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Fourier Analysis of MOAT (VanEck Vectors Morningstar Wide)


MOAT (VanEck Vectors Morningstar Wide) appears to have interesting cyclic behaviour every 19 weeks (.6413*sine), 25 weeks (.6238*sine), and 21 weeks (.5659*sine).

MOAT (VanEck Vectors Morningstar Wide) has an average price of 27.33 (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 4/25/2012 to 1/9/2017 for MOAT (VanEck Vectors Morningstar Wide), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
027.32765   0 
1-1.57613 -3.83302 (1*2π)/247247 weeks
2.90686 -2.78175 (2*2π)/247124 weeks
3.10765 -2.26676 (3*2π)/24782 weeks
4-.36473 -1.54256 (4*2π)/24762 weeks
5-.42273 -.87917 (5*2π)/24749 weeks
6.11685 -.77564 (6*2π)/24741 weeks
7-.03927 -.69852 (7*2π)/24735 weeks
8.07623 -.60721 (8*2π)/24731 weeks
9.03523 -.84144 (9*2π)/24727 weeks
10-.22279 -.62382 (10*2π)/24725 weeks
11.0782 -.43219 (11*2π)/24722 weeks
12.22949 -.56591 (12*2π)/24721 weeks
13.20276 -.64126 (13*2π)/24719 weeks
14-.13212 -.52734 (14*2π)/24718 weeks
15-.2181 -.19045 (15*2π)/24716 weeks
16-.00927 -.37893 (16*2π)/24715 weeks
17-.12544 -.38984 (17*2π)/24715 weeks
18-.11208 -.34677 (18*2π)/24714 weeks
19-.0909 -.20717 (19*2π)/24713 weeks
20.03352 -.27892 (20*2π)/24712 weeks
21-.19223 -.28456 (21*2π)/24712 weeks
22.15951 -.22803 (22*2π)/24711 weeks
23-.03683 -.29957 (23*2π)/24711 weeks
24-.09452 -.16189 (24*2π)/24710 weeks
25-.10791 -.22882 (25*2π)/24710 weeks
26.01293 -.16365 (26*2π)/24710 weeks
27-.01006 -.09835 (27*2π)/2479 weeks
28-.0151 -.14748 (28*2π)/2479 weeks
29-.13674 -.1012 (29*2π)/2479 weeks
30.05796 -.23028 (30*2π)/2478 weeks
31-.00731 -.13237 (31*2π)/2478 weeks
32.03107 -.0955 (32*2π)/2478 weeks
33-.0637 -.2444 (33*2π)/2477 weeks
34-.02514 -.11615 (34*2π)/2477 weeks
35-.09596 -.18203 (35*2π)/2477 weeks
36-.07563 -.10549 (36*2π)/2477 weeks
37.04126 -.1337 (37*2π)/2477 weeks
38-.04203 -.16468 (38*2π)/2477 weeks
39-.02565 -.12373 (39*2π)/2476 weeks
40-.13367 -.18464 (40*2π)/2476 weeks
41-.07756 -.11141 (41*2π)/2476 weeks
42-.1055 -.10219 (42*2π)/2476 weeks
43-.129 -.04701 (43*2π)/2476 weeks
44-.05827 -.0802 (44*2π)/2476 weeks
45.01637 -.11314 (45*2π)/2475 weeks
46-.04316 -.17531 (46*2π)/2475 weeks
47-.07744 -.14438 (47*2π)/2475 weeks
48-.07087 -.03351 (48*2π)/2475 weeks
49-.01473 -.06591 (49*2π)/2475 weeks
50-.05825 -.08517 (50*2π)/2475 weeks
51-.04732 -.08989 (51*2π)/2475 weeks
52-.1035 -.03171 (52*2π)/2475 weeks
53-.04406 -.09369 (53*2π)/2475 weeks
54-.04538 -.1464 (54*2π)/2475 weeks
55-.07746 -.07654 (55*2π)/2474 weeks
56-.11979 -.0429 (56*2π)/2474 weeks
57-.03738 -.06187 (57*2π)/2474 weeks
58-.05602 -.11797 (58*2π)/2474 weeks
59-.01234 -.10999 (59*2π)/2474 weeks
60-.075 -.15913 (60*2π)/2474 weeks
61-.10406 -.02946 (61*2π)/2474 weeks
62-.03592 -.0564 (62*2π)/2474 weeks
63-.04978 -.10659 (63*2π)/2474 weeks
64-.06378 -.1053 (64*2π)/2474 weeks
65-.12158 -.06663 (65*2π)/2474 weeks
66-.0701 -.03543 (66*2π)/2474 weeks
67-.11456 -.0659 (67*2π)/2474 weeks
68-.11492 -.03461 (68*2π)/2474 weeks
69-.10778 -.04378 (69*2π)/2474 weeks
70-.10502 -.03602 (70*2π)/2474 weeks
71-.05079 -.05912 (71*2π)/2473 weeks
72-.06379 -.04153 (72*2π)/2473 weeks
73-.08848 -.05263 (73*2π)/2473 weeks
74-.03136 -.04893 (74*2π)/2473 weeks
75-.03841 -.01594 (75*2π)/2473 weeks
76-.04732 -.06006 (76*2π)/2473 weeks
77-.03463 -.00823 (77*2π)/2473 weeks
78-.06739 -.06498 (78*2π)/2473 weeks
79-.06587 -.06326 (79*2π)/2473 weeks
80-.05714 -.01625 (80*2π)/2473 weeks
81-.05946 -.05693 (81*2π)/2473 weeks
82-.06895 -.04259 (82*2π)/2473 weeks
83-.06828 -.02991 (83*2π)/2473 weeks
84-.08008 -.02286 (84*2π)/2473 weeks
85-.05051 -.05865 (85*2π)/2473 weeks
86-.10192 -.05206 (86*2π)/2473 weeks
87-.09264 .01369 (87*2π)/2473 weeks
88-.02881 -.04349 (88*2π)/2473 weeks
89-.05709 -.02958 (89*2π)/2473 weeks
90-.10757 -.01092 (90*2π)/2473 weeks
91-.114 -.02337 (91*2π)/2473 weeks
92-.12232 .01174 (92*2π)/2473 weeks
93-.04887 -.03272 (93*2π)/2473 weeks
94-.07039 -.0234 (94*2π)/2473 weeks
95-.04359 .0048 (95*2π)/2473 weeks
96-.06784 -.05682 (96*2π)/2473 weeks
97-.06312 -.03036 (97*2π)/2473 weeks
98-.05873 -.01607 (98*2π)/2473 weeks
99-.07233 -.01572 (99*2π)/2472 weeks
100-.06037 -.03107 (100*2π)/2472 weeks
101-.08744 -.0193 (101*2π)/2472 weeks
102-.0479 -.02962 (102*2π)/2472 weeks
103-.05882 -.06321 (103*2π)/2472 weeks
104-.08908 -.01591 (104*2π)/2472 weeks
105-.07623 -.02003 (105*2π)/2472 weeks
106-.08808 -.03177 (106*2π)/2472 weeks
107-.10407 -.06786 (107*2π)/2472 weeks
108-.07694 -.01005 (108*2π)/2472 weeks
109-.03854 .00938 (109*2π)/2472 weeks
110-.07472 -.01588 (110*2π)/2472 weeks
111-.07169 .03903 (111*2π)/2472 weeks
112-.05194 -.01435 (112*2π)/2472 weeks
113-.05348 .00826 (113*2π)/2472 weeks
114-.05738 -.03917 (114*2π)/2472 weeks
115-.06063 .02598 (115*2π)/2472 weeks
116-.07182 -.0124 (116*2π)/2472 weeks
117-.05843 .02409 (117*2π)/2472 weeks
118.00119 .04905 (118*2π)/2472 weeks
119-.03344 -.00975 (119*2π)/2472 weeks
120-.09795 -.00001 (120*2π)/2472 weeks
121-.05092 .02945 (121*2π)/2472 weeks
122-.0163 -.01483 (122*2π)/2472 weeks
123-.06122 -.02232 (123*2π)/2472 weeks
124-.06122 .02232 (124*2π)/2472 weeks
125-.0163 .01483 (125*2π)/2472 weeks
126-.05092 -.02945 (126*2π)/2472 weeks
127-.09795 .00001 (127*2π)/2472 weeks
128-.03344 .00975 (128*2π)/2472 weeks
129.00119 -.04905 (129*2π)/2472 weeks
130-.05843 -.02409 (130*2π)/2472 weeks
131-.07182 .0124 (131*2π)/2472 weeks
132-.06063 -.02598 (132*2π)/2472 weeks
133-.05738 .03917 (133*2π)/2472 weeks
134-.05348 -.00826 (134*2π)/2472 weeks
135-.05194 .01435 (135*2π)/2472 weeks
136-.07169 -.03903 (136*2π)/2472 weeks
137-.07472 .01588 (137*2π)/2472 weeks
138-.03854 -.00938 (138*2π)/2472 weeks
139-.07694 .01005 (139*2π)/2472 weeks
140-.10407 .06786 (140*2π)/2472 weeks
141-.08808 .03177 (141*2π)/2472 weeks
142-.07623 .02003 (142*2π)/2472 weeks
143-.08908 .01591 (143*2π)/2472 weeks
144-.05882 .06321 (144*2π)/2472 weeks
145-.0479 .02962 (145*2π)/2472 weeks
146-.08744 .0193 (146*2π)/2472 weeks
147-.06037 .03107 (147*2π)/2472 weeks
148-.07233 .01572 (148*2π)/2472 weeks
149-.05873 .01607 (149*2π)/2472 weeks
150-.06312 .03036 (150*2π)/2472 weeks
151-.06784 .05682 (151*2π)/2472 weeks
152-.04359 -.0048 (152*2π)/2472 weeks
153-.07039 .0234 (153*2π)/2472 weeks
154-.04887 .03272 (154*2π)/2472 weeks
155-.12232 -.01174 (155*2π)/2472 weeks
156-.114 .02337 (156*2π)/2472 weeks
157-.10757 .01092 (157*2π)/2472 weeks
158-.05709 .02958 (158*2π)/2472 weeks
159-.02881 .04349 (159*2π)/2472 weeks
160-.09264 -.01369 (160*2π)/2472 weeks
161-.10192 .05206 (161*2π)/2472 weeks
162-.05051 .05865 (162*2π)/2472 weeks
163-.08008 .02286 (163*2π)/2472 weeks
164-.06828 .02991 (164*2π)/2472 weeks
165-.06895 .04259 (165*2π)/2471 weeks
166-.05946 .05693 (166*2π)/2471 weeks
167-.05714 .01625 (167*2π)/2471 weeks
168-.06587 .06326 (168*2π)/2471 weeks
169-.06739 .06498 (169*2π)/2471 weeks
170-.03463 .00823 (170*2π)/2471 weeks
171-.04732 .06006 (171*2π)/2471 weeks
172-.03841 .01594 (172*2π)/2471 weeks
173-.03136 .04893 (173*2π)/2471 weeks
174-.08848 .05263 (174*2π)/2471 weeks
175-.06379 .04153 (175*2π)/2471 weeks
176-.05079 .05912 (176*2π)/2471 weeks
177-.10502 .03602 (177*2π)/2471 weeks
178-.10778 .04378 (178*2π)/2471 weeks
179-.11492 .03461 (179*2π)/2471 weeks
180-.11456 .0659 (180*2π)/2471 weeks
181-.0701 .03543 (181*2π)/2471 weeks
182-.12158 .06663 (182*2π)/2471 weeks
183-.06378 .1053 (183*2π)/2471 weeks
184-.04978 .10659 (184*2π)/2471 weeks
185-.03592 .0564 (185*2π)/2471 weeks
186-.10406 .02946 (186*2π)/2471 weeks
187-.075 .15913 (187*2π)/2471 weeks
188-.01234 .10999 (188*2π)/2471 weeks
189-.05602 .11797 (189*2π)/2471 weeks
190-.03738 .06187 (190*2π)/2471 weeks
191-.11979 .0429 (191*2π)/2471 weeks
192-.07746 .07654 (192*2π)/2471 weeks
193-.04538 .1464 (193*2π)/2471 weeks
194-.04406 .09369 (194*2π)/2471 weeks
195-.1035 .03171 (195*2π)/2471 weeks
196-.04732 .08989 (196*2π)/2471 weeks
197-.05825 .08517 (197*2π)/2471 weeks
198-.01473 .06591 (198*2π)/2471 weeks
199-.07087 .03351 (199*2π)/2471 weeks
200-.07744 .14438 (200*2π)/2471 weeks
201-.04316 .17531 (201*2π)/2471 weeks
202.01637 .11314 (202*2π)/2471 weeks
203-.05827 .0802 (203*2π)/2471 weeks
204-.129 .04701 (204*2π)/2471 weeks
205-.1055 .10219 (205*2π)/2471 weeks
206-.07756 .11141 (206*2π)/2471 weeks
207-.13367 .18464 (207*2π)/2471 weeks
208-.02565 .12373 (208*2π)/2471 weeks
209-.04203 .16468 (209*2π)/2471 weeks
210.04126 .1337 (210*2π)/2471 weeks
211-.07563 .10549 (211*2π)/2471 weeks
212-.09596 .18203 (212*2π)/2471 weeks
213-.02514 .11615 (213*2π)/2471 weeks
214-.0637 .2444 (214*2π)/2471 weeks
215.03107 .0955 (215*2π)/2471 weeks
216-.00731 .13237 (216*2π)/2471 weeks
217.05796 .23028 (217*2π)/2471 weeks
218-.13674 .1012 (218*2π)/2471 weeks
219-.0151 .14748 (219*2π)/2471 weeks
220-.01006 .09835 (220*2π)/2471 weeks
221.01293 .16365 (221*2π)/2471 weeks
222-.10791 .22882 (222*2π)/2471 weeks
223-.09452 .16189 (223*2π)/2471 weeks
224-.03683 .29957 (224*2π)/2471 weeks
225.15951 .22803 (225*2π)/2471 weeks
226-.19223 .28456 (226*2π)/2471 weeks
227.03352 .27892 (227*2π)/2471 weeks
228-.0909 .20717 (228*2π)/2471 weeks
229-.11208 .34677 (229*2π)/2471 weeks
230-.12544 .38984 (230*2π)/2471 weeks
231-.00927 .37893 (231*2π)/2471 weeks
232-.2181 .19045 (232*2π)/2471 weeks
233-.13212 .52734 (233*2π)/2471 weeks
234.20276 .64126 (234*2π)/2471 weeks
235.22949 .56591 (235*2π)/2471 weeks
236.0782 .43219 (236*2π)/2471 weeks
237-.22279 .62382 (237*2π)/2471 weeks
238.03523 .84144 (238*2π)/2471 weeks
239.07623 .60721 (239*2π)/2471 weeks
240-.03927 .69852 (240*2π)/2471 weeks
241.11685 .77564 (241*2π)/2471 weeks
242-.42273 .87917 (242*2π)/2471 weeks
243-.36473 1.54256 (243*2π)/2471 weeks
244.10765 2.26676 (244*2π)/2471 weeks
245.90686 2.78175 (245*2π)/2471 weeks

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