Back to list of Stocks    See Also: Seasonal Analysis of SVXYGenetic Algorithms Stock Portfolio Generator, and Best Months to Buy/Sell Stocks

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

SVXY (ProShares Short VIX Short-Term Futures) appears to have interesting cyclic behaviour every 34 weeks (4.9206*cosine), 23 weeks (3.8818*sine), and 26 weeks (3.5334*sine).

SVXY (ProShares Short VIX Short-Term Futures) has an average price of 36.16 (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 4/16/2018 for SVXY (ProShares Short VIX Short-Term Futures), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
036.1586   0
15.61314 -15.09182 (1*2π)/342342 weeks
24.48209 -21.38716 (2*2π)/342171 weeks
3-6.46253 -13.58036 (3*2π)/342114 weeks
4-6.23085 -6.60146 (4*2π)/34286 weeks
5-3.67648 -5.86093 (5*2π)/34268 weeks
6-6.7277 -2.95026 (6*2π)/34257 weeks
7-3.02811 -2.11177 (7*2π)/34249 weeks
8-7.31129 -1.67732 (8*2π)/34243 weeks
9-4.02709 .3475 (9*2π)/34238 weeks
10-4.92061 2.16079 (10*2π)/34234 weeks
11-2.98279 2.32137 (11*2π)/34231 weeks
12-2.07754 1.94914 (12*2π)/34229 weeks
13-1.67698 3.53342 (13*2π)/34226 weeks
14.11944 2.24925 (14*2π)/34224 weeks
15.11078 3.88176 (15*2π)/34223 weeks
161.56565 2.4829 (16*2π)/34221 weeks
171.5279 .89297 (17*2π)/34220 weeks
18.68868 1.518 (18*2π)/34219 weeks
191.69642 1.32468 (19*2π)/34218 weeks
201.11976 .36769 (20*2π)/34217 weeks
211.87955 .99754 (21*2π)/34216 weeks
221.9294 -.02956 (22*2π)/34216 weeks
231.80009 .24362 (23*2π)/34215 weeks
242.24408 -1.39303 (24*2π)/34214 weeks
251.58504 -1.1265 (25*2π)/34214 weeks
261.16893 -1.26842 (26*2π)/34213 weeks
271.0935 -1.86584 (27*2π)/34213 weeks
28-.20002 -1.83531 (28*2π)/34212 weeks
29.24177 -1.90344 (29*2π)/34212 weeks
30-1.50688 -.96148 (30*2π)/34211 weeks
31-.59334 -1.12041 (31*2π)/34211 weeks
32-1.43514 -.88371 (32*2π)/34211 weeks
33-1.06283 -.10108 (33*2π)/34210 weeks
34-.3459 -.11741 (34*2π)/34210 weeks
35-.98756 -.53525 (35*2π)/34210 weeks
36-.48142 .16914 (36*2π)/34210 weeks
37-1.24818 -.08079 (37*2π)/3429 weeks
38-.75954 .3061 (38*2π)/3429 weeks
39-1.05556 .00704 (39*2π)/3429 weeks
40-.74997 .76288 (40*2π)/3429 weeks
41-.13801 1.40834 (41*2π)/3428 weeks
42-.3382 .50891 (42*2π)/3428 weeks
43.09375 .76764 (43*2π)/3428 weeks
44.13516 .31408 (44*2π)/3428 weeks
45.06079 1.03827 (45*2π)/3428 weeks
46.45427 .40982 (46*2π)/3427 weeks
47.39644 .80927 (47*2π)/3427 weeks
48.62488 .43466 (48*2π)/3427 weeks
49.33779 .10905 (49*2π)/3427 weeks
50.64246 .37732 (50*2π)/3427 weeks
51.66256 .20708 (51*2π)/3427 weeks
52.82514 -.20879 (52*2π)/3427 weeks
53.86215 -.27307 (53*2π)/3426 weeks
54.43583 -.78837 (54*2π)/3426 weeks
55.66953 -.73797 (55*2π)/3426 weeks
56-.0185 -1.09149 (56*2π)/3426 weeks
57-.23998 -.5411 (57*2π)/3426 weeks
58-.08646 -.20234 (58*2π)/3426 weeks
59-.16468 -.29837 (59*2π)/3426 weeks
60.01853 -.49009 (60*2π)/3426 weeks
61-.16091 -.62846 (61*2π)/3426 weeks
62-.21562 -.3489 (62*2π)/3426 weeks
63-.57097 -.79497 (63*2π)/3425 weeks
64-.67436 -.13697 (64*2π)/3425 weeks
65-.78724 .06202 (65*2π)/3425 weeks
66-.55585 -.20323 (66*2π)/3425 weeks
67-.52072 .38501 (67*2π)/3425 weeks
68-.252 .15851 (68*2π)/3425 weeks
69-.31916 .38488 (69*2π)/3425 weeks
70-.20177 .27615 (70*2π)/3425 weeks
71-.06653 .37895 (71*2π)/3425 weeks
72-.30128 .46964 (72*2π)/3425 weeks
73.17701 .37702 (73*2π)/3425 weeks
74-.1206 .10827 (74*2π)/3425 weeks
75-.02073 .56305 (75*2π)/3425 weeks
76.07372 .30444 (76*2π)/3425 weeks
77.29825 .1754 (77*2π)/3424 weeks
78.46376 .50839 (78*2π)/3424 weeks
79.53161 -.05496 (79*2π)/3424 weeks
80.44298 -.06767 (80*2π)/3424 weeks
81.33154 -.3598 (81*2π)/3424 weeks
82.28115 -.1384 (82*2π)/3424 weeks
83.24059 -.50977 (83*2π)/3424 weeks
84-.07315 .03503 (84*2π)/3424 weeks
85.12856 -.19539 (85*2π)/3424 weeks
86.05908 -.02923 (86*2π)/3424 weeks
87.57651 -.08898 (87*2π)/3424 weeks
88.08531 -.56062 (88*2π)/3424 weeks
89-.30563 -.4245 (89*2π)/3424 weeks
90-.00753 -.22423 (90*2π)/3424 weeks
91-.20457 -.51549 (91*2π)/3424 weeks
92-.0677 -.08838 (92*2π)/3424 weeks
93-.42168 -.49404 (93*2π)/3424 weeks
94-.38141 -.03769 (94*2π)/3424 weeks
95-.31035 -.15321 (95*2π)/3424 weeks
96-.3888 -.0653 (96*2π)/3424 weeks
97-.45473 .01389 (97*2π)/3424 weeks
98-.31363 .21501 (98*2π)/3423 weeks
99-.23364 .26377 (99*2π)/3423 weeks
100-.12554 .08675 (100*2π)/3423 weeks
101-.07565 .23642 (101*2π)/3423 weeks
102-.43653 .20909 (102*2π)/3423 weeks
103-.2462 .34301 (103*2π)/3423 weeks
104.01252 .53412 (104*2π)/3423 weeks
105.0583 .34911 (105*2π)/3423 weeks
106.33066 .56529 (106*2π)/3423 weeks
107.20394 .30498 (107*2π)/3423 weeks
108.45675 .21691 (108*2π)/3423 weeks
109.48013 .01036 (109*2π)/3423 weeks
110.49132 -.04091 (110*2π)/3423 weeks
111.36883 -.20722 (111*2π)/3423 weeks
112.2872 -.34743 (112*2π)/3423 weeks
113.00864 -.2383 (113*2π)/3423 weeks
114.10049 -.31727 (114*2π)/3423 weeks
115.00597 -.1372 (115*2π)/3423 weeks
116.23103 -.15181 (116*2π)/3423 weeks
117.05765 -.32579 (117*2π)/3423 weeks
118.043 -.42157 (118*2π)/3423 weeks
119-.21919 -.37695 (119*2π)/3423 weeks
120-.16828 -.2709 (120*2π)/3423 weeks
121-.30029 -.2783 (121*2π)/3423 weeks
122-.2372 -.0179 (122*2π)/3423 weeks
123-.18347 -.01904 (123*2π)/3423 weeks
124-.32889 -.10849 (124*2π)/3423 weeks
125-.21408 -.01559 (125*2π)/3423 weeks
126-.21948 .07571 (126*2π)/3423 weeks
127-.04188 .12564 (127*2π)/3423 weeks
128-.37885 -.09273 (128*2π)/3423 weeks
129-.13296 .20317 (129*2π)/3423 weeks
130-.21947 .14786 (130*2π)/3423 weeks
131-.11157 .23232 (131*2π)/3423 weeks
132-.28759 .12142 (132*2π)/3423 weeks
133-.09044 .24781 (133*2π)/3423 weeks
134-.10396 .46787 (134*2π)/3423 weeks
135.16336 .34701 (135*2π)/3423 weeks
136.23714 .31904 (136*2π)/3423 weeks
137.28504 .08235 (137*2π)/3422 weeks
138.10694 .06918 (138*2π)/3422 weeks
139.24686 .09044 (139*2π)/3422 weeks
140.12676 .06687 (140*2π)/3422 weeks
141.22877 -.0228 (141*2π)/3422 weeks
142.20823 -.12349 (142*2π)/3422 weeks
143.39606 -.06671 (143*2π)/3422 weeks
144.08662 -.35235 (144*2π)/3422 weeks
145.02994 -.18902 (145*2π)/3422 weeks
146-.08452 -.21837 (146*2π)/3422 weeks
147-.01687 -.14007 (147*2π)/3422 weeks
148.01241 -.06025 (148*2π)/3422 weeks
149-.21978 -.24545 (149*2π)/3422 weeks
150-.23214 -.03335 (150*2π)/3422 weeks
151.03939 -.12322 (151*2π)/3422 weeks
152-.12791 -.0777 (152*2π)/3422 weeks
153.02594 -.29158 (153*2π)/3422 weeks
154-.43556 -.13597 (154*2π)/3422 weeks
155-.1542 -.12605 (155*2π)/3422 weeks
156-.2577 .02552 (156*2π)/3422 weeks
157-.19663 -.08673 (157*2π)/3422 weeks
158-.21392 .2847 (158*2π)/3422 weeks
159-.23749 .09352 (159*2π)/3422 weeks
160-.18288 .18508 (160*2π)/3422 weeks
161-.17483 .29636 (161*2π)/3422 weeks
162-.03773 .10438 (162*2π)/3422 weeks
163-.10319 .10758 (163*2π)/3422 weeks
164-.00647 .2612 (164*2π)/3422 weeks
165.14274 .18077 (165*2π)/3422 weeks
166-.00798 .2089 (166*2π)/3422 weeks
167.06733 .1724 (167*2π)/3422 weeks
168.00535 .12144 (168*2π)/3422 weeks
169.13264 .36177 (169*2π)/3422 weeks
170.35416 .15884 (170*2π)/3422 weeks
171.29203   (171*2π)/3422 weeks
172.35416 -.15884 (172*2π)/3422 weeks
173.13264 -.36177 (173*2π)/3422 weeks
174.00535 -.12144 (174*2π)/3422 weeks
175.06733 -.1724 (175*2π)/3422 weeks
176-.00798 -.2089 (176*2π)/3422 weeks
177.14274 -.18077 (177*2π)/3422 weeks
178-.00647 -.2612 (178*2π)/3422 weeks
179-.10319 -.10758 (179*2π)/3422 weeks
180-.03773 -.10438 (180*2π)/3422 weeks
181-.17483 -.29636 (181*2π)/3422 weeks
182-.18288 -.18508 (182*2π)/3422 weeks
183-.23749 -.09352 (183*2π)/3422 weeks
184-.21392 -.2847 (184*2π)/3422 weeks
185-.19663 .08673 (185*2π)/3422 weeks
186-.2577 -.02552 (186*2π)/3422 weeks
187-.1542 .12605 (187*2π)/3422 weeks
188-.43556 .13597 (188*2π)/3422 weeks
189.02594 .29158 (189*2π)/3422 weeks
190-.12791 .0777 (190*2π)/3422 weeks
191.03939 .12322 (191*2π)/3422 weeks
192-.23214 .03335 (192*2π)/3422 weeks
193-.21978 .24545 (193*2π)/3422 weeks
194.01241 .06025 (194*2π)/3422 weeks
195-.01687 .14007 (195*2π)/3422 weeks
196-.08452 .21837 (196*2π)/3422 weeks
197.02994 .18902 (197*2π)/3422 weeks
198.08662 .35235 (198*2π)/3422 weeks
199.39606 .06671 (199*2π)/3422 weeks
200.20823 .12349 (200*2π)/3422 weeks
201.22877 .0228 (201*2π)/3422 weeks
202.12676 -.06687 (202*2π)/3422 weeks
203.24686 -.09044 (203*2π)/3422 weeks
204.10694 -.06918 (204*2π)/3422 weeks
205.28504 -.08235 (205*2π)/3422 weeks
206.23714 -.31904 (206*2π)/3422 weeks
207.16336 -.34701 (207*2π)/3422 weeks
208-.10396 -.46787 (208*2π)/3422 weeks
209-.09044 -.24781 (209*2π)/3422 weeks
210-.28759 -.12142 (210*2π)/3422 weeks
211-.11157 -.23232 (211*2π)/3422 weeks
212-.21947 -.14786 (212*2π)/3422 weeks
213-.13296 -.20317 (213*2π)/3422 weeks
214-.37885 .09273 (214*2π)/3422 weeks
215-.04188 -.12564 (215*2π)/3422 weeks
216-.21948 -.07571 (216*2π)/3422 weeks
217-.21408 .01559 (217*2π)/3422 weeks
218-.32889 .10849 (218*2π)/3422 weeks
219-.18347 .01904 (219*2π)/3422 weeks
220-.2372 .0179 (220*2π)/3422 weeks
221-.30029 .2783 (221*2π)/3422 weeks
222-.16828 .2709 (222*2π)/3422 weeks
223-.21919 .37695 (223*2π)/3422 weeks
224.043 .42157 (224*2π)/3422 weeks
225.05765 .32579 (225*2π)/3422 weeks
226.23103 .15181 (226*2π)/3422 weeks
227.00597 .1372 (227*2π)/3422 weeks
228.10049 .31727 (228*2π)/3422 weeks
229.00864 .2383 (229*2π)/3421 weeks
230.2872 .34743 (230*2π)/3421 weeks
231.36883 .20722 (231*2π)/3421 weeks
232.49132 .04091 (232*2π)/3421 weeks
233.48013 -.01036 (233*2π)/3421 weeks
234.45675 -.21691 (234*2π)/3421 weeks
235.20394 -.30498 (235*2π)/3421 weeks
236.33066 -.56529 (236*2π)/3421 weeks
237.0583 -.34911 (237*2π)/3421 weeks
238.01252 -.53412 (238*2π)/3421 weeks
239-.2462 -.34301 (239*2π)/3421 weeks
240-.43653 -.20909 (240*2π)/3421 weeks
241-.07565 -.23642 (241*2π)/3421 weeks
242-.12554 -.08675 (242*2π)/3421 weeks
243-.23364 -.26377 (243*2π)/3421 weeks
244-.31363 -.21501 (244*2π)/3421 weeks
245-.45473 -.01389 (245*2π)/3421 weeks
246-.3888 .0653 (246*2π)/3421 weeks
247-.31035 .15321 (247*2π)/3421 weeks
248-.38141 .03769 (248*2π)/3421 weeks
249-.42168 .49404 (249*2π)/3421 weeks
250-.0677 .08838 (250*2π)/3421 weeks
251-.20457 .51549 (251*2π)/3421 weeks
252-.00753 .22423 (252*2π)/3421 weeks
253-.30563 .4245 (253*2π)/3421 weeks
254.08531 .56062 (254*2π)/3421 weeks
255.57651 .08898 (255*2π)/3421 weeks
256.05908 .02923 (256*2π)/3421 weeks
257.12856 .19539 (257*2π)/3421 weeks
258-.07315 -.03503 (258*2π)/3421 weeks
259.24059 .50977 (259*2π)/3421 weeks
260.28115 .1384 (260*2π)/3421 weeks
261.33154 .3598 (261*2π)/3421 weeks
262.44298 .06767 (262*2π)/3421 weeks
263.53161 .05496 (263*2π)/3421 weeks
264.46376 -.50839 (264*2π)/3421 weeks
265.29825 -.1754 (265*2π)/3421 weeks
266.07372 -.30444 (266*2π)/3421 weeks
267-.02073 -.56305 (267*2π)/3421 weeks
268-.1206 -.10827 (268*2π)/3421 weeks
269.17701 -.37702 (269*2π)/3421 weeks
270-.30128 -.46964 (270*2π)/3421 weeks
271-.06653 -.37895 (271*2π)/3421 weeks
272-.20177 -.27615 (272*2π)/3421 weeks
273-.31916 -.38488 (273*2π)/3421 weeks
274-.252 -.15851 (274*2π)/3421 weeks
275-.52072 -.38501 (275*2π)/3421 weeks
276-.55585 .20323 (276*2π)/3421 weeks
277-.78724 -.06202 (277*2π)/3421 weeks
278-.67436 .13697 (278*2π)/3421 weeks
279-.57097 .79497 (279*2π)/3421 weeks
280-.21562 .3489 (280*2π)/3421 weeks
281-.16091 .62846 (281*2π)/3421 weeks
282.01853 .49009 (282*2π)/3421 weeks
283-.16468 .29837 (283*2π)/3421 weeks
284-.08646 .20234 (284*2π)/3421 weeks
285-.23998 .5411 (285*2π)/3421 weeks
286-.0185 1.09149 (286*2π)/3421 weeks
287.66953 .73797 (287*2π)/3421 weeks
288.43583 .78837 (288*2π)/3421 weeks
289.86215 .27307 (289*2π)/3421 weeks
290.82514 .20879 (290*2π)/3421 weeks
291.66256 -.20708 (291*2π)/3421 weeks
292.64246 -.37732 (292*2π)/3421 weeks
293.33779 -.10905 (293*2π)/3421 weeks
294.62488 -.43466 (294*2π)/3421 weeks
295.39644 -.80927 (295*2π)/3421 weeks
296.45427 -.40982 (296*2π)/3421 weeks
297.06079 -1.03827 (297*2π)/3421 weeks
298.13516 -.31408 (298*2π)/3421 weeks
299.09375 -.76764 (299*2π)/3421 weeks
300-.3382 -.50891 (300*2π)/3421 weeks
301-.13801 -1.40834 (301*2π)/3421 weeks
302-.74997 -.76288 (302*2π)/3421 weeks
303-1.05556 -.00704 (303*2π)/3421 weeks
304-.75954 -.3061 (304*2π)/3421 weeks
305-1.24818 .08079 (305*2π)/3421 weeks
306-.48142 -.16914 (306*2π)/3421 weeks
307-.98756 .53525 (307*2π)/3421 weeks
308-.3459 .11741 (308*2π)/3421 weeks
309-1.06283 .10108 (309*2π)/3421 weeks
310-1.43514 .88371 (310*2π)/3421 weeks
311-.59334 1.12041 (311*2π)/3421 weeks
312-1.50688 .96148 (312*2π)/3421 weeks
313.24177 1.90344 (313*2π)/3421 weeks
314-.20002 1.83531 (314*2π)/3421 weeks
3151.0935 1.86584 (315*2π)/3421 weeks
3161.16893 1.26842 (316*2π)/3421 weeks
3171.58504 1.1265 (317*2π)/3421 weeks
3182.24408 1.39303 (318*2π)/3421 weeks
3191.80009 -.24362 (319*2π)/3421 weeks
3201.9294 .02956 (320*2π)/3421 weeks
3211.87955 -.99754 (321*2π)/3421 weeks
3221.11976 -.36769 (322*2π)/3421 weeks
3231.69642 -1.32468 (323*2π)/3421 weeks
324.68868 -1.518 (324*2π)/3421 weeks
3251.5279 -.89297 (325*2π)/3421 weeks
3261.56565 -2.4829 (326*2π)/3421 weeks
327.11078 -3.88176 (327*2π)/3421 weeks
328.11944 -2.24925 (328*2π)/3421 weeks
329-1.67698 -3.53342 (329*2π)/3421 weeks
330-2.07754 -1.94914 (330*2π)/3421 weeks
331-2.98279 -2.32137 (331*2π)/3421 weeks
332-4.92061 -2.16079 (332*2π)/3421 weeks
333-4.02709 -.3475 (333*2π)/3421 weeks
334-7.31129 1.67732 (334*2π)/3421 weeks
335-3.02811 2.11177 (335*2π)/3421 weeks
336-6.7277 2.95026 (336*2π)/3421 weeks
337-3.67648 5.86093 (337*2π)/3421 weeks
338-6.23085 6.60146 (338*2π)/3421 weeks
339-6.46253 13.58036 (339*2π)/3421 weeks
3404.48209 21.38716 (340*2π)/3421 weeks