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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 33 weeks (42.2631*cosine), 24 weeks (28.6623*sine), and 18 weeks (22.1786*cosine).

RUSS (Direxion Daily Russia Bear 3x Shares ETF) has an average price of 306.95 (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 9/5/2017 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
0306.9469   0 
149.23258 186.6954 (1*2π)/329329 weeks
260.87916 160.3012 (2*2π)/329165 weeks
315.28419 93.59621 (3*2π)/329110 weeks
48.76987 91.1108 (4*2π)/32982 weeks
54.50243 39.5673 (5*2π)/32966 weeks
6-11.51602 73.09513 (6*2π)/32955 weeks
78.73238 73.88747 (7*2π)/32947 weeks
8-67.74454 25.93053 (8*2π)/32941 weeks
9-10.53128 22.65272 (9*2π)/32937 weeks
10-42.26305 -7.74033 (10*2π)/32933 weeks
11-3.5401 .61429 (11*2π)/32930 weeks
1218.42044 -10.13072 (12*2π)/32927 weeks
133.93542 12.57065 (13*2π)/32925 weeks
14-1.26622 28.66231 (14*2π)/32924 weeks
15-14.2783 1.45509 (15*2π)/32922 weeks
16-.02307 -8.08649 (16*2π)/32921 weeks
171.20445 -19.8586 (17*2π)/32919 weeks
1822.17856 9.45437 (18*2π)/32918 weeks
1919.90029 -3.41926 (19*2π)/32917 weeks
2020.47621 13.363 (20*2π)/32916 weeks
2117.94652 17.18557 (21*2π)/32916 weeks
228.83716 22.85888 (22*2π)/32915 weeks
238.39588 20.19828 (23*2π)/32914 weeks
24.74709 11.23512 (24*2π)/32914 weeks
256.48085 24.07265 (25*2π)/32913 weeks
26-2.19071 17.14599 (26*2π)/32913 weeks
27-13.52274 17.90507 (27*2π)/32912 weeks
28-6.507 7.3026 (28*2π)/32912 weeks
29-17.8569 -4.49238 (29*2π)/32911 weeks
307.13108 -4.21668 (30*2π)/32911 weeks
316.77368 -5.50887 (31*2π)/32911 weeks
326.00455 6.28951 (32*2π)/32910 weeks
337.42812 -.21748 (33*2π)/32910 weeks
349.3277 8.65286 (34*2π)/32910 weeks
354.0822 3.7835 (35*2π)/3299 weeks
3610.99912 4.73933 (36*2π)/3299 weeks
3711.54319 9.04864 (37*2π)/3299 weeks
388.97269 15.72462 (38*2π)/3299 weeks
396.30191 14.12879 (39*2π)/3298 weeks
40-1.23418 19.5731 (40*2π)/3298 weeks
41-3.57614 17.56503 (41*2π)/3298 weeks
42-12.84953 6.95115 (42*2π)/3298 weeks
43-1.59413 9.34499 (43*2π)/3298 weeks
44-10.3704 4.92528 (44*2π)/3297 weeks
45-2.95611 7.11915 (45*2π)/3297 weeks
46-9.75996 1.67386 (46*2π)/3297 weeks
47-11.5177 -.30169 (47*2π)/3297 weeks
48-5.62029 -4.23433 (48*2π)/3297 weeks
49-5.03698 -15.89216 (49*2π)/3297 weeks
508.38239 -5.89988 (50*2π)/3297 weeks
517.23099 -10.04785 (51*2π)/3296 weeks
5211.0961 3.67865 (52*2π)/3296 weeks
538.84595 -3.09771 (53*2π)/3296 weeks
548.20919 1.72917 (54*2π)/3296 weeks
559.28782 3.99864 (55*2π)/3296 weeks
569.59653 3.39971 (56*2π)/3296 weeks
579.43828 11.72912 (57*2π)/3296 weeks
585.51503 3.83718 (58*2π)/3296 weeks
59.97697 11.24163 (59*2π)/3296 weeks
603.45086 8.30219 (60*2π)/3295 weeks
611.82229 7.17048 (61*2π)/3295 weeks
62-1.37235 3.40525 (62*2π)/3295 weeks
63-2.03442 6.40826 (63*2π)/3295 weeks
642.24886 5.26813 (64*2π)/3295 weeks
65-.82942 1.4716 (65*2π)/3295 weeks
66-2.42415 4.75159 (66*2π)/3295 weeks
67-2.60899 1.83033 (67*2π)/3295 weeks
68.2444 -.66288 (68*2π)/3295 weeks
694.01085 -4.53974 (69*2π)/3295 weeks
701.98349 5.55951 (70*2π)/3295 weeks
712.32184 2.0894 (71*2π)/3295 weeks
721.37798 1.48457 (72*2π)/3295 weeks
731.75528 .1071 (73*2π)/3295 weeks
74-1.35547 -.35051 (74*2π)/3294 weeks
757.61269 .26804 (75*2π)/3294 weeks
763.0905 .9768 (76*2π)/3294 weeks
773.44754 2.73852 (77*2π)/3294 weeks
782.88878 1.33965 (78*2π)/3294 weeks
792.32614 3.89459 (79*2π)/3294 weeks
806.45063 .80192 (80*2π)/3294 weeks
81-1.34539 3.82316 (81*2π)/3294 weeks
823.65331 5.24323 (82*2π)/3294 weeks
83-1.6831 .89512 (83*2π)/3294 weeks
84.92815 2.36987 (84*2π)/3294 weeks
85-1.97903 -3.08979 (85*2π)/3294 weeks
862.16078 -.05204 (86*2π)/3294 weeks
875.19972 -3.66245 (87*2π)/3294 weeks
882.6807 -1.52464 (88*2π)/3294 weeks
899.15051 -.72241 (89*2π)/3294 weeks
904.5766 1.96097 (90*2π)/3294 weeks
917.01128 3.73121 (91*2π)/3294 weeks
923.94782 -.71305 (92*2π)/3294 weeks
935.24303 6.72568 (93*2π)/3294 weeks
947.06331 2.22854 (94*2π)/3294 weeks
952.63692 6.656 (95*2π)/3293 weeks
962.81303 5.3602 (96*2π)/3293 weeks
97-.26836 4.2469 (97*2π)/3293 weeks
98.15212 2.19293 (98*2π)/3293 weeks
992.68715 -.56447 (99*2π)/3293 weeks
1002.3756 4.60915 (100*2π)/3293 weeks
1012.35165 2.0512 (101*2π)/3293 weeks
102-1.64861 3.22467 (102*2π)/3293 weeks
1034.44694 -.58221 (103*2π)/3293 weeks
1041.44239 -.04435 (104*2π)/3293 weeks
1053.28329 3.90536 (105*2π)/3293 weeks
1064.34354 2.47352 (106*2π)/3293 weeks
107.2268 3.8233 (107*2π)/3293 weeks
108.82217 1.12469 (108*2π)/3293 weeks
109-.56559 3.29615 (109*2π)/3293 weeks
1103.16515 -2.01957 (110*2π)/3293 weeks
111.72335 .00238 (111*2π)/3293 weeks
1124.50136 .99593 (112*2π)/3293 weeks
1133.98883 1.68152 (113*2π)/3293 weeks
1142.69068 1.47144 (114*2π)/3293 weeks
1153.98264 2.82196 (115*2π)/3293 weeks
1163.84636 3.60372 (116*2π)/3293 weeks
1171.76825 5.53081 (117*2π)/3293 weeks
118.30405 4.6882 (118*2π)/3293 weeks
119-.28951 3.72534 (119*2π)/3293 weeks
120-3.33051 3.4485 (120*2π)/3293 weeks
121-2.58288 .1996 (121*2π)/3293 weeks
122-.71825 -2.54245 (122*2π)/3293 weeks
1231.80865 -1.56714 (123*2π)/3293 weeks
1241.56375 -.82863 (124*2π)/3293 weeks
1252.65324 .91474 (125*2π)/3293 weeks
1261.91953 -.43538 (126*2π)/3293 weeks
127-1.16662 -1.38475 (127*2π)/3293 weeks
1287.07993 -1.17018 (128*2π)/3293 weeks
1292.28456 .50346 (129*2π)/3293 weeks
1304.12587 5.8057 (130*2π)/3293 weeks
131-.40597 -.75587 (131*2π)/3293 weeks
132-1.18888 4.03937 (132*2π)/3292 weeks
133.90491 -3.47168 (133*2π)/3292 weeks
134.72974 -.90876 (134*2π)/3292 weeks
1354.60186 -2.44997 (135*2π)/3292 weeks
1361.64888 -1.35444 (136*2π)/3292 weeks
1375.86899 2.28154 (137*2π)/3292 weeks
1383.11838 -1.83917 (138*2π)/3292 weeks
1392.45663 2.83422 (139*2π)/3292 weeks
1405.68888 -1.25673 (140*2π)/3292 weeks
1412.69452 3.32211 (141*2π)/3292 weeks
1425.19266 2.72672 (142*2π)/3292 weeks
1431.32393 6.52864 (143*2π)/3292 weeks
144.20766 4.954 (144*2π)/3292 weeks
145-4.85166 1.66254 (145*2π)/3292 weeks
146-2.31901 .70395 (146*2π)/3292 weeks
147-.12679 -3.22399 (147*2π)/3292 weeks
148-1.77432 -.79164 (148*2π)/3292 weeks
1492.0945 -3.24968 (149*2π)/3292 weeks
150-.81732 -1.84094 (150*2π)/3292 weeks
1513.51747 -2.63379 (151*2π)/3292 weeks
152.09293 -4.28833 (152*2π)/3292 weeks
1536.82379 -2.9528 (153*2π)/3292 weeks
1545.56652 -1.19535 (154*2π)/3292 weeks
1555.87503 1.52118 (155*2π)/3292 weeks
1565.45392 .94886 (156*2π)/3292 weeks
157.78722 3.17271 (157*2π)/3292 weeks
1584.66397 2.12343 (158*2π)/3292 weeks
1592.94087 -.73179 (159*2π)/3292 weeks
1602.18156 3.90967 (160*2π)/3292 weeks
1611.92595 3.18349 (161*2π)/3292 weeks
1621.0628 1.28362 (162*2π)/3292 weeks
163-.9175 3.27922 (163*2π)/3292 weeks
164-1.3132 .25695 (164*2π)/3292 weeks
165-1.3132 -.25695 (165*2π)/3292 weeks
166-.9175 -3.27922 (166*2π)/3292 weeks
1671.0628 -1.28362 (167*2π)/3292 weeks
1681.92595 -3.18349 (168*2π)/3292 weeks
1692.18156 -3.90967 (169*2π)/3292 weeks
1702.94087 .73179 (170*2π)/3292 weeks
1714.66397 -2.12343 (171*2π)/3292 weeks
172.78722 -3.17271 (172*2π)/3292 weeks
1735.45392 -.94886 (173*2π)/3292 weeks
1745.87503 -1.52118 (174*2π)/3292 weeks
1755.56652 1.19535 (175*2π)/3292 weeks
1766.82379 2.9528 (176*2π)/3292 weeks
177.09293 4.28833 (177*2π)/3292 weeks
1783.51747 2.63379 (178*2π)/3292 weeks
179-.81732 1.84094 (179*2π)/3292 weeks
1802.0945 3.24968 (180*2π)/3292 weeks
181-1.77432 .79164 (181*2π)/3292 weeks
182-.12679 3.22399 (182*2π)/3292 weeks
183-2.31901 -.70395 (183*2π)/3292 weeks
184-4.85166 -1.66254 (184*2π)/3292 weeks
185.20766 -4.954 (185*2π)/3292 weeks
1861.32393 -6.52864 (186*2π)/3292 weeks
1875.19266 -2.72672 (187*2π)/3292 weeks
1882.69452 -3.32211 (188*2π)/3292 weeks
1895.68888 1.25673 (189*2π)/3292 weeks
1902.45663 -2.83422 (190*2π)/3292 weeks
1913.11838 1.83917 (191*2π)/3292 weeks
1925.86899 -2.28154 (192*2π)/3292 weeks
1931.64888 1.35444 (193*2π)/3292 weeks
1944.60186 2.44997 (194*2π)/3292 weeks
195.72974 .90876 (195*2π)/3292 weeks
196.90491 3.47168 (196*2π)/3292 weeks
197-1.18888 -4.03937 (197*2π)/3292 weeks
198-.40597 .75587 (198*2π)/3292 weeks
1994.12587 -5.8057 (199*2π)/3292 weeks
2002.28456 -.50346 (200*2π)/3292 weeks
2017.07993 1.17018 (201*2π)/3292 weeks
202-1.16662 1.38475 (202*2π)/3292 weeks
2031.91953 .43538 (203*2π)/3292 weeks
2042.65324 -.91474 (204*2π)/3292 weeks
2051.56375 .82863 (205*2π)/3292 weeks
2061.80865 1.56714 (206*2π)/3292 weeks
207-.71825 2.54245 (207*2π)/3292 weeks
208-2.58288 -.1996 (208*2π)/3292 weeks
209-3.33051 -3.4485 (209*2π)/3292 weeks
210-.28951 -3.72534 (210*2π)/3292 weeks
211.30405 -4.6882 (211*2π)/3292 weeks
2121.76825 -5.53081 (212*2π)/3292 weeks
2133.84636 -3.60372 (213*2π)/3292 weeks
2143.98264 -2.82196 (214*2π)/3292 weeks
2152.69068 -1.47144 (215*2π)/3292 weeks
2163.98883 -1.68152 (216*2π)/3292 weeks
2174.50136 -.99593 (217*2π)/3292 weeks
218.72335 -.00238 (218*2π)/3292 weeks
2193.16515 2.01957 (219*2π)/3292 weeks
220-.56559 -3.29615 (220*2π)/3291 weeks
221.82217 -1.12469 (221*2π)/3291 weeks
222.2268 -3.8233 (222*2π)/3291 weeks
2234.34354 -2.47352 (223*2π)/3291 weeks
2243.28329 -3.90536 (224*2π)/3291 weeks
2251.44239 .04435 (225*2π)/3291 weeks
2264.44694 .58221 (226*2π)/3291 weeks
227-1.64861 -3.22467 (227*2π)/3291 weeks
2282.35165 -2.0512 (228*2π)/3291 weeks
2292.3756 -4.60915 (229*2π)/3291 weeks
2302.68715 .56447 (230*2π)/3291 weeks
231.15212 -2.19293 (231*2π)/3291 weeks
232-.26836 -4.2469 (232*2π)/3291 weeks
2332.81303 -5.3602 (233*2π)/3291 weeks
2342.63692 -6.656 (234*2π)/3291 weeks
2357.06331 -2.22854 (235*2π)/3291 weeks
2365.24303 -6.72568 (236*2π)/3291 weeks
2373.94782 .71305 (237*2π)/3291 weeks
2387.01128 -3.73121 (238*2π)/3291 weeks
2394.5766 -1.96097 (239*2π)/3291 weeks
2409.15051 .72241 (240*2π)/3291 weeks
2412.6807 1.52464 (241*2π)/3291 weeks
2425.19972 3.66245 (242*2π)/3291 weeks
2432.16078 .05204 (243*2π)/3291 weeks
244-1.97903 3.08979 (244*2π)/3291 weeks
245.92815 -2.36987 (245*2π)/3291 weeks
246-1.6831 -.89512 (246*2π)/3291 weeks
2473.65331 -5.24323 (247*2π)/3291 weeks
248-1.34539 -3.82316 (248*2π)/3291 weeks
2496.45063 -.80192 (249*2π)/3291 weeks
2502.32614 -3.89459 (250*2π)/3291 weeks
2512.88878 -1.33965 (251*2π)/3291 weeks
2523.44754 -2.73852 (252*2π)/3291 weeks
2533.0905 -.9768 (253*2π)/3291 weeks
2547.61269 -.26804 (254*2π)/3291 weeks
255-1.35547 .35051 (255*2π)/3291 weeks
2561.75528 -.1071 (256*2π)/3291 weeks
2571.37798 -1.48457 (257*2π)/3291 weeks
2582.32184 -2.0894 (258*2π)/3291 weeks
2591.98349 -5.55951 (259*2π)/3291 weeks
2604.01085 4.53974 (260*2π)/3291 weeks
261.2444 .66288 (261*2π)/3291 weeks
262-2.60899 -1.83033 (262*2π)/3291 weeks
263-2.42415 -4.75159 (263*2π)/3291 weeks
264-.82942 -1.4716 (264*2π)/3291 weeks
2652.24886 -5.26813 (265*2π)/3291 weeks
266-2.03442 -6.40826 (266*2π)/3291 weeks
267-1.37235 -3.40525 (267*2π)/3291 weeks
2681.82229 -7.17048 (268*2π)/3291 weeks
2693.45086 -8.30219 (269*2π)/3291 weeks
270.97697 -11.24163 (270*2π)/3291 weeks
2715.51503 -3.83718 (271*2π)/3291 weeks
2729.43828 -11.72912 (272*2π)/3291 weeks
2739.59653 -3.39971 (273*2π)/3291 weeks
2749.28782 -3.99864 (274*2π)/3291 weeks
2758.20919 -1.72917 (275*2π)/3291 weeks
2768.84595 3.09771 (276*2π)/3291 weeks
27711.0961 -3.67865 (277*2π)/3291 weeks
2787.23099 10.04785 (278*2π)/3291 weeks
2798.38239 5.89988 (279*2π)/3291 weeks
280-5.03698 15.89216 (280*2π)/3291 weeks
281-5.62029 4.23433 (281*2π)/3291 weeks
282-11.5177 .30169 (282*2π)/3291 weeks
283-9.75996 -1.67386 (283*2π)/3291 weeks
284-2.95611 -7.11915 (284*2π)/3291 weeks
285-10.3704 -4.92528 (285*2π)/3291 weeks
286-1.59413 -9.34499 (286*2π)/3291 weeks
287-12.84953 -6.95115 (287*2π)/3291 weeks
288-3.57614 -17.56503 (288*2π)/3291 weeks
289-1.23418 -19.5731 (289*2π)/3291 weeks
2906.30191 -14.12879 (290*2π)/3291 weeks
2918.97269 -15.72462 (291*2π)/3291 weeks
29211.54319 -9.04864 (292*2π)/3291 weeks
29310.99912 -4.73933 (293*2π)/3291 weeks
2944.0822 -3.7835 (294*2π)/3291 weeks
2959.3277 -8.65286 (295*2π)/3291 weeks
2967.42812 .21748 (296*2π)/3291 weeks
2976.00455 -6.28951 (297*2π)/3291 weeks
2986.77368 5.50887 (298*2π)/3291 weeks
2997.13108 4.21668 (299*2π)/3291 weeks
300-17.8569 4.49238 (300*2π)/3291 weeks
301-6.507 -7.3026 (301*2π)/3291 weeks
302-13.52274 -17.90507 (302*2π)/3291 weeks
303-2.19071 -17.14599 (303*2π)/3291 weeks
3046.48085 -24.07265 (304*2π)/3291 weeks
305.74709 -11.23512 (305*2π)/3291 weeks
3068.39588 -20.19828 (306*2π)/3291 weeks
3078.83716 -22.85888 (307*2π)/3291 weeks
30817.94652 -17.18557 (308*2π)/3291 weeks
30920.47621 -13.363 (309*2π)/3291 weeks
31019.90029 3.41926 (310*2π)/3291 weeks
31122.17856 -9.45437 (311*2π)/3291 weeks
3121.20445 19.8586 (312*2π)/3291 weeks
313-.02307 8.08649 (313*2π)/3291 weeks
314-14.2783 -1.45509 (314*2π)/3291 weeks
315-1.26622 -28.66231 (315*2π)/3291 weeks
3163.93542 -12.57065 (316*2π)/3291 weeks
31718.42044 10.13072 (317*2π)/3291 weeks
318-3.5401 -.61429 (318*2π)/3291 weeks
319-42.26305 7.74033 (319*2π)/3291 weeks
320-10.53128 -22.65272 (320*2π)/3291 weeks
321-67.74454 -25.93053 (321*2π)/3291 weeks
3228.73238 -73.88747 (322*2π)/3291 weeks
323-11.51602 -73.09513 (323*2π)/3291 weeks
3244.50243 -39.5673 (324*2π)/3291 weeks
3258.76987 -91.1108 (325*2π)/3291 weeks
32615.28419 -93.59621 (326*2π)/3291 weeks
32760.87916 -160.3012 (327*2π)/3291 weeks



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