301 weeks
307-.20671 .81045 (307*2π)/3301 weeks
308-.04637 .46395 (308*2π)/3301 weeks
309-.19641 .67157 (309*2π)/3301 weeks
310-.24876 .85323 (310*2π)/3301 weeks
311.19461 .77847 (311*2π)/3301 weeks
312-.12771 .6206 (312*2π)/3301 weeks
313-.37436 .61882 (313*2π)/3301 weeks
314-.47672 1.14316 (314*2π)/3301 weeks
315-.05176 1.01787 (315*2π)/3301 weeks
316.09328 .7173 (316*2π)/3301 weeks
317-.41525 .96687 (317*2π)/3301 weeks
318.23339 1.14205 (318*2π)/3301 weeks
319-.38828 .92925 (319*2π)/3301 weeks
320-.17458 .53863 (320*2π)/3301 weeks
321-.10475 1.45825 (321*2π)/3301 weeks
322-.24753 1.92618 (322*2π)/3301 weeks
323-.40976 2.15063 (323*2π)/3301 weeks
324.76647 2.31007 (324*2π)/3301 weeks
325.60524 2.82002 (325*2π)/3301 weeks
326-.76838 2.93705 (326*2π)/3301 weeks
327-.3806 5.84803 (327*2π)/3301 weeks
3281.2468 7.20073 (328*2π)/3301 weeks



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