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Fourier Analysis of RUSL (Direxion Daily Russia Bull 3X Shares)

RUSL (Direxion Daily Russia Bull 3X Shares) appears to have interesting cyclic behaviour every 30 weeks (73.4494*sine), 33 weeks (71.5942*sine), and 36 weeks (68.8699*sine).

RUSL (Direxion Daily Russia Bull 3X Shares) has an average price of 230.69 (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 4/23/2018 for RUSL (Direxion Daily Russia Bull 3X Shares), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0230.6908   0
1151.7897 203.7296 (1*2π)/362362 weeks
280.62451 65.35427 (2*2π)/362181 weeks
386.83807 86.1895 (3*2π)/362121 weeks
465.55627 70.01031 (4*2π)/36291 weeks
563.93819 71.97851 (5*2π)/36272 weeks
645.26463 61.18786 (6*2π)/36260 weeks
740.57342 51.57646 (7*2π)/36252 weeks
860.5381 37.28715 (8*2π)/36245 weeks
960.18529 81.63229 (9*2π)/36240 weeks
1029.22798 68.86987 (10*2π)/36236 weeks
1136.97909 71.59424 (11*2π)/36233 weeks
1215.42304 73.44935 (12*2π)/36230 weeks
132.1744 62.19749 (13*2π)/36228 weeks
14-1.19257 49.97588 (14*2π)/36226 weeks
151.49781 34.05085 (15*2π)/36224 weeks
1618.32156 39.66586 (16*2π)/36223 weeks
1712.34561 46.97288 (17*2π)/36221 weeks
186.52907 51.18427 (18*2π)/36220 weeks
19-7.55312 49.80015 (19*2π)/36219 weeks
20-5.11456 37.29385 (20*2π)/36218 weeks
21-6.93935 41.25476 (21*2π)/36217 weeks
22-15.63418 32.33191 (22*2π)/36216 weeks
23-14.59513 23.83462 (23*2π)/36216 weeks
24-12.55309 16.66057 (24*2π)/36215 weeks
25-6.32888 13.76746 (25*2π)/36214 weeks
26-3.11686 14.40386 (26*2π)/36214 weeks
27-4.61673 13.50166 (27*2π)/36213 weeks
28-2.51706 9.1361 (28*2π)/36213 weeks
292.01126 7.92611 (29*2π)/36212 weeks
303.36888 13.18736 (30*2π)/36212 weeks
312.38009 8.50099 (31*2π)/36212 weeks
326.29725 15.97384 (32*2π)/36211 weeks
33-2.26972 13.43731 (33*2π)/36211 weeks
34-.66411 10.25922 (34*2π)/36211 weeks
35.8225 6.28178 (35*2π)/36210 weeks
363.54666 8.3758 (36*2π)/36210 weeks
371.10877 5.92536 (37*2π)/36210 weeks
386.4572 5.26459 (38*2π)/36210 weeks
394.66359 8.80637 (39*2π)/3629 weeks
403.92507 5.36079 (40*2π)/3629 weeks
414.73701 4.43135 (41*2π)/3629 weeks
428.07846 2.22912 (42*2π)/3629 weeks
439.78949 4.46761 (43*2π)/3628 weeks
4411.2439 2.89754 (44*2π)/3628 weeks
4515.30062 2.98527 (45*2π)/3628 weeks
4618.18003 8.4482 (46*2π)/3628 weeks
4713.3501 11.32221 (47*2π)/3628 weeks
4815.01303 10.36002 (48*2π)/3628 weeks
4914.01222 14.69723 (49*2π)/3627 weeks
5011.90311 12.5828 (50*2π)/3627 weeks
5113.61691 14.72106 (51*2π)/3627 weeks
5211.19971 15.50175 (52*2π)/3627 weeks
5312.75093 16.83377 (53*2π)/3627 weeks
548.51023 23.1649 (54*2π)/3627 weeks
552.48414 19.49833 (55*2π)/3627 weeks
561.04911 19.47579 (56*2π)/3626 weeks
57-2.48814 14.7479 (57*2π)/3626 weeks
58.10146 13.65757 (58*2π)/3626 weeks
59-2.52233 12.91604 (59*2π)/3626 weeks
60-2.17971 9.60711 (60*2π)/3626 weeks
61-.56132 9.92321 (61*2π)/3626 weeks
62-2.31142 7.66663 (62*2π)/3626 weeks
63.87367 5.69266 (63*2π)/3626 weeks
64.00397 6.85288 (64*2π)/3626 weeks
65.92134 5.74529 (65*2π)/3626 weeks
66.56352 4.65573 (66*2π)/3625 weeks
671.34268 4.28998 (67*2π)/3625 weeks
682.99279 3.19188 (68*2π)/3625 weeks
694.52779 3.22636 (69*2π)/3625 weeks
704.53434 4.71097 (70*2π)/3625 weeks
714.60218 4.1598 (71*2π)/3625 weeks
724.32715 3.92612 (72*2π)/3625 weeks
736.19523 3.24648 (73*2π)/3625 weeks
747.45767 4.57907 (74*2π)/3625 weeks
757.19041 6.40514 (75*2π)/3625 weeks
763.82927 6.8156 (76*2π)/3625 weeks
774.74207 2.57593 (77*2π)/3625 weeks
787.5148 3.90098 (78*2π)/3625 weeks
797.23118 5.58842 (79*2π)/3625 weeks
807.45988 5.19993 (80*2π)/3625 weeks
818.51167 6.60705 (81*2π)/3624 weeks
826.92432 9.33529 (82*2π)/3624 weeks
835.01454 7.30452 (83*2π)/3624 weeks
846.244 8.02496 (84*2π)/3624 weeks
854.72898 8.78894 (85*2π)/3624 weeks
863.99026 8.37305 (86*2π)/3624 weeks
873.17736 9.00234 (87*2π)/3624 weeks
88.73945 6.858 (88*2π)/3624 weeks
893.62389 4.90263 (89*2π)/3624 weeks
903.47225 5.70553 (90*2π)/3624 weeks
914.7393 6.26981 (91*2π)/3624 weeks
923.34428 7.75212 (92*2π)/3624 weeks
933.09177 7.10672 (93*2π)/3624 weeks
942.30689 8.07156 (94*2π)/3624 weeks
951.16147 7.05263 (95*2π)/3624 weeks
96.90827 6.63817 (96*2π)/3624 weeks
97.06284 7.02148 (97*2π)/3624 weeks
98-2.22414 5.54128 (98*2π)/3624 weeks
99-.84813 2.91538 (99*2π)/3624 weeks
100.36113 2.94295 (100*2π)/3624 weeks
101.37939 3.17638 (101*2π)/3624 weeks
102-.37415 2.47058 (102*2π)/3624 weeks
103-.02916 2.45059 (103*2π)/3624 weeks
104-.44747 .52756 (104*2π)/3623 weeks
1051.34586 -.29764 (105*2π)/3623 weeks
1061.59236 -.49002 (106*2π)/3623 weeks
1073.10884 -1.1545 (107*2π)/3623 weeks
1083.65352 1.2038 (108*2π)/3623 weeks
1092.16317 .30068 (109*2π)/3623 weeks
1103.1354 -.86754 (110*2π)/3623 weeks
1114.36871 -1.49307 (111*2π)/3623 weeks
1126.0633 .08855 (112*2π)/3623 weeks
1134.75588 1.9228 (113*2π)/3623 weeks
1143.67341 1.25981 (114*2π)/3623 weeks
1153.3186 -.14998 (115*2π)/3623 weeks
1164.70177 .15761 (116*2π)/3623 weeks
1174.65044 -.31113 (117*2π)/3623 weeks
1185.55072 .63374 (118*2π)/3623 weeks
1194.67873 .74223 (119*2π)/3623 weeks
1206.24934 .21595 (120*2π)/3623 weeks
1216.00748 2.76355 (121*2π)/3623 weeks
1225.11997 2.4686 (122*2π)/3623 weeks
1234.27995 2.98813 (123*2π)/3623 weeks
1243.36733 1.89658 (124*2π)/3623 weeks
1253.99544 1.29584 (125*2π)/3623 weeks
1263.1371 1.23677 (126*2π)/3623 weeks
1273.59957 -.04371 (127*2π)/3623 weeks
1284.4246 -.89817 (128*2π)/3623 weeks
1296.51347 -.36087 (129*2π)/3623 weeks
1305.8813 .48893 (130*2π)/3623 weeks
1316.65794 -.0668 (131*2π)/3623 weeks
1327.11474 .70476 (132*2π)/3623 weeks
1337.82717 1.93295 (133*2π)/3623 weeks
1346.29288 3.50474 (134*2π)/3623 weeks
1355.52479 3.03874 (135*2π)/3623 weeks
1365.03786 2.6254 (136*2π)/3623 weeks
1375.4032 2.61738 (137*2π)/3623 weeks
1384.46732 2.49599 (138*2π)/3623 weeks
1395.57724 2.04177 (139*2π)/3623 weeks
1404.1482 4.55645 (140*2π)/3623 weeks
1411.80308 1.73876 (141*2π)/3623 weeks
1423.33095 .51735 (142*2π)/3623 weeks
1434.25877 -.72825 (143*2π)/3623 weeks
1445.66886 1.01656 (144*2π)/3623 weeks
1454.79686 .5924 (145*2π)/3622 weeks
1465.44454 1.76583 (146*2π)/3622 weeks
1474.66417 1.74969 (147*2π)/3622 weeks
1484.68243 1.54307 (148*2π)/3622 weeks
1494.14792 1.63329 (149*2π)/3622 weeks
1503.65942 1.20335 (150*2π)/3622 weeks
1514.26747 .65611 (151*2π)/3622 weeks
1523.62078 .99099 (152*2π)/3622 weeks
1534.48453 .67866 (153*2π)/3622 weeks
1543.66242 1.11645 (154*2π)/3622 weeks
1553.98161 -.27897 (155*2π)/3622 weeks
1563.87727 .07125 (156*2π)/3622 weeks
1573.4487 -1.51296 (157*2π)/3622 weeks
1585.86793 -2.0085 (158*2π)/3622 weeks
1597.055 -1.02085 (159*2π)/3622 weeks
1607.39901 .32321 (160*2π)/3622 weeks
1616.72715 1.41265 (161*2π)/3622 weeks
1626.31025 .92955 (162*2π)/3622 weeks
1637.03393 2.1078 (163*2π)/3622 weeks
1645.80568 2.62636 (164*2π)/3622 weeks
1655.53256 2.86336 (165*2π)/3622 weeks
1664.02624 2.54807 (166*2π)/3622 weeks
1674.53752 2.12333 (167*2π)/3622 weeks
1682.83705 3.05641 (168*2π)/3622 weeks
1692.38835 1.0669 (169*2π)/3622 weeks
1702.89889 .52139 (170*2π)/3622 weeks
1713.18673 -.27817 (171*2π)/3622 weeks
1723.64154 -.65468 (172*2π)/3622 weeks
1734.97003 -.53622 (173*2π)/3622 weeks
1744.3366 .40908 (174*2π)/3622 weeks
1753.14486 .10024 (175*2π)/3622 weeks
1763.96829 -1.68228 (176*2π)/3622 weeks
1774.87488 -1.55061 (177*2π)/3622 weeks
1785.24127 -.9023 (178*2π)/3622 weeks
1795.23597 -1.68021 (179*2π)/3622 weeks
1806.44085 -.74559 (180*2π)/3622 weeks
1816.22778   (181*2π)/3622 weeks
1826.44085 .74559 (182*2π)/3622 weeks
1835.23597 1.68021 (183*2π)/3622 weeks
1845.24127 .9023 (184*2π)/3622 weeks
1854.87488 1.55061 (185*2π)/3622 weeks
1863.96829 1.68228 (186*2π)/3622 weeks
1873.14486 -.10024 (187*2π)/3622 weeks
1884.3366 -.40908 (188*2π)/3622 weeks
1894.97003 .53622 (189*2π)/3622 weeks
1903.64154 .65468 (190*2π)/3622 weeks
1913.18673 .27817 (191*2π)/3622 weeks
1922.89889 -.52139 (192*2π)/3622 weeks
1932.38835 -1.0669 (193*2π)/3622 weeks
1942.83705 -3.05641 (194*2π)/3622 weeks
1954.53752 -2.12333 (195*2π)/3622 weeks
1964.02624 -2.54807 (196*2π)/3622 weeks
1975.53256 -2.86336 (197*2π)/3622 weeks
1985.80568 -2.62636 (198*2π)/3622 weeks
1997.03393 -2.1078 (199*2π)/3622 weeks
2006.31025 -.92955 (200*2π)/3622 weeks
2016.72715 -1.41265 (201*2π)/3622 weeks
2027.39901 -.32321 (202*2π)/3622 weeks
2037.055 1.02085 (203*2π)/3622 weeks
2045.86793 2.0085 (204*2π)/3622 weeks
2053.4487 1.51296 (205*2π)/3622 weeks
2063.87727 -.07125 (206*2π)/3622 weeks
2073.98161 .27897 (207*2π)/3622 weeks
2083.66242 -1.11645 (208*2π)/3622 weeks
2094.48453 -.67866 (209*2π)/3622 weeks
2103.62078 -.99099 (210*2π)/3622 weeks
2114.26747 -.65611 (211*2π)/3622 weeks
2123.65942 -1.20335 (212*2π)/3622 weeks
2134.14792 -1.63329 (213*2π)/3622 weeks
2144.68243 -1.54307 (214*2π)/3622 weeks
2154.66417 -1.74969 (215*2π)/3622 weeks
2165.44454 -1.76583 (216*2π)/3622 weeks
2174.79686 -.5924 (217*2π)/3622 weeks
2185.66886 -1.01656 (218*2π)/3622 weeks
2194.25877 .72825 (219*2π)/3622 weeks
2203.33095 -.51735 (220*2π)/3622 weeks
2211.80308 -1.73876 (221*2π)/3622 weeks
2224.1482 -4.55645 (222*2π)/3622 weeks
2235.57724 -2.04177 (223*2π)/3622 weeks
2244.46732 -2.49599 (224*2π)/3622 weeks
2255.4032 -2.61738 (225*2π)/3622 weeks
2265.03786 -2.6254 (226*2π)/3622 weeks
2275.52479 -3.03874 (227*2π)/3622 weeks
2286.29288 -3.50474 (228*2π)/3622 weeks
2297.82717 -1.93295 (229*2π)/3622 weeks
2307.11474 -.70476 (230*2π)/3622 weeks
2316.65794 .0668 (231*2π)/3622 weeks
2325.8813 -.48893 (232*2π)/3622 weeks
2336.51347 .36087 (233*2π)/3622 weeks
2344.4246 .89817 (234*2π)/3622 weeks
2353.59957 .04371 (235*2π)/3622 weeks
2363.1371 -1.23677 (236*2π)/3622 weeks
2373.99544 -1.29584 (237*2π)/3622 weeks
2383.36733 -1.89658 (238*2π)/3622 weeks
2394.27995 -2.98813 (239*2π)/3622 weeks
2405.11997 -2.4686 (240*2π)/3622 weeks
2416.00748 -2.76355 (241*2π)/3622 weeks
2426.24934 -.21595 (242*2π)/3621 weeks
2434.67873 -.74223 (243*2π)/3621 weeks
2445.55072 -.63374 (244*2π)/3621 weeks
2454.65044 .31113 (245*2π)/3621 weeks
2464.70177 -.15761 (246*2π)/3621 weeks
2473.3186 .14998 (247*2π)/3621 weeks
2483.67341 -1.25981 (248*2π)/3621 weeks
2494.75588 -1.9228 (249*2π)/3621 weeks
2506.0633 -.08855 (250*2π)/3621 weeks
2514.36871 1.49307 (251*2π)/3621 weeks
2523.1354 .86754 (252*2π)/3621 weeks
2532.16317 -.30068 (253*2π)/3621 weeks
2543.65352 -1.2038 (254*2π)/3621 weeks
2553.10884 1.1545 (255*2π)/3621 weeks
2561.59236 .49002 (256*2π)/3621 weeks
2571.34586 .29764 (257*2π)/3621 weeks
258-.44747 -.52756 (258*2π)/3621 weeks
259-.02916 -2.45059 (259*2π)/3621 weeks
260-.37415 -2.47058 (260*2π)/3621 weeks
261.37939 -3.17638 (261*2π)/3621 weeks
262.36113 -2.94295 (262*2π)/3621 weeks
263-.84813 -2.91538 (263*2π)/3621 weeks
264-2.22414 -5.54128 (264*2π)/3621 weeks
265.06284 -7.02148 (265*2π)/3621 weeks
266.90827 -6.63817 (266*2π)/3621 weeks
2671.16147 -7.05263 (267*2π)/3621 weeks
2682.30689 -8.07156 (268*2π)/3621 weeks
2693.09177 -7.10672 (269*2π)/3621 weeks
2703.34428 -7.75212 (270*2π)/3621 weeks
2714.7393 -6.26981 (271*2π)/3621 weeks
2723.47225 -5.70553 (272*2π)/3621 weeks
2733.62389 -4.90263 (273*2π)/3621 weeks
274.73945 -6.858 (274*2π)/3621 weeks
2753.17736 -9.00234 (275*2π)/3621 weeks
2763.99026 -8.37305 (276*2π)/3621 weeks
2774.72898 -8.78894 (277*2π)/3621 weeks
2786.244 -8.02496 (278*2π)/3621 weeks
2795.01454 -7.30452 (279*2π)/3621 weeks
2806.92432 -9.33529 (280*2π)/3621 weeks
2818.51167 -6.60705 (281*2π)/3621 weeks
2827.45988 -5.19993 (282*2π)/3621 weeks
2837.23118 -5.58842 (283*2π)/3621 weeks
2847.5148 -3.90098 (284*2π)/3621 weeks
2854.74207 -2.57593 (285*2π)/3621 weeks
2863.82927 -6.8156 (286*2π)/3621 weeks
2877.19041 -6.40514 (287*2π)/3621 weeks
2887.45767 -4.57907 (288*2π)/3621 weeks
2896.19523 -3.24648 (289*2π)/3621 weeks
2904.32715 -3.92612 (290*2π)/3621 weeks
2914.60218 -4.1598 (291*2π)/3621 weeks
2924.53434 -4.71097 (292*2π)/3621 weeks
2934.52779 -3.22636 (293*2π)/3621 weeks
2942.99279 -3.19188 (294*2π)/3621 weeks
2951.34268 -4.28998 (295*2π)/3621 weeks
296.56352 -4.65573 (296*2π)/3621 weeks
297.92134 -5.74529 (297*2π)/3621 weeks
298.00397 -6.85288 (298*2π)/3621 weeks
299.87367 -5.69266 (299*2π)/3621 weeks
300-2.31142 -7.66663 (300*2π)/3621 weeks
301-.56132 -9.92321 (301*2π)/3621 weeks
302-2.17971 -9.60711 (302*2π)/3621 weeks
303-2.52233 -12.91604 (303*2π)/3621 weeks
304.10146 -13.65757 (304*2π)/3621 weeks
305-2.48814 -14.7479 (305*2π)/3621 weeks
3061.04911 -19.47579 (306*2π)/3621 weeks
3072.48414 -19.49833 (307*2π)/3621 weeks
3088.51023 -23.1649 (308*2π)/3621 weeks
30912.75093 -16.83377 (309*2π)/3621 weeks
31011.19971 -15.50175 (310*2π)/3621 weeks
31113.61691 -14.72106 (311*2π)/3621 weeks
31211.90311 -12.5828 (312*2π)/3621 weeks
31314.01222 -14.69723 (313*2π)/3621 weeks
31415.01303 -10.36002 (314*2π)/3621 weeks
31513.3501 -11.32221 (315*2π)/3621 weeks
31618.18003 -8.4482 (316*2π)/3621 weeks
31715.30062 -2.98527 (317*2π)/3621 weeks
31811.2439 -2.89754 (318*2π)/3621 weeks
3199.78949 -4.46761 (319*2π)/3621 weeks
3208.07846 -2.22912 (320*2π)/3621 weeks
3214.73701 -4.43135 (321*2π)/3621 weeks
3223.92507 -5.36079 (322*2π)/3621 weeks
3234.66359 -8.80637 (323*2π)/3621 weeks
3246.4572 -5.26459 (324*2π)/3621 weeks
3251.10877 -5.92536 (325*2π)/3621 weeks
3263.54666 -8.3758 (326*2π)/3621 weeks
327.8225 -6.28178 (327*2π)/3621 weeks
328-.66411 -10.25922 (328*2π)/3621 weeks
329-2.26972 -13.43731 (329*2π)/3621 weeks
3306.29725 -15.97384 (330*2π)/3621 weeks
3312.38009 -8.50099 (331*2π)/3621 weeks
3323.36888 -13.18736 (332*2π)/3621 weeks
3332.01126 -7.92611 (333*2π)/3621 weeks
334-2.51706 -9.1361 (334*2π)/3621 weeks
335-4.61673 -13.50166 (335*2π)/3621 weeks
336-3.11686 -14.40386 (336*2π)/3621 weeks
337-6.32888 -13.76746 (337*2π)/3621 weeks
338-12.55309 -16.66057 (338*2π)/3621 weeks
339-14.59513 -23.83462 (339*2π)/3621 weeks
340-15.63418 -32.33191 (340*2π)/3621 weeks
341-6.93935 -41.25476 (341*2π)/3621 weeks
342-5.11456 -37.29385 (342*2π)/3621 weeks
343-7.55312 -49.80015 (343*2π)/3621 weeks
3446.52907 -51.18427 (344*2π)/3621 weeks
34512.34561 -46.97288 (345*2π)/3621 weeks
34618.32156 -39.66586 (346*2π)/3621 weeks
3471.49781 -34.05085 (347*2π)/3621 weeks
348-1.19257 -49.97588 (348*2π)/3621 weeks
3492.1744 -62.19749 (349*2π)/3621 weeks
35015.42304 -73.44935 (350*2π)/3621 weeks
35136.97909 -71.59424 (351*2π)/3621 weeks
35229.22798 -68.86987 (352*2π)/3621 weeks
35360.18529 -81.63229 (353*2π)/3621 weeks
35460.5381 -37.28715 (354*2π)/3621 weeks
35540.57342 -51.57646 (355*2π)/3621 weeks
35645.26463 -61.18786 (356*2π)/3621 weeks
35763.93819 -71.97851 (357*2π)/3621 weeks
35865.55627 -70.01031 (358*2π)/3621 weeks
35986.83807 -86.1895 (359*2π)/3621 weeks
36080.62451 -65.35427 (360*2π)/3621 weeks