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Fourier Analysis of USMV (ISHARES EDGE MSCI MIN VOL USA ETF ISHARES EDGE MSCI MIN VOL USA ETF)


USMV (ISHARES EDGE MSCI MIN VOL USA ETF ISHARES EDGE MSCI MIN VOL USA ETF) appears to have interesting cyclic behaviour every 29 weeks (1.0956*sine), 32 weeks (.9799*sine), and 32 weeks (.2209*cosine).

USMV (ISHARES EDGE MSCI MIN VOL USA ETF ISHARES EDGE MSCI MIN VOL USA ETF) has an average price of 36.18 (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 10/20/2011 to 11/6/2017 for USMV (ISHARES EDGE MSCI MIN VOL USA ETF ISHARES EDGE MSCI MIN VOL USA ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
036.17772   0 
1-.05331 -8.52587 (1*2π)/317317 weeks
2.52038 -4.4259 (2*2π)/317159 weeks
3-.12015 -3.16697 (3*2π)/317106 weeks
4.29157 -1.83042 (4*2π)/31779 weeks
5-.002 -2.18069 (5*2π)/31763 weeks
6-.51315 -1.65518 (6*2π)/31753 weeks
7-.25399 -1.34002 (7*2π)/31745 weeks
8.08905 -.8632 (8*2π)/31740 weeks
9.17944 -.89701 (9*2π)/31735 weeks
10-.22088 -.97989 (10*2π)/31732 weeks
11-.19476 -1.09561 (11*2π)/31729 weeks
12-.06381 -.74142 (12*2π)/31726 weeks
13-.10389 -.75799 (13*2π)/31724 weeks
14-.03883 -.5421 (14*2π)/31723 weeks
15.10913 -.63169 (15*2π)/31721 weeks
16-.10315 -.7051 (16*2π)/31720 weeks
17-.19889 -.53495 (17*2π)/31719 weeks
18.02316 -.34012 (18*2π)/31718 weeks
19-.04309 -.66379 (19*2π)/31717 weeks
20-.16406 -.53463 (20*2π)/31716 weeks
21-.07518 -.35236 (21*2π)/31715 weeks
22-.18568 -.44197 (22*2π)/31714 weeks
23-.08743 -.48442 (23*2π)/31714 weeks
24-.02412 -.36513 (24*2π)/31713 weeks
25-.09757 -.32486 (25*2π)/31713 weeks
26-.01507 -.23438 (26*2π)/31712 weeks
27.01703 -.47 (27*2π)/31712 weeks
28-.08631 -.25368 (28*2π)/31711 weeks
29-.10357 -.35906 (29*2π)/31711 weeks
30-.17593 -.38097 (30*2π)/31711 weeks
31-.12107 -.24403 (31*2π)/31710 weeks
32-.01263 -.22575 (32*2π)/31710 weeks
33-.09482 -.35957 (33*2π)/31710 weeks
34-.06872 -.21456 (34*2π)/3179 weeks
35-.08804 -.27975 (35*2π)/3179 weeks
36-.09079 -.19256 (36*2π)/3179 weeks
37-.14377 -.24719 (37*2π)/3179 weeks
38.00907 -.26295 (38*2π)/3178 weeks
39-.13916 -.15115 (39*2π)/3178 weeks
40-.11503 -.17631 (40*2π)/3178 weeks
41-.07122 -.24061 (41*2π)/3178 weeks
42-.06588 -.19079 (42*2π)/3178 weeks
43-.09997 -.23372 (43*2π)/3177 weeks
44-.0398 -.21637 (44*2π)/3177 weeks
45-.10215 -.19833 (45*2π)/3177 weeks
46-.10685 -.20997 (46*2π)/3177 weeks
47-.12977 -.18723 (47*2π)/3177 weeks
48-.11134 -.13105 (48*2π)/3177 weeks
49-.08588 -.16067 (49*2π)/3176 weeks
50-.13893 -.11211 (50*2π)/3176 weeks
51-.11217 -.17043 (51*2π)/3176 weeks
52-.15695 -.12438 (52*2π)/3176 weeks
53-.0904 -.11556 (53*2π)/3176 weeks
54-.05089 -.16073 (54*2π)/3176 weeks
55-.06629 -.13125 (55*2π)/3176 weeks
56-.10451 -.13708 (56*2π)/3176 weeks
57-.11537 -.13657 (57*2π)/3176 weeks
58-.03596 -.09776 (58*2π)/3175 weeks
59-.1003 -.162 (59*2π)/3175 weeks
60-.08176 -.14083 (60*2π)/3175 weeks
61-.12324 -.08609 (61*2π)/3175 weeks
62-.09778 -.15678 (62*2π)/3175 weeks
63-.1432 -.10397 (63*2π)/3175 weeks
64-.04448 -.09855 (64*2π)/3175 weeks
65-.09713 -.16286 (65*2π)/3175 weeks
66-.11077 -.11803 (66*2π)/3175 weeks
67-.05173 -.06215 (67*2π)/3175 weeks
68-.07463 -.16505 (68*2π)/3175 weeks
69-.15493 -.16192 (69*2π)/3175 weeks
70-.0746 -.07942 (70*2π)/3175 weeks
71-.07528 -.086 (71*2π)/3174 weeks
72-.15211 -.13846 (72*2π)/3174 weeks
73-.08884 -.05073 (73*2π)/3174 weeks
74-.0914 -.10319 (74*2π)/3174 weeks
75-.07199 -.08473 (75*2π)/3174 weeks
76-.10339 -.14368 (76*2π)/3174 weeks
77-.10424 -.05455 (77*2π)/3174 weeks
78-.0785 -.13173 (78*2π)/3174 weeks
79-.12369 -.06025 (79*2π)/3174 weeks
80-.04412 -.10602 (80*2π)/3174 weeks
81-.09585 -.16562 (81*2π)/3174 weeks
82-.12949 -.10377 (82*2π)/3174 weeks
83-.1338 -.03842 (83*2π)/3174 weeks
84-.04807 -.10615 (84*2π)/3174 weeks
85-.10716 -.08111 (85*2π)/3174 weeks
86-.08183 -.07921 (86*2π)/3174 weeks
87-.11943 -.09152 (87*2π)/3174 weeks
88-.08294 -.10858 (88*2π)/3174 weeks
89-.08707 -.0592 (89*2π)/3174 weeks
90-.06332 -.04606 (90*2π)/3174 weeks
91-.08358 -.10419 (91*2π)/3173 weeks
92-.0634 -.10635 (92*2π)/3173 weeks
93-.0788 -.08787 (93*2π)/3173 weeks
94-.08828 -.10274 (94*2π)/3173 weeks
95-.06859 -.05392 (95*2π)/3173 weeks
96-.08968 -.0414 (96*2π)/3173 weeks
97-.09521 -.06377 (97*2π)/3173 weeks
98-.08569 -.04335 (98*2π)/3173 weeks
99-.10327 -.08246 (99*2π)/3173 weeks
100-.06855 -.01836 (100*2π)/3173 weeks
101-.05488 -.0638 (101*2π)/3173 weeks
102-.08816 -.07069 (102*2π)/3173 weeks
103-.08721 -.05487 (103*2π)/3173 weeks
104-.08077 -.03683 (104*2π)/3173 weeks
105-.05478 -.04355 (105*2π)/3173 weeks
106-.07658 -.03686 (106*2π)/3173 weeks
107-.06736 -.06052 (107*2π)/3173 weeks
108-.10744 -.0655 (108*2π)/3173 weeks
109-.07657 -.02619 (109*2π)/3173 weeks
110-.09849 -.04252 (110*2π)/3173 weeks
111-.06356 -.03121 (111*2π)/3173 weeks
112-.06879 -.04494 (112*2π)/3173 weeks
113-.14606 -.03013 (113*2π)/3173 weeks
114-.11373 -.04585 (114*2π)/3173 weeks
115-.06785 -.0056 (115*2π)/3173 weeks
116-.08672 -.03016 (116*2π)/3173 weeks
117-.11769 -.0495 (117*2π)/3173 weeks
118-.11735 -.0256 (118*2π)/3173 weeks
119-.0651 -.05786 (119*2π)/3173 weeks
120-.10996 -.0362 (120*2π)/3173 weeks
121-.08772 -.05063 (121*2π)/3173 weeks
122-.13133 -.04212 (122*2π)/3173 weeks
123-.06381 -.00987 (123*2π)/3173 weeks
124-.13239 -.02443 (124*2π)/3173 weeks
125-.08648 -.01849 (125*2π)/3173 weeks
126-.10008 -.03501 (126*2π)/3173 weeks
127-.10406 -.00058 (127*2π)/3172 weeks
128-.09652 -.03935 (128*2π)/3172 weeks
129-.10685 -.0324 (129*2π)/3172 weeks
130-.11072 -.0335 (130*2π)/3172 weeks
131-.08073 -.0233 (131*2π)/3172 weeks
132-.0722 -.03577 (132*2π)/3172 weeks
133-.12234 -.02821 (133*2π)/3172 weeks
134-.07815 .00047 (134*2π)/3172 weeks
135-.0893 -.01834 (135*2π)/3172 weeks
136-.09864 -.01089 (136*2π)/3172 weeks
137-.0967 -.00925 (137*2π)/3172 weeks
138-.12141 -.05288 (138*2π)/3172 weeks
139-.11501 -.03154 (139*2π)/3172 weeks
140-.07942 -.01726 (140*2π)/3172 weeks
141-.08961 -.01513 (141*2π)/3172 weeks
142-.07093 .02156 (142*2π)/3172 weeks
143-.10386 -.05387 (143*2π)/3172 weeks
144-.07588 .00812 (144*2π)/3172 weeks
145-.0854 -.01807 (145*2π)/3172 weeks
146-.06623 -.00178 (146*2π)/3172 weeks
147-.11887 -.0094 (147*2π)/3172 weeks
148-.0963 .00027 (148*2π)/3172 weeks
149-.08509 -.00469 (149*2π)/3172 weeks
150-.0913 -.02964 (150*2π)/3172 weeks
151-.08283 -.04551 (151*2π)/3172 weeks
152-.09387 .01781 (152*2π)/3172 weeks
153-.0812 .01143 (153*2π)/3172 weeks
154-.12105 -.01032 (154*2π)/3172 weeks
155-.08462 .03687 (155*2π)/3172 weeks
156-.06162 -.01566 (156*2π)/3172 weeks
157-.1249 -.01307 (157*2π)/3172 weeks
158-.09874 .00316 (158*2π)/3172 weeks
159-.09874 -.00316 (159*2π)/3172 weeks
160-.1249 .01307 (160*2π)/3172 weeks
161-.06162 .01566 (161*2π)/3172 weeks
162-.08462 -.03687 (162*2π)/3172 weeks
163-.12105 .01032 (163*2π)/3172 weeks
164-.0812 -.01143 (164*2π)/3172 weeks
165-.09387 -.01781 (165*2π)/3172 weeks
166-.08283 .04551 (166*2π)/3172 weeks
167-.0913 .02964 (167*2π)/3172 weeks
168-.08509 .00469 (168*2π)/3172 weeks
169-.0963 -.00027 (169*2π)/3172 weeks
170-.11887 .0094 (170*2π)/3172 weeks
171-.06623 .00178 (171*2π)/3172 weeks
172-.0854 .01807 (172*2π)/3172 weeks
173-.07588 -.00812 (173*2π)/3172 weeks
174-.10386 .05387 (174*2π)/3172 weeks
175-.07093 -.02156 (175*2π)/3172 weeks
176-.08961 .01513 (176*2π)/3172 weeks
177-.07942 .01726 (177*2π)/3172 weeks
178-.11501 .03154 (178*2π)/3172 weeks
179-.12141 .05288 (179*2π)/3172 weeks
180-.0967 .00925 (180*2π)/3172 weeks
181-.09864 .01089 (181*2π)/3172 weeks
182-.0893 .01834 (182*2π)/3172 weeks
183-.07815 -.00047 (183*2π)/3172 weeks
184-.12234 .02821 (184*2π)/3172 weeks
185-.0722 .03577 (185*2π)/3172 weeks
186-.08073 .0233 (186*2π)/3172 weeks
187-.11072 .0335 (187*2π)/3172 weeks
188-.10685 .0324 (188*2π)/3172 weeks
189-.09652 .03935 (189*2π)/3172 weeks
190-.10406 .00058 (190*2π)/3172 weeks
191-.10008 .03501 (191*2π)/3172 weeks
192-.08648 .01849 (192*2π)/3172 weeks
193-.13239 .02443 (193*2π)/3172 weeks
194-.06381 .00987 (194*2π)/3172 weeks
195-.13133 .04212 (195*2π)/3172 weeks
196-.08772 .05063 (196*2π)/3172 weeks
197-.10996 .0362 (197*2π)/3172 weeks
198-.0651 .05786 (198*2π)/3172 weeks
199-.11735 .0256 (199*2π)/3172 weeks
200-.11769 .0495 (200*2π)/3172 weeks
201-.08672 .03016 (201*2π)/3172 weeks
202-.06785 .0056 (202*2π)/3172 weeks
203-.11373 .04585 (203*2π)/3172 weeks
204-.14606 .03013 (204*2π)/3172 weeks
205-.06879 .04494 (205*2π)/3172 weeks
206-.06356 .03121 (206*2π)/3172 weeks
207-.09849 .04252 (207*2π)/3172 weeks
208-.07657 .02619 (208*2π)/3172 weeks
209-.10744 .0655 (209*2π)/3172 weeks
210-.06736 .06052 (210*2π)/3172 weeks
211-.07658 .03686 (211*2π)/3172 weeks
212-.05478 .04355 (212*2π)/3171 weeks
213-.08077 .03683 (213*2π)/3171 weeks
214-.08721 .05487 (214*2π)/3171 weeks
215-.08816 .07069 (215*2π)/3171 weeks
216-.05488 .0638 (216*2π)/3171 weeks
217-.06855 .01836 (217*2π)/3171 weeks
218-.10327 .08246 (218*2π)/3171 weeks
219-.08569 .04335 (219*2π)/3171 weeks
220-.09521 .06377 (220*2π)/3171 weeks
221-.08968 .0414 (221*2π)/3171 weeks
222-.06859 .05392 (222*2π)/3171 weeks
223-.08828 .10274 (223*2π)/3171 weeks
224-.0788 .08787 (224*2π)/3171 weeks
225-.0634 .10635 (225*2π)/3171 weeks
226-.08358 .10419 (226*2π)/3171 weeks
227-.06332 .04606 (227*2π)/3171 weeks
228-.08707 .0592 (228*2π)/3171 weeks
229-.08294 .10858 (229*2π)/3171 weeks
230-.11943 .09152 (230*2π)/3171 weeks
231-.08183 .07921 (231*2π)/3171 weeks
232-.10716 .08111 (232*2π)/3171 weeks
233-.04807 .10615 (233*2π)/3171 weeks
234-.1338 .03842 (234*2π)/3171 weeks
235-.12949 .10377 (235*2π)/3171 weeks
236-.09585 .16562 (236*2π)/3171 weeks
237-.04412 .10602 (237*2π)/3171 weeks
238-.12369 .06025 (238*2π)/3171 weeks
239-.0785 .13173 (239*2π)/3171 weeks
240-.10424 .05455 (240*2π)/3171 weeks
241-.10339 .14368 (241*2π)/3171 weeks
242-.07199 .08473 (242*2π)/3171 weeks
243-.0914 .10319 (243*2π)/3171 weeks
244-.08884 .05073 (244*2π)/3171 weeks
245-.15211 .13846 (245*2π)/3171 weeks
246-.07528 .086 (246*2π)/3171 weeks
247-.0746 .07942 (247*2π)/3171 weeks
248-.15493 .16192 (248*2π)/3171 weeks
249-.07463 .16505 (249*2π)/3171 weeks
250-.05173 .06215 (250*2π)/3171 weeks
251-.11077 .11803 (251*2π)/3171 weeks
252-.09713 .16286 (252*2π)/3171 weeks
253-.04448 .09855 (253*2π)/3171 weeks
254-.1432 .10397 (254*2π)/3171 weeks
255-.09778 .15678 (255*2π)/3171 weeks
256-.12324 .08609 (256*2π)/3171 weeks
257-.08176 .14083 (257*2π)/3171 weeks
258-.1003 .162 (258*2π)/3171 weeks
259-.03596 .09776 (259*2π)/3171 weeks
260-.11537 .13657 (260*2π)/3171 weeks
261-.10451 .13708 (261*2π)/3171 weeks
262-.06629 .13125 (262*2π)/3171 weeks
263-.05089 .16073 (263*2π)/3171 weeks
264-.0904 .11556 (264*2π)/3171 weeks
265-.15695 .12438 (265*2π)/3171 weeks
266-.11217 .17043 (266*2π)/3171 weeks
267-.13893 .11211 (267*2π)/3171 weeks
268-.08588 .16067 (268*2π)/3171 weeks
269-.11134 .13105 (269*2π)/3171 weeks
270-.12977 .18723 (270*2π)/3171 weeks
271-.10685 .20997 (271*2π)/3171 weeks
272-.10215 .19833 (272*2π)/3171 weeks
273-.0398 .21637 (273*2π)/3171 weeks
274-.09997 .23372 (274*2π)/3171 weeks
275-.06588 .19079 (275*2π)/3171 weeks
276-.07122 .24061 (276*2π)/3171 weeks
277-.11503 .17631 (277*2π)/3171 weeks
278-.13916 .15115 (278*2π)/3171 weeks
279.00907 .26295 (279*2π)/3171 weeks
280-.14377 .24719 (280*2π)/3171 weeks
281-.09079 .19256 (281*2π)/3171 weeks
282-.08804 .27975 (282*2π)/3171 weeks
283-.06872 .21456 (283*2π)/3171 weeks
284-.09482 .35957 (284*2π)/3171 weeks
285-.01263 .22575 (285*2π)/3171 weeks
286-.12107 .24403 (286*2π)/3171 weeks
287-.17593 .38097 (287*2π)/3171 weeks
288-.10357 .35906 (288*2π)/3171 weeks
289-.08631 .25368 (289*2π)/3171 weeks
290.01703 .47 (290*2π)/3171 weeks
291-.01507 .23438 (291*2π)/3171 weeks
292-.09757 .32486 (292*2π)/3171 weeks
293-.02412 .36513 (293*2π)/3171 weeks
294-.08743 .48442 (294*2π)/3171 weeks
295-.18568 .44197 (295*2π)/3171 weeks
296-.07518 .35236 (296*2π)/3171 weeks
297-.16406 .53463 (297*2π)/3171 weeks
298-.04309 .66379 (298*2π)/3171 weeks
299.02316 .34012 (299*2π)/3171 weeks
300-.19889 .53495 (300*2π)/3171 weeks
301-.10315 .7051 (301*2π)/3171 weeks
302.10913 .63169 (302*2π)/3171 weeks
303-.03883 .5421 (303*2π)/3171 weeks
304-.10389 .75799 (304*2π)/3171 weeks
305-.06381 .74142 (305*2π)/3171 weeks
306-.19476 1.09561 (306*2π)/3171 weeks
307-.22088 .97989 (307*2π)/3171 weeks
308.17944 .89701 (308*2π)/3171 weeks
309.08905 .8632 (309*2π)/3171 weeks
310-.25399 1.34002 (310*2π)/3171 weeks
311-.51315 1.65518 (311*2π)/3171 weeks
312-.002 2.18069 (312*2π)/3171 weeks
313.29157 1.83042 (313*2π)/3171 weeks
314-.12015 3.16697 (314*2π)/3171 weeks
315.52038 4.4259 (315*2π)/3171 weeks



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