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Fourier Analysis of RUSS (Direxion Daily Russia Bear 3x Shares ETF)


RUSS (Direxion Daily Russia Bear 3x Shares ETF) appears to have interesting cyclic behaviour every 32 weeks (5.6212*sine), 27 weeks (4.9926*cosine), and 17 weeks (4.7996*cosine).

RUSS (Direxion Daily Russia Bear 3x Shares ETF) has an average price of 63.73 (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 5/25/2011 to 7/10/2017 for RUSS (Direxion Daily Russia Bear 3x Shares ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
063.73268   0 
111.8293 36.15794 (1*2π)/321321 weeks
212.77021 32.18441 (2*2π)/321161 weeks
34.96335 18.16638 (3*2π)/321107 weeks
42.32817 17.84335 (4*2π)/32180 weeks
54.49092 7.57631 (5*2π)/32164 weeks
6-2.04769 11.82226 (6*2π)/32154 weeks
7.24515 16.61837 (7*2π)/32146 weeks
8-10.00318 .07349 (8*2π)/32140 weeks
9-3.01942 4.94998 (9*2π)/32136 weeks
10-4.56331 -5.62123 (10*2π)/32132 weeks
11-1.46962 -2.14908 (11*2π)/32129 weeks
124.99263 -.14149 (12*2π)/32127 weeks
131.98552 .72193 (13*2π)/32125 weeks
14-3.28836 3.00775 (14*2π)/32123 weeks
15-2.48582 -1.94666 (15*2π)/32121 weeks
16-.31687 -1.84588 (16*2π)/32120 weeks
174.63666 -4.67863 (17*2π)/32119 weeks
181.46601 -.09802 (18*2π)/32118 weeks
194.79962 .59964 (19*2π)/32117 weeks
203.34638 2.22828 (20*2π)/32116 weeks
212.64612 3.79403 (21*2π)/32115 weeks
22.86614 3.13669 (22*2π)/32115 weeks
23-.57984 3.70104 (23*2π)/32114 weeks
241.84047 3.01696 (24*2π)/32113 weeks
25-1.14304 3.88646 (25*2π)/32113 weeks
26-1.65116 4.30539 (26*2π)/32112 weeks
27-2.31529 .96977 (27*2π)/32112 weeks
28-3.69942 1.08408 (28*2π)/32111 weeks
29.75174 -2.351 (29*2π)/32111 weeks
30.48153 -.97066 (30*2π)/32111 weeks
311.86877 1.08088 (31*2π)/32110 weeks
321.13156 -.11996 (32*2π)/32110 weeks
332.27559 1.29875 (33*2π)/32110 weeks
34.79602 .81322 (34*2π)/3219 weeks
352.22636 .53671 (35*2π)/3219 weeks
362.3847 1.47287 (36*2π)/3219 weeks
372.00491 2.82105 (37*2π)/3219 weeks
381.2404 2.50122 (38*2π)/3218 weeks
39-.21713 3.67856 (39*2π)/3218 weeks
40-.79526 3.21158 (40*2π)/3218 weeks
41-2.70202 .94826 (41*2π)/3218 weeks
42-.55561 1.65304 (42*2π)/3218 weeks
43-2.24315 .45198 (43*2π)/3217 weeks
44-1.04021 1.32813 (44*2π)/3217 weeks
45-2.081 -.04726 (45*2π)/3217 weeks
46-2.6643 -.72755 (46*2π)/3217 weeks
47-1.6798 -.98064 (47*2π)/3217 weeks
48-.34162 -3.66968 (48*2π)/3217 weeks
49.98039 -1.00301 (49*2π)/3217 weeks
502.10895 -1.96175 (50*2π)/3216 weeks
511.0659 .6432 (51*2π)/3216 weeks
522.04802 -.12899 (52*2π)/3216 weeks
531.68191 .23087 (53*2π)/3216 weeks
541.54171 .79914 (54*2π)/3216 weeks
552.19046 .99668 (55*2π)/3216 weeks
56.5238 2.30207 (56*2π)/3216 weeks
571.79369 1.84977 (57*2π)/3216 weeks
58.19947 1.24984 (58*2π)/3216 weeks
59.11455 1.61265 (59*2π)/3215 weeks
60-.23995 1.67629 (60*2π)/3215 weeks
61.47983 1.11763 (61*2π)/3215 weeks
62.04036 .29111 (62*2π)/3215 weeks
63-.51027 .91181 (63*2π)/3215 weeks
64.21069 .92043 (64*2π)/3215 weeks
65-.36865 .26228 (65*2π)/3215 weeks
66-.21901 -.48992 (66*2π)/3215 weeks
67-.03712 -.88723 (67*2π)/3215 weeks
681.2556 .75996 (68*2π)/3215 weeks
69.29782 -.00283 (69*2π)/3215 weeks
70.11436 .07655 (70*2π)/3215 weeks
71.04719 -.14579 (71*2π)/3215 weeks
72-.24816 .12412 (72*2π)/3214 weeks
731.27707 -.64448 (73*2π)/3214 weeks
74.35071 .15456 (74*2π)/3214 weeks
75.56243 .41166 (75*2π)/3214 weeks
76.33152 .203 (76*2π)/3214 weeks
77.37916 .72283 (77*2π)/3214 weeks
781.00891 -.01098 (78*2π)/3214 weeks
79-.46206 .84389 (79*2π)/3214 weeks
80.57418 1.05638 (80*2π)/3214 weeks
81-.49214 .17208 (81*2π)/3214 weeks
82.00496 .53649 (82*2π)/3214 weeks
83-.40305 -.70777 (83*2π)/3214 weeks
84.20693 .00275 (84*2π)/3214 weeks
851.12955 -.52632 (85*2π)/3214 weeks
86.56984 -.50199 (86*2π)/3214 weeks
871.83291 .19662 (87*2π)/3214 weeks
88.96951 .2018 (88*2π)/3214 weeks
891.11248 .95178 (89*2π)/3214 weeks
901.43375 -.19391 (90*2π)/3214 weeks
91.51725 .95432 (91*2π)/3214 weeks
921.53327 .96712 (92*2π)/3213 weeks
93.40323 .96958 (93*2π)/3213 weeks
94.31594 1.10441 (94*2π)/3213 weeks
95-.08861 .51666 (95*2π)/3213 weeks
96-.05514 .12085 (96*2π)/3213 weeks
97.92724 .19767 (97*2π)/3213 weeks
98.042 .46021 (98*2π)/3213 weeks
99.30692 .70145 (99*2π)/3213 weeks
100-.28413 -.46915 (100*2π)/3213 weeks
101.34214 .48794 (101*2π)/3213 weeks
102.89714 .1412 (102*2π)/3213 weeks
103.27338 .23122 (103*2π)/3213 weeks
104.20825 .98876 (104*2π)/3213 weeks
105-.17446 .38413 (105*2π)/3213 weeks
106.17762 .59515 (106*2π)/3213 weeks
107-.24371 -.45978 (107*2π)/3213 weeks
108.1734 .41612 (108*2π)/3213 weeks
109.77518 -.02343 (109*2π)/3213 weeks
110.63347 .34074 (110*2π)/3213 weeks
111.42613 .51177 (111*2π)/3213 weeks
112.78348 .57385 (112*2π)/3213 weeks
113.71461 .75168 (113*2π)/3213 weeks
114.44629 1.2014 (114*2π)/3213 weeks
115.08247 1.01323 (115*2π)/3213 weeks
116-.0815 .78869 (116*2π)/3213 weeks
117-.62139 .80653 (117*2π)/3213 weeks
118-.52407 .05369 (118*2π)/3213 weeks
119-.1725 -.53696 (119*2π)/3213 weeks
120.36731 -.36207 (120*2π)/3213 weeks
121.31464 -.22716 (121*2π)/3213 weeks
122.49505 .14283 (122*2π)/3213 weeks
123.39633 -.13339 (123*2π)/3213 weeks
124-.25466 -.55719 (124*2π)/3213 weeks
1251.37385 -.04973 (125*2π)/3213 weeks
126.52394 -.12321 (126*2π)/3213 weeks
127.30938 1.22807 (127*2π)/3213 weeks
128.18906 -.23488 (128*2π)/3213 weeks
129-.79775 .41219 (129*2π)/3212 weeks
130.3165 -.51712 (130*2π)/3212 weeks
131-.02851 -.44606 (131*2π)/3212 weeks
132.83816 -.07336 (132*2π)/3212 weeks
133.59623 -.58575 (133*2π)/3212 weeks
134.36397 .63828 (134*2π)/3212 weeks
1351.03961 .02894 (135*2π)/3212 weeks
136.11447 .09455 (136*2π)/3212 weeks
1371.2505 .58543 (137*2π)/3212 weeks
138.5672 .36547 (138*2π)/3212 weeks
139.89572 1.17227 (139*2π)/3212 weeks
140-.08854 1.03109 (140*2π)/3212 weeks
141-.63138 1.21069 (141*2π)/3212 weeks
142-.43722 -.00343 (142*2π)/3212 weeks
143-.63611 -.39767 (143*2π)/3212 weeks
144.09757 .00944 (144*2π)/3212 weeks
145-.01739 -.80947 (145*2π)/3212 weeks
146.20106 -.09168 (146*2π)/3212 weeks
147.48218 -.92216 (147*2π)/3212 weeks
148.08012 -.40368 (148*2π)/3212 weeks
1491.24435 -1.10869 (149*2π)/3212 weeks
1501.10411 -.31321 (150*2π)/3212 weeks
1511.29542 .05066 (151*2π)/3212 weeks
152.91419 .04944 (152*2π)/3212 weeks
153.38837 .8003 (153*2π)/3212 weeks
154.88937 .05954 (154*2π)/3212 weeks
155.26661 -.16422 (155*2π)/3212 weeks
156.47472 .76372 (156*2π)/3212 weeks
157.30315 .53967 (157*2π)/3212 weeks
158.02475 .21222 (158*2π)/3212 weeks
159-.30645 .66201 (159*2π)/3212 weeks
160-.4297 .0448 (160*2π)/3212 weeks
161-.4297 -.0448 (161*2π)/3212 weeks
162-.30645 -.66201 (162*2π)/3212 weeks
163.02475 -.21222 (163*2π)/3212 weeks
164.30315 -.53967 (164*2π)/3212 weeks
165.47472 -.76372 (165*2π)/3212 weeks
166.26661 .16422 (166*2π)/3212 weeks
167.88937 -.05954 (167*2π)/3212 weeks
168.38837 -.8003 (168*2π)/3212 weeks
169.91419 -.04944 (169*2π)/3212 weeks
1701.29542 -.05066 (170*2π)/3212 weeks
1711.10411 .31321 (171*2π)/3212 weeks
1721.24435 1.10869 (172*2π)/3212 weeks
173.08012 .40368 (173*2π)/3212 weeks
174.48218 .92216 (174*2π)/3212 weeks
175.20106 .09168 (175*2π)/3212 weeks
176-.01739 .80947 (176*2π)/3212 weeks
177.09757 -.00944 (177*2π)/3212 weeks
178-.63611 .39767 (178*2π)/3212 weeks
179-.43722 .00343 (179*2π)/3212 weeks
180-.63138 -1.21069 (180*2π)/3212 weeks
181-.08854 -1.03109 (181*2π)/3212 weeks
182.89572 -1.17227 (182*2π)/3212 weeks
183.5672 -.36547 (183*2π)/3212 weeks
1841.2505 -.58543 (184*2π)/3212 weeks
185.11447 -.09455 (185*2π)/3212 weeks
1861.03961 -.02894 (186*2π)/3212 weeks
187.36397 -.63828 (187*2π)/3212 weeks
188.59623 .58575 (188*2π)/3212 weeks
189.83816 .07336 (189*2π)/3212 weeks
190-.02851 .44606 (190*2π)/3212 weeks
191.3165 .51712 (191*2π)/3212 weeks
192-.79775 -.41219 (192*2π)/3212 weeks
193.18906 .23488 (193*2π)/3212 weeks
194.30938 -1.22807 (194*2π)/3212 weeks
195.52394 .12321 (195*2π)/3212 weeks
1961.37385 .04973 (196*2π)/3212 weeks
197-.25466 .55719 (197*2π)/3212 weeks
198.39633 .13339 (198*2π)/3212 weeks
199.49505 -.14283 (199*2π)/3212 weeks
200.31464 .22716 (200*2π)/3212 weeks
201.36731 .36207 (201*2π)/3212 weeks
202-.1725 .53696 (202*2π)/3212 weeks
203-.52407 -.05369 (203*2π)/3212 weeks
204-.62139 -.80653 (204*2π)/3212 weeks
205-.0815 -.78869 (205*2π)/3212 weeks
206.08247 -1.01323 (206*2π)/3212 weeks
207.44629 -1.2014 (207*2π)/3212 weeks
208.71461 -.75168 (208*2π)/3212 weeks
209.78348 -.57385 (209*2π)/3212 weeks
210.42613 -.51177 (210*2π)/3212 weeks
211.63347 -.34074 (211*2π)/3212 weeks
212.77518 .02343 (212*2π)/3212 weeks
213.1734 -.41612 (213*2π)/3212 weeks
214-.24371 .45978 (214*2π)/3212 weeks
215.17762 -.59515 (215*2π)/3211 weeks
216-.17446 -.38413 (216*2π)/3211 weeks
217.20825 -.98876 (217*2π)/3211 weeks
218.27338 -.23122 (218*2π)/3211 weeks
219.89714 -.1412 (219*2π)/3211 weeks
220.34214 -.48794 (220*2π)/3211 weeks
221-.28413 .46915 (221*2π)/3211 weeks
222.30692 -.70145 (222*2π)/3211 weeks
223.042 -.46021 (223*2π)/3211 weeks
224.92724 -.19767 (224*2π)/3211 weeks
225-.05514 -.12085 (225*2π)/3211 weeks
226-.08861 -.51666 (226*2π)/3211 weeks
227.31594 -1.10441 (227*2π)/3211 weeks
228.40323 -.96958 (228*2π)/3211 weeks
2291.53327 -.96712 (229*2π)/3211 weeks
230.51725 -.95432 (230*2π)/3211 weeks
2311.43375 .19391 (231*2π)/3211 weeks
2321.11248 -.95178 (232*2π)/3211 weeks
233.96951 -.2018 (233*2π)/3211 weeks
2341.83291 -.19662 (234*2π)/3211 weeks
235.56984 .50199 (235*2π)/3211 weeks
2361.12955 .52632 (236*2π)/3211 weeks
237.20693 -.00275 (237*2π)/3211 weeks
238-.40305 .70777 (238*2π)/3211 weeks
239.00496 -.53649 (239*2π)/3211 weeks
240-.49214 -.17208 (240*2π)/3211 weeks
241.57418 -1.05638 (241*2π)/3211 weeks
242-.46206 -.84389 (242*2π)/3211 weeks
2431.00891 .01098 (243*2π)/3211 weeks
244.37916 -.72283 (244*2π)/3211 weeks
245.33152 -.203 (245*2π)/3211 weeks
246.56243 -.41166 (246*2π)/3211 weeks
247.35071 -.15456 (247*2π)/3211 weeks
2481.27707 .64448 (248*2π)/3211 weeks
249-.24816 -.12412 (249*2π)/3211 weeks
250.04719 .14579 (250*2π)/3211 weeks
251.11436 -.07655 (251*2π)/3211 weeks
252.29782 .00283 (252*2π)/3211 weeks
2531.2556 -.75996 (253*2π)/3211 weeks
254-.03712 .88723 (254*2π)/3211 weeks
255-.21901 .48992 (255*2π)/3211 weeks
256-.36865 -.26228 (256*2π)/3211 weeks
257.21069 -.92043 (257*2π)/3211 weeks
258-.51027 -.91181 (258*2π)/3211 weeks
259.04036 -.29111 (259*2π)/3211 weeks
260.47983 -1.11763 (260*2π)/3211 weeks
261-.23995 -1.67629 (261*2π)/3211 weeks
262.11455 -1.61265 (262*2π)/3211 weeks
263.19947 -1.24984 (263*2π)/3211 weeks
2641.79369 -1.84977 (264*2π)/3211 weeks
265.5238 -2.30207 (265*2π)/3211 weeks
2662.19046 -.99668 (266*2π)/3211 weeks
2671.54171 -.79914 (267*2π)/3211 weeks
2681.68191 -.23087 (268*2π)/3211 weeks
2692.04802 .12899 (269*2π)/3211 weeks
2701.0659 -.6432 (270*2π)/3211 weeks
2712.10895 1.96175 (271*2π)/3211 weeks
272.98039 1.00301 (272*2π)/3211 weeks
273-.34162 3.66968 (273*2π)/3211 weeks
274-1.6798 .98064 (274*2π)/3211 weeks
275-2.6643 .72755 (275*2π)/3211 weeks
276-2.081 .04726 (276*2π)/3211 weeks
277-1.04021 -1.32813 (277*2π)/3211 weeks
278-2.24315 -.45198 (278*2π)/3211 weeks
279-.55561 -1.65304 (279*2π)/3211 weeks
280-2.70202 -.94826 (280*2π)/3211 weeks
281-.79526 -3.21158 (281*2π)/3211 weeks
282-.21713 -3.67856 (282*2π)/3211 weeks
2831.2404 -2.50122 (283*2π)/3211 weeks
2842.00491 -2.82105 (284*2π)/3211 weeks
2852.3847 -1.47287 (285*2π)/3211 weeks
2862.22636 -.53671 (286*2π)/3211 weeks
287.79602 -.81322 (287*2π)/3211 weeks
2882.27559 -1.29875 (288*2π)/3211 weeks
2891.13156 .11996 (289*2π)/3211 weeks
2901.86877 -1.08088 (290*2π)/3211 weeks
291.48153 .97066 (291*2π)/3211 weeks
292.75174 2.351 (292*2π)/3211 weeks
293-3.69942 -1.08408 (293*2π)/3211 weeks
294-2.31529 -.96977 (294*2π)/3211 weeks
295-1.65116 -4.30539 (295*2π)/3211 weeks
296-1.14304 -3.88646 (296*2π)/3211 weeks
2971.84047 -3.01696 (297*2π)/3211 weeks
298-.57984 -3.70104 (298*2π)/3211 weeks
299.86614 -3.13669 (299*2π)/3211 weeks
3002.64612 -3.79403 (300*2π)/3211 weeks
3013.34638 -2.22828 (301*2π)/3211 weeks
3024.79962 -.59964 (302*2π)/3211 weeks
3031.46601 .09802 (303*2π)/3211 weeks
3044.63666 4.67863 (304*2π)/3211 weeks
305-.31687 1.84588 (305*2π)/3211 weeks
306-2.48582 1.94666 (306*2π)/3211 weeks
307-3.28836 -3.00775 (307*2π)/3211 weeks
3081.98552 -.72193 (308*2π)/3211 weeks
3094.99263 .14149 (309*2π)/3211 weeks
310-1.46962 2.14908 (310*2π)/3211 weeks
311-4.56331 5.62123 (311*2π)/3211 weeks
312-3.01942 -4.94998 (312*2π)/3211 weeks
313-10.00318 -.07349 (313*2π)/3211 weeks
314.24515 -16.61837 (314*2π)/3211 weeks
315-2.04769 -11.82226 (315*2π)/3211 weeks
3164.49092 -7.57631 (316*2π)/3211 weeks
3172.32817 -17.84335 (317*2π)/3211 weeks
3184.96335 -18.16638 (318*2π)/3211 weeks
31912.77021 -32.18441 (319*2π)/3211 weeks



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