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Fourier Analysis of FRAK (VanEck Vectors Unconventional Oil & Gas ETF)

FRAK (VanEck Vectors Unconventional Oil & Gas ETF) appears to have interesting cyclic behaviour every 27 weeks (.7749*sine), 32 weeks (.5678*cosine), and 27 weeks (.2899*cosine).

FRAK (VanEck Vectors Unconventional Oil & Gas ETF) has an average price of 20.39 (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.

Fourier Analysis

Using data from 2/15/2012 to 4/16/2018 for FRAK (VanEck Vectors Unconventional Oil & Gas ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
020.38563   0
1-1.96946 6.18023 (1*2π)/323323 weeks
2-.82739 -1.76042 (2*2π)/323162 weeks
3.40994 1.95206 (3*2π)/323108 weeks
4.5006 .55263 (4*2π)/32381 weeks
5.66845 -.48506 (5*2π)/32365 weeks
6-.21512 .88337 (6*2π)/32354 weeks
7.05569 -.59604 (7*2π)/32346 weeks
8.31196 .65822 (8*2π)/32340 weeks
9-.35536 .29612 (9*2π)/32336 weeks
10.56777 .22195 (10*2π)/32332 weeks
11.05387 .07592 (11*2π)/32329 weeks
12.28991 .77485 (12*2π)/32327 weeks
13.17572 .20545 (13*2π)/32325 weeks
14-.07836 .48534 (14*2π)/32323 weeks
15.26016 .32179 (15*2π)/32322 weeks
16-.22988 .1372 (16*2π)/32320 weeks
17-.04612 .27395 (17*2π)/32319 weeks
18.10645 .12409 (18*2π)/32318 weeks
19.1446 .24678 (19*2π)/32317 weeks
20.04093 .09837 (20*2π)/32316 weeks
21.03192 .13278 (21*2π)/32315 weeks
22.05105 .22015 (22*2π)/32315 weeks
23.15299 .11516 (23*2π)/32314 weeks
24.05815 .04959 (24*2π)/32313 weeks
25.16461 .02835 (25*2π)/32313 weeks
26.01757 .01347 (26*2π)/32312 weeks
27.16088 .0824 (27*2π)/32312 weeks
28-.12683 -.01513 (28*2π)/32312 weeks
29.19565 -.02741 (29*2π)/32311 weeks
30-.02901 .24411 (30*2π)/32311 weeks
31.08364 .03979 (31*2π)/32310 weeks
32.01518 .2046 (32*2π)/32310 weeks
33-.00641 -.08931 (33*2π)/32310 weeks
34.09089 .12786 (34*2π)/32310 weeks
35-.00764 .19223 (35*2π)/3239 weeks
36-.06251 .04787 (36*2π)/3239 weeks
37.05668 .10882 (37*2π)/3239 weeks
38-.13447 .03338 (38*2π)/3239 weeks
39.14084 .19323 (39*2π)/3238 weeks
40.06538 .17824 (40*2π)/3238 weeks
41.18717 .15014 (41*2π)/3238 weeks
42-.10669 -.02493 (42*2π)/3238 weeks
43.10444 .07987 (43*2π)/3238 weeks
44.02631 .09151 (44*2π)/3237 weeks
45.07592 -.06095 (45*2π)/3237 weeks
46.00683 .14236 (46*2π)/3237 weeks
47-.00351 -.03265 (47*2π)/3237 weeks
48.00705 .13053 (48*2π)/3237 weeks
49.0027 -.05234 (49*2π)/3237 weeks
50.01859 .01422 (50*2π)/3236 weeks
51-.03168 -.00383 (51*2π)/3236 weeks
52.14085 .06991 (52*2π)/3236 weeks
53.04356 -.0032 (53*2π)/3236 weeks
54.02403 -.03069 (54*2π)/3236 weeks
55-.0054 .05644 (55*2π)/3236 weeks
56.13143 -.02678 (56*2π)/3236 weeks
57-.04174 .07945 (57*2π)/3236 weeks
58.05364 .06468 (58*2π)/3236 weeks
59.06525 -.00312 (59*2π)/3235 weeks
60-.06986 .01736 (60*2π)/3235 weeks
61.08923 .05639 (61*2π)/3235 weeks
62.00931 -.0462 (62*2π)/3235 weeks
63.0479 .09074 (63*2π)/3235 weeks
64.10787 .08352 (64*2π)/3235 weeks
65.01026 .05274 (65*2π)/3235 weeks
66.09737 .05314 (66*2π)/3235 weeks
67.05305 .0679 (67*2π)/3235 weeks
68-.02466 .05511 (68*2π)/3235 weeks
69-.00029 .00665 (69*2π)/3235 weeks
70.02175 .04161 (70*2π)/3235 weeks
71.04425 .05291 (71*2π)/3235 weeks
72.03067 .07468 (72*2π)/3234 weeks
73.00181 -.03569 (73*2π)/3234 weeks
74.07849 .06559 (74*2π)/3234 weeks
75.03337 .01962 (75*2π)/3234 weeks
76.07875 -.00128 (76*2π)/3234 weeks
77.03863 .09778 (77*2π)/3234 weeks
78.0343 -.03942 (78*2π)/3234 weeks
79-.03885 .07525 (79*2π)/3234 weeks
80.05167 -.03978 (80*2π)/3234 weeks
81.02176 -.00895 (81*2π)/3234 weeks
82-.01534 .02046 (82*2π)/3234 weeks
83.0615 -.01625 (83*2π)/3234 weeks
84-.04284 -.01261 (84*2π)/3234 weeks
85.05563 .00388 (85*2π)/3234 weeks
86-.02404 .00064 (86*2π)/3234 weeks
87.04133 .00748 (87*2π)/3234 weeks
88.03483 .04532 (88*2π)/3234 weeks
89-.03062 .04766 (89*2π)/3234 weeks
90.02652 .07592 (90*2π)/3234 weeks
91.01554 .01024 (91*2π)/3234 weeks
92.00444 .03584 (92*2π)/3234 weeks
93.03889 .01281 (93*2π)/3233 weeks
94.02338 .00143 (94*2π)/3233 weeks
95.04241 .00235 (95*2π)/3233 weeks
96.03896 -.03258 (96*2π)/3233 weeks
97.03924 .03392 (97*2π)/3233 weeks
98.06192 .06168 (98*2π)/3233 weeks
99.03896 .03279 (99*2π)/3233 weeks
100.0442 .0434 (100*2π)/3233 weeks
101-.05154 .05328 (101*2π)/3233 weeks
102.0499 .05233 (102*2π)/3233 weeks
103.03526 .028 (103*2π)/3233 weeks
104.02126 .05731 (104*2π)/3233 weeks
105.03343 .0497 (105*2π)/3233 weeks
106.02314 .02416 (106*2π)/3233 weeks
107.01533 .01995 (107*2π)/3233 weeks
108-.00336 -.02812 (108*2π)/3233 weeks
109-.00763 -.00518 (109*2π)/3233 weeks
110.04264 -.00617 (110*2π)/3233 weeks
111-.02035 .00652 (111*2π)/3233 weeks
112.03146 -.02939 (112*2π)/3233 weeks
113-.02081 -.00058 (113*2π)/3233 weeks
114.04699 -.00221 (114*2π)/3233 weeks
115.01606 .02528 (115*2π)/3233 weeks
116-.03405 .01827 (116*2π)/3233 weeks
117.00179 .00422 (117*2π)/3233 weeks
118.03311 .04253 (118*2π)/3233 weeks
119.03158 .01813 (119*2π)/3233 weeks
120.02847 .06066 (120*2π)/3233 weeks
121-.0155 .05872 (121*2π)/3233 weeks
122.02517 .00511 (122*2π)/3233 weeks
123.01316 .05999 (123*2π)/3233 weeks
124.02073 .03212 (124*2π)/3233 weeks
125-.00865 .01314 (125*2π)/3233 weeks
126.00376 .01302 (126*2π)/3233 weeks
127.02627 -.03151 (127*2π)/3233 weeks
128.04288 .02794 (128*2π)/3233 weeks
129.02359 .00086 (129*2π)/3233 weeks
130.04334 -.01731 (130*2π)/3232 weeks
131.0196 .00858 (131*2π)/3232 weeks
132.00468 .01512 (132*2π)/3232 weeks
133.088 .01117 (133*2π)/3232 weeks
134.00444 -.02979 (134*2π)/3232 weeks
135.07349 .03788 (135*2π)/3232 weeks
136-.02445 -.02428 (136*2π)/3232 weeks
137.03324 .00097 (137*2π)/3232 weeks
138.01917 .03061 (138*2π)/3232 weeks
139.04617 -.01472 (139*2π)/3232 weeks
140.07148 .05008 (140*2π)/3232 weeks
141.02924 .03525 (141*2π)/3232 weeks
142.01865 .07043 (142*2π)/3232 weeks
143-.00639 -.0238 (143*2π)/3232 weeks
144.04076 .01191 (144*2π)/3232 weeks
145.00019 -.0104 (145*2π)/3232 weeks
146.05266 .02501 (146*2π)/3232 weeks
147-.02572 .01453 (147*2π)/3232 weeks
148.04077 -.01906 (148*2π)/3232 weeks
149.01907 .05725 (149*2π)/3232 weeks
150.01854 -.0421 (150*2π)/3232 weeks
151.04688 .01071 (151*2π)/3232 weeks
152.00177 -.06265 (152*2π)/3232 weeks
153.0338 .01372 (153*2π)/3232 weeks
154-.01121 -.0625 (154*2π)/3232 weeks
155.05876 .04755 (155*2π)/3232 weeks
156.03406 -.02001 (156*2π)/3232 weeks
157.06769 .00215 (157*2π)/3232 weeks
158.00462 .01965 (158*2π)/3232 weeks
159.02449 -.04717 (159*2π)/3232 weeks
160.03701 .01093 (160*2π)/3232 weeks
161.05955 -.02698 (161*2π)/3232 weeks
162.05955 .02698 (162*2π)/3232 weeks
163.03701 -.01093 (163*2π)/3232 weeks
164.02449 .04717 (164*2π)/3232 weeks
165.00462 -.01965 (165*2π)/3232 weeks
166.06769 -.00215 (166*2π)/3232 weeks
167.03406 .02001 (167*2π)/3232 weeks
168.05876 -.04755 (168*2π)/3232 weeks
169-.01121 .0625 (169*2π)/3232 weeks
170.0338 -.01372 (170*2π)/3232 weeks
171.00177 .06265 (171*2π)/3232 weeks
172.04688 -.01071 (172*2π)/3232 weeks
173.01854 .0421 (173*2π)/3232 weeks
174.01907 -.05725 (174*2π)/3232 weeks
175.04077 .01906 (175*2π)/3232 weeks
176-.02572 -.01453 (176*2π)/3232 weeks
177.05266 -.02501 (177*2π)/3232 weeks
178.00019 .0104 (178*2π)/3232 weeks
179.04076 -.01191 (179*2π)/3232 weeks
180-.00639 .0238 (180*2π)/3232 weeks
181.01865 -.07043 (181*2π)/3232 weeks
182.02924 -.03525 (182*2π)/3232 weeks
183.07148 -.05008 (183*2π)/3232 weeks
184.04617 .01472 (184*2π)/3232 weeks
185.01917 -.03061 (185*2π)/3232 weeks
186.03324 -.00097 (186*2π)/3232 weeks
187-.02445 .02428 (187*2π)/3232 weeks
188.07349 -.03788 (188*2π)/3232 weeks
189.00444 .02979 (189*2π)/3232 weeks
190.088 -.01117 (190*2π)/3232 weeks
191.00468 -.01512 (191*2π)/3232 weeks
192.0196 -.00858 (192*2π)/3232 weeks
193.04334 .01731 (193*2π)/3232 weeks
194.02359 -.00086 (194*2π)/3232 weeks
195.04288 -.02794 (195*2π)/3232 weeks
196.02627 .03151 (196*2π)/3232 weeks
197.00376 -.01302 (197*2π)/3232 weeks
198-.00865 -.01314 (198*2π)/3232 weeks
199.02073 -.03212 (199*2π)/3232 weeks
200.01316 -.05999 (200*2π)/3232 weeks
201.02517 -.00511 (201*2π)/3232 weeks
202-.0155 -.05872 (202*2π)/3232 weeks
203.02847 -.06066 (203*2π)/3232 weeks
204.03158 -.01813 (204*2π)/3232 weeks
205.03311 -.04253 (205*2π)/3232 weeks
206.00179 -.00422 (206*2π)/3232 weeks
207-.03405 -.01827 (207*2π)/3232 weeks
208.01606 -.02528 (208*2π)/3232 weeks
209.04699 .00221 (209*2π)/3232 weeks
210-.02081 .00058 (210*2π)/3232 weeks
211.03146 .02939 (211*2π)/3232 weeks
212-.02035 -.00652 (212*2π)/3232 weeks
213.04264 .00617 (213*2π)/3232 weeks
214-.00763 .00518 (214*2π)/3232 weeks
215-.00336 .02812 (215*2π)/3232 weeks
216.01533 -.01995 (216*2π)/3231 weeks
217.02314 -.02416 (217*2π)/3231 weeks
218.03343 -.0497 (218*2π)/3231 weeks
219.02126 -.05731 (219*2π)/3231 weeks
220.03526 -.028 (220*2π)/3231 weeks
221.0499 -.05233 (221*2π)/3231 weeks
222-.05154 -.05328 (222*2π)/3231 weeks
223.0442 -.0434 (223*2π)/3231 weeks
224.03896 -.03279 (224*2π)/3231 weeks
225.06192 -.06168 (225*2π)/3231 weeks
226.03924 -.03392 (226*2π)/3231 weeks
227.03896 .03258 (227*2π)/3231 weeks
228.04241 -.00235 (228*2π)/3231 weeks
229.02338 -.00143 (229*2π)/3231 weeks
230.03889 -.01281 (230*2π)/3231 weeks
231.00444 -.03584 (231*2π)/3231 weeks
232.01554 -.01024 (232*2π)/3231 weeks
233.02652 -.07592 (233*2π)/3231 weeks
234-.03062 -.04766 (234*2π)/3231 weeks
235.03483 -.04532 (235*2π)/3231 weeks
236.04133 -.00748 (236*2π)/3231 weeks
237-.02404 -.00064 (237*2π)/3231 weeks
238.05563 -.00388 (238*2π)/3231 weeks
239-.04284 .01261 (239*2π)/3231 weeks
240.0615 .01625 (240*2π)/3231 weeks
241-.01534 -.02046 (241*2π)/3231 weeks
242.02176 .00895 (242*2π)/3231 weeks
243.05167 .03978 (243*2π)/3231 weeks
244-.03885 -.07525 (244*2π)/3231 weeks
245.0343 .03942 (245*2π)/3231 weeks
246.03863 -.09778 (246*2π)/3231 weeks
247.07875 .00128 (247*2π)/3231 weeks
248.03337 -.01962 (248*2π)/3231 weeks
249.07849 -.06559 (249*2π)/3231 weeks
250.00181 .03569 (250*2π)/3231 weeks
251.03067 -.07468 (251*2π)/3231 weeks
252.04425 -.05291 (252*2π)/3231 weeks
253.02175 -.04161 (253*2π)/3231 weeks
254-.00029 -.00665 (254*2π)/3231 weeks
255-.02466 -.05511 (255*2π)/3231 weeks
256.05305 -.0679 (256*2π)/3231 weeks
257.09737 -.05314 (257*2π)/3231 weeks
258.01026 -.05274 (258*2π)/3231 weeks
259.10787 -.08352 (259*2π)/3231 weeks
260.0479 -.09074 (260*2π)/3231 weeks
261.00931 .0462 (261*2π)/3231 weeks
262.08923 -.05639 (262*2π)/3231 weeks
263-.06986 -.01736 (263*2π)/3231 weeks
264.06525 .00312 (264*2π)/3231 weeks
265.05364 -.06468 (265*2π)/3231 weeks
266-.04174 -.07945 (266*2π)/3231 weeks
267.13143 .02678 (267*2π)/3231 weeks
268-.0054 -.05644 (268*2π)/3231 weeks
269.02403 .03069 (269*2π)/3231 weeks
270.04356 .0032 (270*2π)/3231 weeks
271.14085 -.06991 (271*2π)/3231 weeks
272-.03168 .00383 (272*2π)/3231 weeks
273.01859 -.01422 (273*2π)/3231 weeks
274.0027 .05234 (274*2π)/3231 weeks
275.00705 -.13053 (275*2π)/3231 weeks
276-.00351 .03265 (276*2π)/3231 weeks
277.00683 -.14236 (277*2π)/3231 weeks
278.07592 .06095 (278*2π)/3231 weeks
279.02631 -.09151 (279*2π)/3231 weeks
280.10444 -.07987 (280*2π)/3231 weeks
281-.10669 .02493 (281*2π)/3231 weeks
282.18717 -.15014 (282*2π)/3231 weeks
283.06538 -.17824 (283*2π)/3231 weeks
284.14084 -.19323 (284*2π)/3231 weeks
285-.13447 -.03338 (285*2π)/3231 weeks
286.05668 -.10882 (286*2π)/3231 weeks
287-.06251 -.04787 (287*2π)/3231 weeks
288-.00764 -.19223 (288*2π)/3231 weeks
289.09089 -.12786 (289*2π)/3231 weeks
290-.00641 .08931 (290*2π)/3231 weeks
291.01518 -.2046 (291*2π)/3231 weeks
292.08364 -.03979 (292*2π)/3231 weeks
293-.02901 -.24411 (293*2π)/3231 weeks
294.19565 .02741 (294*2π)/3231 weeks
295-.12683 .01513 (295*2π)/3231 weeks
296.16088 -.0824 (296*2π)/3231 weeks
297.01757 -.01347 (297*2π)/3231 weeks
298.16461 -.02835 (298*2π)/3231 weeks
299.05815 -.04959 (299*2π)/3231 weeks
300.15299 -.11516 (300*2π)/3231 weeks
301.05105 -.22015 (301*2π)/3231 weeks
302.03192 -.13278 (302*2π)/3231 weeks
303.04093 -.09837 (303*2π)/3231 weeks
304.1446 -.24678 (304*2π)/3231 weeks
305.10645 -.12409 (305*2π)/3231 weeks
306-.04612 -.27395 (306*2π)/3231 weeks
307-.22988 -.1372 (307*2π)/3231 weeks
308.26016 -.32179 (308*2π)/3231 weeks
309-.07836 -.48534 (309*2π)/3231 weeks
310.17572 -.20545 (310*2π)/3231 weeks
311.28991 -.77485 (311*2π)/3231 weeks
312.05387 -.07592 (312*2π)/3231 weeks
313.56777 -.22195 (313*2π)/3231 weeks
314-.35536 -.29612 (314*2π)/3231 weeks
315.31196 -.65822 (315*2π)/3231 weeks
316.05569 .59604 (316*2π)/3231 weeks
317-.21512 -.88337 (317*2π)/3231 weeks
318.66845 .48506 (318*2π)/3231 weeks
319.5006 -.55263 (319*2π)/3231 weeks
320.40994 -1.95206 (320*2π)/3231 weeks
321-.82739 1.76042 (321*2π)/3231 weeks