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Fourier Analysis of XIV (VelocityShares Daily Inverse VIX Short-Term ETN)

XIV (VelocityShares Daily Inverse VIX Short-Term ETN) appears to have interesting cyclic behaviour every 34 weeks (4.3227*sine), 38 weeks (3.688*sine), and 22 weeks (3.6121*cosine).

XIV (VelocityShares Daily Inverse VIX Short-Term ETN) has an average price of 34.82 (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 11/30/2010 to 3/23/2018 for XIV (VelocityShares Daily Inverse VIX Short-Term ETN), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
034.81557   0
18.0971 -16.73977 (1*2π)/379379 weeks
213.45481 -16.69171 (2*2π)/379190 weeks
32.30695 -15.07002 (3*2π)/379126 weeks
4-1.49885 -8.667 (4*2π)/37995 weeks
5-1.37177 -4.84476 (5*2π)/37976 weeks
6-1.00011 -6.73829 (6*2π)/37963 weeks
7-3.56459 -4.35051 (7*2π)/37954 weeks
8-.34918 -4.098 (8*2π)/37947 weeks
9-3.56197 -6.4047 (9*2π)/37942 weeks
10-2.23427 -3.68797 (10*2π)/37938 weeks
11-3.28752 -4.32274 (11*2π)/37934 weeks
12-2.6505 -2.50022 (12*2π)/37932 weeks
13-2.35231 -1.6112 (13*2π)/37929 weeks
14-2.82041 -2.2827 (14*2π)/37927 weeks
15-3.39415 -.68942 (15*2π)/37925 weeks
16-2.09892 -1.3847 (16*2π)/37924 weeks
17-3.61212 -.09331 (17*2π)/37922 weeks
18-3.01076 .56103 (18*2π)/37921 weeks
19-1.75372 .57744 (19*2π)/37920 weeks
20-1.94946 -.53454 (20*2π)/37919 weeks
21-2.33523 -.07241 (21*2π)/37918 weeks
22-1.47099 .37311 (22*2π)/37917 weeks
23-1.97862 -.37664 (23*2π)/37916 weeks
24-2.06122 .43286 (24*2π)/37916 weeks
25-1.58687 .40149 (25*2π)/37915 weeks
26-2.4715 .43747 (26*2π)/37915 weeks
27-1.52456 1.37235 (27*2π)/37914 weeks
28-1.71951 1.20925 (28*2π)/37914 weeks
29-1.62437 .98252 (29*2π)/37913 weeks
30-1.73905 1.33991 (30*2π)/37913 weeks
31-.75059 1.55983 (31*2π)/37912 weeks
32-1.11217 1.11587 (32*2π)/37912 weeks
33.13442 2.08084 (33*2π)/37911 weeks
34-.25621 .91506 (34*2π)/37911 weeks
35-.2722 1.50543 (35*2π)/37911 weeks
36.46163 1.31077 (36*2π)/37911 weeks
37.45107 .88285 (37*2π)/37910 weeks
38-.23975 .63184 (38*2π)/37910 weeks
39-.13809 1.29035 (39*2π)/37910 weeks
40.04596 .53998 (40*2π)/3799 weeks
41-.16052 1.29026 (41*2π)/3799 weeks
42.13566 .8811 (42*2π)/3799 weeks
43-.22355 .81289 (43*2π)/3799 weeks
44.42606 1.22403 (44*2π)/3799 weeks
45.63419 1.31882 (45*2π)/3798 weeks
46.66569 .26507 (46*2π)/3798 weeks
47.55876 .86297 (47*2π)/3798 weeks
48.62753 .59873 (48*2π)/3798 weeks
49.15467 .49062 (49*2π)/3798 weeks
50.65182 .97069 (50*2π)/3798 weeks
51.52092 .40021 (51*2π)/3797 weeks
52.44737 .80495 (52*2π)/3797 weeks
53.58396 .42831 (53*2π)/3797 weeks
54.51622 .08406 (54*2π)/3797 weeks
55.44918 .46725 (55*2π)/3797 weeks
56.71231 .33751 (56*2π)/3797 weeks
57.8742 .48523 (57*2π)/3797 weeks
58.825 .25128 (58*2π)/3797 weeks
591.0261 .27284 (59*2π)/3796 weeks
60.72526 -.16974 (60*2π)/3796 weeks
61.99904 .0321 (61*2π)/3796 weeks
62.86311 -.5087 (62*2π)/3796 weeks
63.35228 -.40352 (63*2π)/3796 weeks
64.15895 -.26101 (64*2π)/3796 weeks
65.43035 -.18046 (65*2π)/3796 weeks
66.37993 .05016 (66*2π)/3796 weeks
67.5395 -.03847 (67*2π)/3796 weeks
68.59858 -.24741 (68*2π)/3796 weeks
69.48913 -.00507 (69*2π)/3795 weeks
70.84731 -.46648 (70*2π)/3795 weeks
71.38458 -.51678 (71*2π)/3795 weeks
72.37099 -.68404 (72*2π)/3795 weeks
73.41802 -.26068 (73*2π)/3795 weeks
74.22164 -.68908 (74*2π)/3795 weeks
75.05109 -.39496 (75*2π)/3795 weeks
76.26742 -.45653 (76*2π)/3795 weeks
77.07706 -.3733 (77*2π)/3795 weeks
78.14873 -.35778 (78*2π)/3795 weeks
79.0049 -.22553 (79*2π)/3795 weeks
80.08121 -.56244 (80*2π)/3795 weeks
81-.21005 -.3491 (81*2π)/3795 weeks
82.0863 -.13989 (82*2π)/3795 weeks
83.15065 -.53918 (83*2π)/3795 weeks
84-.09293 -.36983 (84*2π)/3795 weeks
85-.1859 -.54961 (85*2π)/3794 weeks
86.09463 -.52489 (86*2π)/3794 weeks
87-.37782 -.61406 (87*2π)/3794 weeks
88-.28442 -.32957 (88*2π)/3794 weeks
89-.31406 -.33887 (89*2π)/3794 weeks
90-.3291 -.0463 (90*2π)/3794 weeks
91-.23058 -.21378 (91*2π)/3794 weeks
92-.52052 -.06424 (92*2π)/3794 weeks
93.01374 .10641 (93*2π)/3794 weeks
94-.1869 -.16118 (94*2π)/3794 weeks
95-.11931 -.06535 (95*2π)/3794 weeks
96.08349 -.29546 (96*2π)/3794 weeks
97-.49936 -.55022 (97*2π)/3794 weeks
98-.53052 -.26726 (98*2π)/3794 weeks
99-.27521 .05375 (99*2π)/3794 weeks
100-.19421 -.20526 (100*2π)/3794 weeks
101-.50806 -.10433 (101*2π)/3794 weeks
102-.1019 -.0485 (102*2π)/3794 weeks
103-.5821 -.1789 (103*2π)/3794 weeks
104-.40767 .15078 (104*2π)/3794 weeks
105-.31873 -.0204 (105*2π)/3794 weeks
106-.4077 .00194 (106*2π)/3794 weeks
107-.40996 .01932 (107*2π)/3794 weeks
108-.43892 .13807 (108*2π)/3794 weeks
109-.29802 .13715 (109*2π)/3793 weeks
110-.19625 .19165 (110*2π)/3793 weeks
111-.15782 .01572 (111*2π)/3793 weeks
112-.08915 .17464 (112*2π)/3793 weeks
113-.39732 -.02674 (113*2π)/3793 weeks
114-.33409 .17322 (114*2π)/3793 weeks
115-.4245 .38281 (115*2π)/3793 weeks
116-.23262 .37475 (116*2π)/3793 weeks
117-.42705 .36834 (117*2π)/3793 weeks
118-.08246 .48265 (118*2π)/3793 weeks
119-.27622 .47362 (119*2π)/3793 weeks
120-.12017 .49748 (120*2π)/3793 weeks
121.00887 .44229 (121*2π)/3793 weeks
122.02587 .4937 (122*2π)/3793 weeks
123.12111 .38885 (123*2π)/3793 weeks
124.21093 .37882 (124*2π)/3793 weeks
125.26296 .16676 (125*2π)/3793 weeks
126.11912 .28976 (126*2π)/3793 weeks
127.15965 .14809 (127*2π)/3793 weeks
128-.01382 .17191 (128*2π)/3793 weeks
129.02317 .41319 (129*2π)/3793 weeks
130.07464 .33103 (130*2π)/3793 weeks
131.17275 .40695 (131*2π)/3793 weeks
132.28533 .24872 (132*2π)/3793 weeks
133.18656 .21675 (133*2π)/3793 weeks
134.28598 .21676 (134*2π)/3793 weeks
135.28347 -.00078 (135*2π)/3793 weeks
136.24524 .05779 (136*2π)/3793 weeks
137.19364 .20114 (137*2π)/3793 weeks
138.29087 .07591 (138*2π)/3793 weeks
139.27434 .14388 (139*2π)/3793 weeks
140.23976 .09128 (140*2π)/3793 weeks
141.01151 .03714 (141*2π)/3793 weeks
142.27773 .3027 (142*2π)/3793 weeks
143.22153 -.01676 (143*2π)/3793 weeks
144.24429 .10308 (144*2π)/3793 weeks
145.29511 .02497 (145*2π)/3793 weeks
146.14982 .13675 (146*2π)/3793 weeks
147.38483 .05412 (147*2π)/3793 weeks
148.35717 .15446 (148*2π)/3793 weeks
149.46799 -.065 (149*2π)/3793 weeks
150.34092 -.11678 (150*2π)/3793 weeks
151.34449 -.21716 (151*2π)/3793 weeks
152.16817 -.2245 (152*2π)/3792 weeks
153.14517 -.0785 (153*2π)/3792 weeks
154.23057 -.15721 (154*2π)/3792 weeks
155.13023 -.1076 (155*2π)/3792 weeks
156.21915 -.2189 (156*2π)/3792 weeks
157.2221 -.2502 (157*2π)/3792 weeks
158.2239 -.13313 (158*2π)/3792 weeks
159.20945 -.46024 (159*2π)/3792 weeks
160-.00193 -.30511 (160*2π)/3792 weeks
161.07617 -.258 (161*2π)/3792 weeks
162-.03883 -.20109 (162*2π)/3792 weeks
163.04445 -.1742 (163*2π)/3792 weeks
164.06418 -.08884 (164*2π)/3792 weeks
165-.03567 -.35195 (165*2π)/3792 weeks
166-.08663 -.21621 (166*2π)/3792 weeks
167.08404 -.01325 (167*2π)/3792 weeks
168.07188 -.20278 (168*2π)/3792 weeks
169.10381 -.03981 (169*2π)/3792 weeks
170.20424 -.35526 (170*2π)/3792 weeks
171-.18253 -.2528 (171*2π)/3792 weeks
172.02338 -.27646 (172*2π)/3792 weeks
173-.10474 -.22713 (173*2π)/3792 weeks
174.03419 -.22652 (174*2π)/3792 weeks
175-.29455 -.2569 (175*2π)/3792 weeks
176-.05258 -.22788 (176*2π)/3792 weeks
177-.14044 -.23031 (177*2π)/3792 weeks
178-.13301 -.23069 (178*2π)/3792 weeks
179-.24309 -.05476 (179*2π)/3792 weeks
180-.13324 -.13423 (180*2π)/3792 weeks
181-.11224 -.24127 (181*2π)/3792 weeks
182-.21991 -.16386 (182*2π)/3792 weeks
183-.21387 -.01302 (183*2π)/3792 weeks
184-.15466 -.16347 (184*2π)/3792 weeks
185-.16126 -.10668 (185*2π)/3792 weeks
186-.11527 -.07231 (186*2π)/3792 weeks
187-.17808 -.25844 (187*2π)/3792 weeks
188-.41261 -.13677 (188*2π)/3792 weeks
189-.42259 .01196 (189*2π)/3792 weeks
190-.42259 -.01196 (190*2π)/3792 weeks
191-.41261 .13677 (191*2π)/3792 weeks
192-.17808 .25844 (192*2π)/3792 weeks
193-.11527 .07231 (193*2π)/3792 weeks
194-.16126 .10668 (194*2π)/3792 weeks
195-.15466 .16347 (195*2π)/3792 weeks
196-.21387 .01302 (196*2π)/3792 weeks
197-.21991 .16386 (197*2π)/3792 weeks
198-.11224 .24127 (198*2π)/3792 weeks
199-.13324 .13423 (199*2π)/3792 weeks
200-.24309 .05476 (200*2π)/3792 weeks
201-.13301 .23069 (201*2π)/3792 weeks
202-.14044 .23031 (202*2π)/3792 weeks
203-.05258 .22788 (203*2π)/3792 weeks
204-.29455 .2569 (204*2π)/3792 weeks
205.03419 .22652 (205*2π)/3792 weeks
206-.10474 .22713 (206*2π)/3792 weeks
207.02338 .27646 (207*2π)/3792 weeks
208-.18253 .2528 (208*2π)/3792 weeks
209.20424 .35526 (209*2π)/3792 weeks
210.10381 .03981 (210*2π)/3792 weeks
211.07188 .20278 (211*2π)/3792 weeks
212.08404 .01325 (212*2π)/3792 weeks
213-.08663 .21621 (213*2π)/3792 weeks
214-.03567 .35195 (214*2π)/3792 weeks
215.06418 .08884 (215*2π)/3792 weeks
216.04445 .1742 (216*2π)/3792 weeks
217-.03883 .20109 (217*2π)/3792 weeks
218.07617 .258 (218*2π)/3792 weeks
219-.00193 .30511 (219*2π)/3792 weeks
220.20945 .46024 (220*2π)/3792 weeks
221.2239 .13313 (221*2π)/3792 weeks
222.2221 .2502 (222*2π)/3792 weeks
223.21915 .2189 (223*2π)/3792 weeks
224.13023 .1076 (224*2π)/3792 weeks
225.23057 .15721 (225*2π)/3792 weeks
226.14517 .0785 (226*2π)/3792 weeks
227.16817 .2245 (227*2π)/3792 weeks
228.34449 .21716 (228*2π)/3792 weeks
229.34092 .11678 (229*2π)/3792 weeks
230.46799 .065 (230*2π)/3792 weeks
231.35717 -.15446 (231*2π)/3792 weeks
232.38483 -.05412 (232*2π)/3792 weeks
233.14982 -.13675 (233*2π)/3792 weeks
234.29511 -.02497 (234*2π)/3792 weeks
235.24429 -.10308 (235*2π)/3792 weeks
236.22153 .01676 (236*2π)/3792 weeks
237.27773 -.3027 (237*2π)/3792 weeks
238.01151 -.03714 (238*2π)/3792 weeks
239.23976 -.09128 (239*2π)/3792 weeks
240.27434 -.14388 (240*2π)/3792 weeks
241.29087 -.07591 (241*2π)/3792 weeks
242.19364 -.20114 (242*2π)/3792 weeks
243.24524 -.05779 (243*2π)/3792 weeks
244.28347 .00078 (244*2π)/3792 weeks
245.28598 -.21676 (245*2π)/3792 weeks
246.18656 -.21675 (246*2π)/3792 weeks
247.28533 -.24872 (247*2π)/3792 weeks
248.17275 -.40695 (248*2π)/3792 weeks
249.07464 -.33103 (249*2π)/3792 weeks
250.02317 -.41319 (250*2π)/3792 weeks
251-.01382 -.17191 (251*2π)/3792 weeks
252.15965 -.14809 (252*2π)/3792 weeks
253.11912 -.28976 (253*2π)/3791 weeks
254.26296 -.16676 (254*2π)/3791 weeks
255.21093 -.37882 (255*2π)/3791 weeks
256.12111 -.38885 (256*2π)/3791 weeks
257.02587 -.4937 (257*2π)/3791 weeks
258.00887 -.44229 (258*2π)/3791 weeks
259-.12017 -.49748 (259*2π)/3791 weeks
260-.27622 -.47362 (260*2π)/3791 weeks
261-.08246 -.48265 (261*2π)/3791 weeks
262-.42705 -.36834 (262*2π)/3791 weeks
263-.23262 -.37475 (263*2π)/3791 weeks
264-.4245 -.38281 (264*2π)/3791 weeks
265-.33409 -.17322 (265*2π)/3791 weeks
266-.39732 .02674 (266*2π)/3791 weeks
267-.08915 -.17464 (267*2π)/3791 weeks
268-.15782 -.01572 (268*2π)/3791 weeks
269-.19625 -.19165 (269*2π)/3791 weeks
270-.29802 -.13715 (270*2π)/3791 weeks
271-.43892 -.13807 (271*2π)/3791 weeks
272-.40996 -.01932 (272*2π)/3791 weeks
273-.4077 -.00194 (273*2π)/3791 weeks
274-.31873 .0204 (274*2π)/3791 weeks
275-.40767 -.15078 (275*2π)/3791 weeks
276-.5821 .1789 (276*2π)/3791 weeks
277-.1019 .0485 (277*2π)/3791 weeks
278-.50806 .10433 (278*2π)/3791 weeks
279-.19421 .20526 (279*2π)/3791 weeks
280-.27521 -.05375 (280*2π)/3791 weeks
281-.53052 .26726 (281*2π)/3791 weeks
282-.49936 .55022 (282*2π)/3791 weeks
283.08349 .29546 (283*2π)/3791 weeks
284-.11931 .06535 (284*2π)/3791 weeks
285-.1869 .16118 (285*2π)/3791 weeks
286.01374 -.10641 (286*2π)/3791 weeks
287-.52052 .06424 (287*2π)/3791 weeks
288-.23058 .21378 (288*2π)/3791 weeks
289-.3291 .0463 (289*2π)/3791 weeks
290-.31406 .33887 (290*2π)/3791 weeks
291-.28442 .32957 (291*2π)/3791 weeks
292-.37782 .61406 (292*2π)/3791 weeks
293.09463 .52489 (293*2π)/3791 weeks
294-.1859 .54961 (294*2π)/3791 weeks
295-.09293 .36983 (295*2π)/3791 weeks
296.15065 .53918 (296*2π)/3791 weeks
297.0863 .13989 (297*2π)/3791 weeks
298-.21005 .3491 (298*2π)/3791 weeks
299.08121 .56244 (299*2π)/3791 weeks
300.0049 .22553 (300*2π)/3791 weeks
301.14873 .35778 (301*2π)/3791 weeks
302.07706 .3733 (302*2π)/3791 weeks
303.26742 .45653 (303*2π)/3791 weeks
304.05109 .39496 (304*2π)/3791 weeks
305.22164 .68908 (305*2π)/3791 weeks
306.41802 .26068 (306*2π)/3791 weeks
307.37099 .68404 (307*2π)/3791 weeks
308.38458 .51678 (308*2π)/3791 weeks
309.84731 .46648 (309*2π)/3791 weeks
310.48913 .00507 (310*2π)/3791 weeks
311.59858 .24741 (311*2π)/3791 weeks
312.5395 .03847 (312*2π)/3791 weeks
313.37993 -.05016 (313*2π)/3791 weeks
314.43035 .18046 (314*2π)/3791 weeks
315.15895 .26101 (315*2π)/3791 weeks
316.35228 .40352 (316*2π)/3791 weeks
317.86311 .5087 (317*2π)/3791 weeks
318.99904 -.0321 (318*2π)/3791 weeks
319.72526 .16974 (319*2π)/3791 weeks
3201.0261 -.27284 (320*2π)/3791 weeks
321.825 -.25128 (321*2π)/3791 weeks
322.8742 -.48523 (322*2π)/3791 weeks
323.71231 -.33751 (323*2π)/3791 weeks
324.44918 -.46725 (324*2π)/3791 weeks
325.51622 -.08406 (325*2π)/3791 weeks
326.58396 -.42831 (326*2π)/3791 weeks
327.44737 -.80495 (327*2π)/3791 weeks
328.52092 -.40021 (328*2π)/3791 weeks
329.65182 -.97069 (329*2π)/3791 weeks
330.15467 -.49062 (330*2π)/3791 weeks
331.62753 -.59873 (331*2π)/3791 weeks
332.55876 -.86297 (332*2π)/3791 weeks
333.66569 -.26507 (333*2π)/3791 weeks
334.63419 -1.31882 (334*2π)/3791 weeks
335.42606 -1.22403 (335*2π)/3791 weeks
336-.22355 -.81289 (336*2π)/3791 weeks
337.13566 -.8811 (337*2π)/3791 weeks
338-.16052 -1.29026 (338*2π)/3791 weeks
339.04596 -.53998 (339*2π)/3791 weeks
340-.13809 -1.29035 (340*2π)/3791 weeks
341-.23975 -.63184 (341*2π)/3791 weeks
342.45107 -.88285 (342*2π)/3791 weeks
343.46163 -1.31077 (343*2π)/3791 weeks
344-.2722 -1.50543 (344*2π)/3791 weeks
345-.25621 -.91506 (345*2π)/3791 weeks
346.13442 -2.08084 (346*2π)/3791 weeks
347-1.11217 -1.11587 (347*2π)/3791 weeks
348-.75059 -1.55983 (348*2π)/3791 weeks
349-1.73905 -1.33991 (349*2π)/3791 weeks
350-1.62437 -.98252 (350*2π)/3791 weeks
351-1.71951 -1.20925 (351*2π)/3791 weeks
352-1.52456 -1.37235 (352*2π)/3791 weeks
353-2.4715 -.43747 (353*2π)/3791 weeks
354-1.58687 -.40149 (354*2π)/3791 weeks
355-2.06122 -.43286 (355*2π)/3791 weeks
356-1.97862 .37664 (356*2π)/3791 weeks
357-1.47099 -.37311 (357*2π)/3791 weeks
358-2.33523 .07241 (358*2π)/3791 weeks
359-1.94946 .53454 (359*2π)/3791 weeks
360-1.75372 -.57744 (360*2π)/3791 weeks
361-3.01076 -.56103 (361*2π)/3791 weeks
362-3.61212 .09331 (362*2π)/3791 weeks
363-2.09892 1.3847 (363*2π)/3791 weeks
364-3.39415 .68942 (364*2π)/3791 weeks
365-2.82041 2.2827 (365*2π)/3791 weeks
366-2.35231 1.6112 (366*2π)/3791 weeks
367-2.6505 2.50022 (367*2π)/3791 weeks
368-3.28752 4.32274 (368*2π)/3791 weeks
369-2.23427 3.68797 (369*2π)/3791 weeks
370-3.56197 6.4047 (370*2π)/3791 weeks
371-.34918 4.098 (371*2π)/3791 weeks
372-3.56459 4.35051 (372*2π)/3791 weeks
373-1.00011 6.73829 (373*2π)/3791 weeks
374-1.37177 4.84476 (374*2π)/3791 weeks
375-1.49885 8.667 (375*2π)/3791 weeks
3762.30695 15.07002 (376*2π)/3791 weeks
37713.45481 16.69171 (377*2π)/3791 weeks