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Fourier Analysis of SVXY (ProShares Short VIX Short-Term Futures ETF)


SVXY (ProShares Short VIX Short-Term Futures ETF) appears to have interesting cyclic behaviour every 29 weeks (3.3736*sine), 32 weeks (3.0095*sine), and 20 weeks (1.0237*cosine).

SVXY (ProShares Short VIX Short-Term Futures ETF) has an average price of 32.8 (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 10/4/2011 to 10/9/2017 for SVXY (ProShares Short VIX Short-Term Futures ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
032.79997   0 
12.36295 -9.78866 (1*2π)/315315 weeks
29.43621 -12.57743 (2*2π)/315158 weeks
31.99072 -12.08961 (3*2π)/315105 weeks
4-1.19562 -8.3675 (4*2π)/31579 weeks
5.96743 -4.36555 (5*2π)/31563 weeks
6-.53728 -6.62967 (6*2π)/31553 weeks
7-1.75251 -1.60004 (7*2π)/31545 weeks
8.76799 -4.19302 (8*2π)/31539 weeks
9-.27289 -1.93467 (9*2π)/31535 weeks
10.22621 -3.00954 (10*2π)/31532 weeks
11-.03132 -3.37361 (11*2π)/31529 weeks
12-.53025 -1.70847 (12*2π)/31526 weeks
13.75405 -2.66401 (13*2π)/31524 weeks
14-.95194 -1.12779 (14*2π)/31523 weeks
15-.13293 -.79814 (15*2π)/31521 weeks
161.02371 -1.19025 (16*2π)/31520 weeks
17.17359 -1.96843 (17*2π)/31519 weeks
18-.29715 -1.15039 (18*2π)/31518 weeks
19.79209 -1.5575 (19*2π)/31517 weeks
20-.03821 -1.64243 (20*2π)/31516 weeks
21.31624 -.98482 (21*2π)/31515 weeks
22.24428 -2.20295 (22*2π)/31514 weeks
23.051 -1.22871 (23*2π)/31514 weeks
24-.05705 -.99743 (24*2π)/31513 weeks
25.46919 -1.12668 (25*2π)/31513 weeks
26-.2823 -1.49426 (26*2π)/31512 weeks
27.72117 -.77939 (27*2π)/31512 weeks
28-.60582 -1.7434 (28*2π)/31511 weeks
29-.16484 -.83105 (29*2π)/31511 weeks
30.23699 -1.38686 (30*2π)/31511 weeks
31.00068 -1.71973 (31*2π)/31510 weeks
32-.73638 -1.25865 (32*2π)/31510 weeks
33.10389 -1.03285 (33*2π)/31510 weeks
34-.82134 -1.09813 (34*2π)/3159 weeks
35-.26001 -.92365 (35*2π)/3159 weeks
36-.52689 -1.48822 (36*2π)/3159 weeks
37-.55623 -.99823 (37*2π)/3159 weeks
38-.73523 -.10175 (38*2π)/3158 weeks
39-.3674 -.8905 (39*2π)/3158 weeks
40-.51597 -.56225 (40*2π)/3158 weeks
41.14664 -.50234 (41*2π)/3158 weeks
42-.52547 -.86309 (42*2π)/3158 weeks
43-.13958 -.39525 (43*2π)/3157 weeks
44-.36477 -.7082 (44*2π)/3157 weeks
45-.70623 -.65007 (45*2π)/3157 weeks
46-.31491 -.35098 (46*2π)/3157 weeks
47-.41237 -.35835 (47*2π)/3157 weeks
48-.23491 -.53118 (48*2π)/3157 weeks
49-.21844 -.26196 (49*2π)/3156 weeks
50-.22588 -.73484 (50*2π)/3156 weeks
51-.10997 -.17834 (51*2π)/3156 weeks
52.28198 -.56258 (52*2π)/3156 weeks
53.15599 -.72143 (53*2π)/3156 weeks
54-.18404 -.66594 (54*2π)/3156 weeks
55-.21545 -.88881 (55*2π)/3156 weeks
56-.33566 -.79689 (56*2π)/3156 weeks
57-.16839 -.55559 (57*2π)/3156 weeks
58-.48855 -1.01536 (58*2π)/3155 weeks
59-.48084 -.47887 (59*2π)/3155 weeks
60-.65327 -.45466 (60*2π)/3155 weeks
61-.2224 -.75062 (61*2π)/3155 weeks
62-.59527 -.47495 (62*2π)/3155 weeks
63-.26147 -.39131 (63*2π)/3155 weeks
64-.45136 -.43914 (64*2π)/3155 weeks
65-.31722 -.41602 (65*2π)/3155 weeks
66-.41349 -.1793 (66*2π)/3155 weeks
67-.27126 -.58347 (67*2π)/3155 weeks
68-.68494 -.4825 (68*2π)/3155 weeks
69-.43486 -.09385 (69*2π)/3155 weeks
70-.49344 -.37399 (70*2π)/3155 weeks
71-.33455 -.45831 (71*2π)/3154 weeks
72-.46568 .02455 (72*2π)/3154 weeks
73-.20674 -.24022 (73*2π)/3154 weeks
74-.32772 -.1831 (74*2π)/3154 weeks
75-.09211 -.30863 (75*2π)/3154 weeks
76-.39359 -.26179 (76*2π)/3154 weeks
77.06545 .02586 (77*2π)/3154 weeks
78-.18669 -.37754 (78*2π)/3154 weeks
79-.10452 -.175 (79*2π)/3154 weeks
80.2381 -.42359 (80*2π)/3154 weeks
81-.34021 -.5998 (81*2π)/3154 weeks
82-.59477 -.4429 (82*2π)/3154 weeks
83-.28017 -.16632 (83*2π)/3154 weeks
84-.22925 -.52402 (84*2π)/3154 weeks
85-.36282 -.00702 (85*2π)/3154 weeks
86-.09651 -.46655 (86*2π)/3154 weeks
87-.40159 -.36866 (87*2π)/3154 weeks
88-.29924 -.26803 (88*2π)/3154 weeks
89-.29344 -.24784 (89*2π)/3154 weeks
90-.14454 -.29193 (90*2π)/3154 weeks
91-.18466 -.31205 (91*2π)/3153 weeks
92-.21998 -.49625 (92*2π)/3153 weeks
93-.15671 -.33617 (93*2π)/3153 weeks
94-.54476 -.45205 (94*2π)/3153 weeks
95-.44289 -.41046 (95*2π)/3153 weeks
96-.40802 -.18729 (96*2π)/3153 weeks
97-.29453 -.39437 (97*2π)/3153 weeks
98-.45828 -.08472 (98*2π)/3153 weeks
99-.40729 -.35603 (99*2π)/3153 weeks
100-.44222 -.27202 (100*2π)/3153 weeks
101-.35009 -.23277 (101*2π)/3153 weeks
102-.45245 -.20887 (102*2π)/3153 weeks
103-.46141 -.25005 (103*2π)/3153 weeks
104-.56995 -.06267 (104*2π)/3153 weeks
105-.41153 -.19326 (105*2π)/3153 weeks
106-.51474 -.03366 (106*2π)/3153 weeks
107-.30989 .10201 (107*2π)/3153 weeks
108-.34274 -.04112 (108*2π)/3153 weeks
109-.2078 -.00426 (109*2π)/3153 weeks
110-.24795 -.1735 (110*2π)/3153 weeks
111-.29122 -.0662 (111*2π)/3153 weeks
112-.11894 -.12087 (112*2π)/3153 weeks
113-.24554 -.15644 (113*2π)/3153 weeks
114-.41927 -.12542 (114*2π)/3153 weeks
115-.25676 -.1325 (115*2π)/3153 weeks
116-.26952 -.05977 (116*2π)/3153 weeks
117-.10507 -.00821 (117*2π)/3153 weeks
118-.38158 -.33962 (118*2π)/3153 weeks
119-.27763 -.00491 (119*2π)/3153 weeks
120-.30194 -.11438 (120*2π)/3153 weeks
121-.31693 .04915 (121*2π)/3153 weeks
122-.21158 -.20388 (122*2π)/3153 weeks
123-.13147 -.07053 (123*2π)/3153 weeks
124-.26988 -.26233 (124*2π)/3153 weeks
125-.27436 -.1703 (125*2π)/3153 weeks
126-.38157 -.25418 (126*2π)/3153 weeks
127-.49123 -.10177 (127*2π)/3152 weeks
128-.3272 -.0694 (128*2π)/3152 weeks
129-.47132 -.05064 (129*2π)/3152 weeks
130-.37678 -.05922 (130*2π)/3152 weeks
131-.36817 -.12833 (131*2π)/3152 weeks
132-.32152 .20346 (132*2π)/3152 weeks
133-.18457 -.04795 (133*2π)/3152 weeks
134-.29655 -.00397 (134*2π)/3152 weeks
135-.23432 -.10253 (135*2π)/3152 weeks
136-.23857 -.06065 (136*2π)/3152 weeks
137-.51258 -.02039 (137*2π)/3152 weeks
138-.33523 .08471 (138*2π)/3152 weeks
139-.1392 -.11243 (139*2π)/3152 weeks
140-.31031 -.0065 (140*2π)/3152 weeks
141-.05638 -.17037 (141*2π)/3152 weeks
142-.49792 -.22722 (142*2π)/3152 weeks
143-.22863 -.10098 (143*2π)/3152 weeks
144-.37114 -.08022 (144*2π)/3152 weeks
145-.10999 -.08288 (145*2π)/3152 weeks
146-.4493 -.02317 (146*2π)/3152 weeks
147-.30882 -.05121 (147*2π)/3152 weeks
148-.29414 -.00685 (148*2π)/3152 weeks
149-.38018 -.2077 (149*2π)/3152 weeks
150-.42086 -.11292 (150*2π)/3152 weeks
151-.30659 .00935 (151*2π)/3152 weeks
152-.19862 -.06116 (152*2π)/3152 weeks
153-.38547 -.05321 (153*2π)/3152 weeks
154-.33044 -.05973 (154*2π)/3152 weeks
155-.33369 -.21998 (155*2π)/3152 weeks
156-.57187 -.09885 (156*2π)/3152 weeks
157-.50932 .03668 (157*2π)/3152 weeks
158-.50932 -.03668 (158*2π)/3152 weeks
159-.57187 .09885 (159*2π)/3152 weeks
160-.33369 .21998 (160*2π)/3152 weeks
161-.33044 .05973 (161*2π)/3152 weeks
162-.38547 .05321 (162*2π)/3152 weeks
163-.19862 .06116 (163*2π)/3152 weeks
164-.30659 -.00935 (164*2π)/3152 weeks
165-.42086 .11292 (165*2π)/3152 weeks
166-.38018 .2077 (166*2π)/3152 weeks
167-.29414 .00685 (167*2π)/3152 weeks
168-.30882 .05121 (168*2π)/3152 weeks
169-.4493 .02317 (169*2π)/3152 weeks
170-.10999 .08288 (170*2π)/3152 weeks
171-.37114 .08022 (171*2π)/3152 weeks
172-.22863 .10098 (172*2π)/3152 weeks
173-.49792 .22722 (173*2π)/3152 weeks
174-.05638 .17037 (174*2π)/3152 weeks
175-.31031 .0065 (175*2π)/3152 weeks
176-.1392 .11243 (176*2π)/3152 weeks
177-.33523 -.08471 (177*2π)/3152 weeks
178-.51258 .02039 (178*2π)/3152 weeks
179-.23857 .06065 (179*2π)/3152 weeks
180-.23432 .10253 (180*2π)/3152 weeks
181-.29655 .00397 (181*2π)/3152 weeks
182-.18457 .04795 (182*2π)/3152 weeks
183-.32152 -.20346 (183*2π)/3152 weeks
184-.36817 .12833 (184*2π)/3152 weeks
185-.37678 .05922 (185*2π)/3152 weeks
186-.47132 .05064 (186*2π)/3152 weeks
187-.3272 .0694 (187*2π)/3152 weeks
188-.49123 .10177 (188*2π)/3152 weeks
189-.38157 .25418 (189*2π)/3152 weeks
190-.27436 .1703 (190*2π)/3152 weeks
191-.26988 .26233 (191*2π)/3152 weeks
192-.13147 .07053 (192*2π)/3152 weeks
193-.21158 .20388 (193*2π)/3152 weeks
194-.31693 -.04915 (194*2π)/3152 weeks
195-.30194 .11438 (195*2π)/3152 weeks
196-.27763 .00491 (196*2π)/3152 weeks
197-.38158 .33962 (197*2π)/3152 weeks
198-.10507 .00821 (198*2π)/3152 weeks
199-.26952 .05977 (199*2π)/3152 weeks
200-.25676 .1325 (200*2π)/3152 weeks
201-.41927 .12542 (201*2π)/3152 weeks
202-.24554 .15644 (202*2π)/3152 weeks
203-.11894 .12087 (203*2π)/3152 weeks
204-.29122 .0662 (204*2π)/3152 weeks
205-.24795 .1735 (205*2π)/3152 weeks
206-.2078 .00426 (206*2π)/3152 weeks
207-.34274 .04112 (207*2π)/3152 weeks
208-.30989 -.10201 (208*2π)/3152 weeks
209-.51474 .03366 (209*2π)/3152 weeks
210-.41153 .19326 (210*2π)/3152 weeks
211-.56995 .06267 (211*2π)/3151 weeks
212-.46141 .25005 (212*2π)/3151 weeks
213-.45245 .20887 (213*2π)/3151 weeks
214-.35009 .23277 (214*2π)/3151 weeks
215-.44222 .27202 (215*2π)/3151 weeks
216-.40729 .35603 (216*2π)/3151 weeks
217-.45828 .08472 (217*2π)/3151 weeks
218-.29453 .39437 (218*2π)/3151 weeks
219-.40802 .18729 (219*2π)/3151 weeks
220-.44289 .41046 (220*2π)/3151 weeks
221-.54476 .45205 (221*2π)/3151 weeks
222-.15671 .33617 (222*2π)/3151 weeks
223-.21998 .49625 (223*2π)/3151 weeks
224-.18466 .31205 (224*2π)/3151 weeks
225-.14454 .29193 (225*2π)/3151 weeks
226-.29344 .24784 (226*2π)/3151 weeks
227-.29924 .26803 (227*2π)/3151 weeks
228-.40159 .36866 (228*2π)/3151 weeks
229-.09651 .46655 (229*2π)/3151 weeks
230-.36282 .00702 (230*2π)/3151 weeks
231-.22925 .52402 (231*2π)/3151 weeks
232-.28017 .16632 (232*2π)/3151 weeks
233-.59477 .4429 (233*2π)/3151 weeks
234-.34021 .5998 (234*2π)/3151 weeks
235.2381 .42359 (235*2π)/3151 weeks
236-.10452 .175 (236*2π)/3151 weeks
237-.18669 .37754 (237*2π)/3151 weeks
238.06545 -.02586 (238*2π)/3151 weeks
239-.39359 .26179 (239*2π)/3151 weeks
240-.09211 .30863 (240*2π)/3151 weeks
241-.32772 .1831 (241*2π)/3151 weeks
242-.20674 .24022 (242*2π)/3151 weeks
243-.46568 -.02455 (243*2π)/3151 weeks
244-.33455 .45831 (244*2π)/3151 weeks
245-.49344 .37399 (245*2π)/3151 weeks
246-.43486 .09385 (246*2π)/3151 weeks
247-.68494 .4825 (247*2π)/3151 weeks
248-.27126 .58347 (248*2π)/3151 weeks
249-.41349 .1793 (249*2π)/3151 weeks
250-.31722 .41602 (250*2π)/3151 weeks
251-.45136 .43914 (251*2π)/3151 weeks
252-.26147 .39131 (252*2π)/3151 weeks
253-.59527 .47495 (253*2π)/3151 weeks
254-.2224 .75062 (254*2π)/3151 weeks
255-.65327 .45466 (255*2π)/3151 weeks
256-.48084 .47887 (256*2π)/3151 weeks
257-.48855 1.01536 (257*2π)/3151 weeks
258-.16839 .55559 (258*2π)/3151 weeks
259-.33566 .79689 (259*2π)/3151 weeks
260-.21545 .88881 (260*2π)/3151 weeks
261-.18404 .66594 (261*2π)/3151 weeks
262.15599 .72143 (262*2π)/3151 weeks
263.28198 .56258 (263*2π)/3151 weeks
264-.10997 .17834 (264*2π)/3151 weeks
265-.22588 .73484 (265*2π)/3151 weeks
266-.21844 .26196 (266*2π)/3151 weeks
267-.23491 .53118 (267*2π)/3151 weeks
268-.41237 .35835 (268*2π)/3151 weeks
269-.31491 .35098 (269*2π)/3151 weeks
270-.70623 .65007 (270*2π)/3151 weeks
271-.36477 .7082 (271*2π)/3151 weeks
272-.13958 .39525 (272*2π)/3151 weeks
273-.52547 .86309 (273*2π)/3151 weeks
274.14664 .50234 (274*2π)/3151 weeks
275-.51597 .56225 (275*2π)/3151 weeks
276-.3674 .8905 (276*2π)/3151 weeks
277-.73523 .10175 (277*2π)/3151 weeks
278-.55623 .99823 (278*2π)/3151 weeks
279-.52689 1.48822 (279*2π)/3151 weeks
280-.26001 .92365 (280*2π)/3151 weeks
281-.82134 1.09813 (281*2π)/3151 weeks
282.10389 1.03285 (282*2π)/3151 weeks
283-.73638 1.25865 (283*2π)/3151 weeks
284.00068 1.71973 (284*2π)/3151 weeks
285.23699 1.38686 (285*2π)/3151 weeks
286-.16484 .83105 (286*2π)/3151 weeks
287-.60582 1.7434 (287*2π)/3151 weeks
288.72117 .77939 (288*2π)/3151 weeks
289-.2823 1.49426 (289*2π)/3151 weeks
290.46919 1.12668 (290*2π)/3151 weeks
291-.05705 .99743 (291*2π)/3151 weeks
292.051 1.22871 (292*2π)/3151 weeks
293.24428 2.20295 (293*2π)/3151 weeks
294.31624 .98482 (294*2π)/3151 weeks
295-.03821 1.64243 (295*2π)/3151 weeks
296.79209 1.5575 (296*2π)/3151 weeks
297-.29715 1.15039 (297*2π)/3151 weeks
298.17359 1.96843 (298*2π)/3151 weeks
2991.02371 1.19025 (299*2π)/3151 weeks
300-.13293 .79814 (300*2π)/3151 weeks
301-.95194 1.12779 (301*2π)/3151 weeks
302.75405 2.66401 (302*2π)/3151 weeks
303-.53025 1.70847 (303*2π)/3151 weeks
304-.03132 3.37361 (304*2π)/3151 weeks
305.22621 3.00954 (305*2π)/3151 weeks
306-.27289 1.93467 (306*2π)/3151 weeks
307.76799 4.19302 (307*2π)/3151 weeks
308-1.75251 1.60004 (308*2π)/3151 weeks
309-.53728 6.62967 (309*2π)/3151 weeks
310.96743 4.36555 (310*2π)/3151 weeks
311-1.19562 8.3675 (311*2π)/3151 weeks
3121.99072 12.08961 (312*2π)/3151 weeks
3139.43621 12.57743 (313*2π)/3151 weeks



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