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Fourier Analysis of RUSL (DIREXION DAILY RUSSIA BULL 3X SHARES DIREXION DAILY RUSSIA BULL 3X SHARES)


RUSL (DIREXION DAILY RUSSIA BULL 3X SHARES DIREXION DAILY RUSSIA BULL 3X SHARES) appears to have interesting cyclic behaviour every 32 weeks (81.4657*sine), 29 weeks (73.5649*sine), and 35 weeks (65.7935*sine).

RUSL (DIREXION DAILY RUSSIA BULL 3X SHARES DIREXION DAILY RUSSIA BULL 3X SHARES) has an average price of 240.56 (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 1/16/2018 for RUSL (DIREXION DAILY RUSSIA BULL 3X SHARES DIREXION DAILY RUSSIA BULL 3X SHARES), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0240.5647   0 
1146.7102 211.6318 (1*2π)/348348 weeks
290.28488 67.39425 (2*2π)/348174 weeks
385.76659 91.16454 (3*2π)/348116 weeks
468.69767 72.47851 (4*2π)/34887 weeks
562.09777 78.5985 (5*2π)/34870 weeks
648.37422 63.00504 (6*2π)/34858 weeks
744.05586 48.91526 (7*2π)/34850 weeks
877.27491 50.70844 (8*2π)/34844 weeks
945.70392 87.43687 (9*2π)/34839 weeks
1035.15316 65.79346 (10*2π)/34835 weeks
1128.22579 81.4657 (11*2π)/34832 weeks
129.02533 73.56487 (12*2π)/34829 weeks
13.66003 58.45927 (13*2π)/34827 weeks
14-1.80271 44.5547 (14*2π)/34825 weeks
1516.02602 34.82811 (15*2π)/34823 weeks
1615.64315 48.82112 (16*2π)/34822 weeks
1710.4357 52.68084 (17*2π)/34820 weeks
18-1.94809 55.12753 (18*2π)/34819 weeks
19-6.74874 39.2356 (19*2π)/34818 weeks
20-4.81002 42.07043 (20*2π)/34817 weeks
21-15.95076 35.43432 (21*2π)/34817 weeks
22-15.40174 25.44047 (22*2π)/34816 weeks
23-13.43369 17.77366 (23*2π)/34815 weeks
24-6.65033 14.14311 (24*2π)/34815 weeks
25-3.14467 14.86209 (25*2π)/34814 weeks
26-4.76219 13.76091 (26*2π)/34813 weeks
27-2.06689 9.21455 (27*2π)/34813 weeks
283.22129 8.36083 (28*2π)/34812 weeks
292.62528 13.79544 (29*2π)/34812 weeks
304.96033 8.55013 (30*2π)/34812 weeks
314.14986 18.05975 (31*2π)/34811 weeks
32-1.6889 11.62816 (32*2π)/34811 weeks
33-1.00808 9.39739 (33*2π)/34811 weeks
343.03994 6.3976 (34*2π)/34810 weeks
352.48319 8.93451 (35*2π)/34810 weeks
363.84239 3.9139 (36*2π)/34810 weeks
377.36194 7.68783 (37*2π)/3489 weeks
383.51586 6.85532 (38*2π)/3489 weeks
395.26428 4.81514 (39*2π)/3489 weeks
406.62848 2.00205 (40*2π)/3489 weeks
4110.56522 3.34292 (41*2π)/3488 weeks
4210.54545 2.65427 (42*2π)/3488 weeks
4314.15707 2.207 (43*2π)/3488 weeks
4418.61523 6.8858 (44*2π)/3488 weeks
4514.62281 12.31057 (45*2π)/3488 weeks
4615.16881 10.39733 (46*2π)/3488 weeks
4715.17781 14.98829 (47*2π)/3487 weeks
4812.18849 13.2305 (48*2π)/3487 weeks
4914.22071 15.26488 (49*2π)/3487 weeks
5011.68096 16.22459 (50*2π)/3487 weeks
5113.45666 17.92553 (51*2π)/3487 weeks
527.96232 24.40024 (52*2π)/3487 weeks
532.67772 19.93808 (53*2π)/3487 weeks
54.07941 20.14292 (54*2π)/3486 weeks
55-1.99538 14.15275 (55*2π)/3486 weeks
56-.32041 14.60175 (56*2π)/3486 weeks
57-2.93125 12.17199 (57*2π)/3486 weeks
58-1.41985 9.15729 (58*2π)/3486 weeks
59-1.82056 10.05156 (59*2π)/3486 weeks
60-1.80574 6.17447 (60*2π)/3486 weeks
611.11825 7.23683 (61*2π)/3486 weeks
62.1722 5.89237 (62*2π)/3486 weeks
63.43752 5.79934 (63*2π)/3486 weeks
641.50985 4.4314 (64*2π)/3485 weeks
652.16404 3.01951 (65*2π)/3485 weeks
663.77209 2.98482 (66*2π)/3485 weeks
674.93739 4.53679 (67*2π)/3485 weeks
684.388 4.21927 (68*2π)/3485 weeks
694.42118 4.31171 (69*2π)/3485 weeks
705.89979 3.07281 (70*2π)/3485 weeks
717.46976 4.35904 (71*2π)/3485 weeks
727.36461 6.38116 (72*2π)/3485 weeks
733.98707 7.31776 (73*2π)/3485 weeks
744.60965 2.7215 (74*2π)/3485 weeks
757.68721 4.13204 (75*2π)/3485 weeks
767.31458 5.89184 (76*2π)/3485 weeks
777.7937 5.53781 (77*2π)/3485 weeks
788.84106 7.32951 (78*2π)/3484 weeks
796.31866 9.8621 (79*2π)/3484 weeks
805.54659 7.43045 (80*2π)/3484 weeks
816.15318 8.95625 (81*2π)/3484 weeks
824.51264 9.1096 (82*2π)/3484 weeks
834.01994 8.81778 (83*2π)/3484 weeks
841.98828 9.30031 (84*2π)/3484 weeks
851.31248 5.37143 (85*2π)/3484 weeks
863.8605 6.27178 (86*2π)/3484 weeks
874.23327 5.90361 (87*2π)/3484 weeks
884.53467 7.93117 (88*2π)/3484 weeks
892.9657 7.52251 (89*2π)/3484 weeks
903.00357 8.14161 (90*2π)/3484 weeks
911.13345 7.81825 (91*2π)/3484 weeks
92.84968 7.16471 (92*2π)/3484 weeks
93.40921 7.39651 (93*2π)/3484 weeks
94-1.96121 6.65376 (94*2π)/3484 weeks
95-1.33969 3.22493 (95*2π)/3484 weeks
96.20191 3.02279 (96*2π)/3484 weeks
97.31657 3.31763 (97*2π)/3484 weeks
98-.51799 2.72025 (98*2π)/3484 weeks
99-.1165 2.58729 (99*2π)/3484 weeks
100-.57608 .52582 (100*2π)/3483 weeks
1011.35226 -.21548 (101*2π)/3483 weeks
1021.6451 -.55457 (102*2π)/3483 weeks
1033.58065 -1.02695 (103*2π)/3483 weeks
1043.22572 1.45142 (104*2π)/3483 weeks
1052.16744 -.02306 (105*2π)/3483 weeks
1063.35922 -.83918 (106*2π)/3483 weeks
1075.27842 -1.19546 (107*2π)/3483 weeks
1086.24529 1.20561 (108*2π)/3483 weeks
1094.25333 1.98757 (109*2π)/3483 weeks
1103.4753 1.20853 (110*2π)/3483 weeks
1114.52942 -.31047 (111*2π)/3483 weeks
1124.66062 .38758 (112*2π)/3483 weeks
1135.8826 .16008 (113*2π)/3483 weeks
1145.49735 1.23594 (114*2π)/3483 weeks
1155.84654 .04945 (115*2π)/3483 weeks
1167.30771 2.20744 (116*2π)/3483 weeks
1175.53998 2.51212 (117*2π)/3483 weeks
1185.03791 2.99508 (118*2π)/3483 weeks
1193.67053 2.18018 (119*2π)/3483 weeks
1204.13929 1.1771 (120*2π)/3483 weeks
1213.4909 1.40359 (121*2π)/3483 weeks
1223.76203 -.09871 (122*2π)/3483 weeks
1234.60139 -1.01361 (123*2π)/3483 weeks
1246.8392 -.53044 (124*2π)/3483 weeks
1256.15246 .39345 (125*2π)/3483 weeks
1267.09127 -.09334 (126*2π)/3483 weeks
1277.56418 .6952 (127*2π)/3483 weeks
1288.21701 2.28382 (128*2π)/3483 weeks
1296.24181 3.43268 (129*2π)/3483 weeks
1305.59157 3.05382 (130*2π)/3483 weeks
1315.24374 2.4904 (131*2π)/3483 weeks
1325.37001 2.97364 (132*2π)/3483 weeks
1334.72671 2.11699 (133*2π)/3483 weeks
1346.15705 3.19789 (134*2π)/3483 weeks
1352.45486 4.00133 (135*2π)/3483 weeks
1362.66493 .59294 (136*2π)/3483 weeks
1373.40152 .03365 (137*2π)/3483 weeks
1385.87759 -.05582 (138*2π)/3483 weeks
1394.90919 1.29399 (139*2π)/3483 weeks
1406.02675 1.20019 (140*2π)/3482 weeks
1415.04255 1.85185 (141*2π)/3482 weeks
1424.78772 1.51311 (142*2π)/3482 weeks
1434.43298 1.80029 (143*2π)/3482 weeks
1443.91105 1.4637 (144*2π)/3482 weeks
1454.30256 .63112 (145*2π)/3482 weeks
1463.94947 1.21098 (146*2π)/3482 weeks
1474.70405 .56918 (147*2π)/3482 weeks
1483.92147 1.14753 (148*2π)/3482 weeks
1494.1592 -.3543 (149*2π)/3482 weeks
1504.02875 .00481 (150*2π)/3482 weeks
1513.72634 -1.85635 (151*2π)/3482 weeks
1526.31284 -2.0517 (152*2π)/3482 weeks
1537.51275 -.90615 (153*2π)/3482 weeks
1547.71658 .56293 (154*2π)/3482 weeks
1556.75227 1.45552 (155*2π)/3482 weeks
1566.9562 .90314 (156*2π)/3482 weeks
1576.89544 2.62258 (157*2π)/3482 weeks
1585.85182 2.64555 (158*2π)/3482 weeks
1595.12269 3.35296 (159*2π)/3482 weeks
1604.32654 2.17583 (160*2π)/3482 weeks
1614.58883 3.07617 (161*2π)/3482 weeks
1622.32412 1.83447 (162*2π)/3482 weeks
1632.89602 .49044 (163*2π)/3482 weeks
1642.96553 -.11624 (164*2π)/3482 weeks
1653.58071 -.59752 (165*2π)/3482 weeks
1664.61707 -1.08813 (166*2π)/3482 weeks
1674.66836 .33222 (167*2π)/3482 weeks
1683.56445 .38599 (168*2π)/3482 weeks
1693.61839 -1.70614 (169*2π)/3482 weeks
1704.83525 -1.65108 (170*2π)/3482 weeks
1715.43746 -1.02326 (171*2π)/3482 weeks
1725.24723 -1.67234 (172*2π)/3482 weeks
1736.67615 -.82205 (173*2π)/3482 weeks
1746.46449   (174*2π)/3482 weeks
1756.67615 .82205 (175*2π)/3482 weeks
1765.24723 1.67234 (176*2π)/3482 weeks
1775.43746 1.02326 (177*2π)/3482 weeks
1784.83525 1.65108 (178*2π)/3482 weeks
1793.61839 1.70614 (179*2π)/3482 weeks
1803.56445 -.38599 (180*2π)/3482 weeks
1814.66836 -.33222 (181*2π)/3482 weeks
1824.61707 1.08813 (182*2π)/3482 weeks
1833.58071 .59752 (183*2π)/3482 weeks
1842.96553 .11624 (184*2π)/3482 weeks
1852.89602 -.49044 (185*2π)/3482 weeks
1862.32412 -1.83447 (186*2π)/3482 weeks
1874.58883 -3.07617 (187*2π)/3482 weeks
1884.32654 -2.17583 (188*2π)/3482 weeks
1895.12269 -3.35296 (189*2π)/3482 weeks
1905.85182 -2.64555 (190*2π)/3482 weeks
1916.89544 -2.62258 (191*2π)/3482 weeks
1926.9562 -.90314 (192*2π)/3482 weeks
1936.75227 -1.45552 (193*2π)/3482 weeks
1947.71658 -.56293 (194*2π)/3482 weeks
1957.51275 .90615 (195*2π)/3482 weeks
1966.31284 2.0517 (196*2π)/3482 weeks
1973.72634 1.85635 (197*2π)/3482 weeks
1984.02875 -.00481 (198*2π)/3482 weeks
1994.1592 .3543 (199*2π)/3482 weeks
2003.92147 -1.14753 (200*2π)/3482 weeks
2014.70405 -.56918 (201*2π)/3482 weeks
2023.94947 -1.21098 (202*2π)/3482 weeks
2034.30256 -.63112 (203*2π)/3482 weeks
2043.91105 -1.4637 (204*2π)/3482 weeks
2054.43298 -1.80029 (205*2π)/3482 weeks
2064.78772 -1.51311 (206*2π)/3482 weeks
2075.04255 -1.85185 (207*2π)/3482 weeks
2086.02675 -1.20019 (208*2π)/3482 weeks
2094.90919 -1.29399 (209*2π)/3482 weeks
2105.87759 .05582 (210*2π)/3482 weeks
2113.40152 -.03365 (211*2π)/3482 weeks
2122.66493 -.59294 (212*2π)/3482 weeks
2132.45486 -4.00133 (213*2π)/3482 weeks
2146.15705 -3.19789 (214*2π)/3482 weeks
2154.72671 -2.11699 (215*2π)/3482 weeks
2165.37001 -2.97364 (216*2π)/3482 weeks
2175.24374 -2.4904 (217*2π)/3482 weeks
2185.59157 -3.05382 (218*2π)/3482 weeks
2196.24181 -3.43268 (219*2π)/3482 weeks
2208.21701 -2.28382 (220*2π)/3482 weeks
2217.56418 -.6952 (221*2π)/3482 weeks
2227.09127 .09334 (222*2π)/3482 weeks
2236.15246 -.39345 (223*2π)/3482 weeks
2246.8392 .53044 (224*2π)/3482 weeks
2254.60139 1.01361 (225*2π)/3482 weeks
2263.76203 .09871 (226*2π)/3482 weeks
2273.4909 -1.40359 (227*2π)/3482 weeks
2284.13929 -1.1771 (228*2π)/3482 weeks
2293.67053 -2.18018 (229*2π)/3482 weeks
2305.03791 -2.99508 (230*2π)/3482 weeks
2315.53998 -2.51212 (231*2π)/3482 weeks
2327.30771 -2.20744 (232*2π)/3482 weeks
2335.84654 -.04945 (233*2π)/3481 weeks
2345.49735 -1.23594 (234*2π)/3481 weeks
2355.8826 -.16008 (235*2π)/3481 weeks
2364.66062 -.38758 (236*2π)/3481 weeks
2374.52942 .31047 (237*2π)/3481 weeks
2383.4753 -1.20853 (238*2π)/3481 weeks
2394.25333 -1.98757 (239*2π)/3481 weeks
2406.24529 -1.20561 (240*2π)/3481 weeks
2415.27842 1.19546 (241*2π)/3481 weeks
2423.35922 .83918 (242*2π)/3481 weeks
2432.16744 .02306 (243*2π)/3481 weeks
2443.22572 -1.45142 (244*2π)/3481 weeks
2453.58065 1.02695 (245*2π)/3481 weeks
2461.6451 .55457 (246*2π)/3481 weeks
2471.35226 .21548 (247*2π)/3481 weeks
248-.57608 -.52582 (248*2π)/3481 weeks
249-.1165 -2.58729 (249*2π)/3481 weeks
250-.51799 -2.72025 (250*2π)/3481 weeks
251.31657 -3.31763 (251*2π)/3481 weeks
252.20191 -3.02279 (252*2π)/3481 weeks
253-1.33969 -3.22493 (253*2π)/3481 weeks
254-1.96121 -6.65376 (254*2π)/3481 weeks
255.40921 -7.39651 (255*2π)/3481 weeks
256.84968 -7.16471 (256*2π)/3481 weeks
2571.13345 -7.81825 (257*2π)/3481 weeks
2583.00357 -8.14161 (258*2π)/3481 weeks
2592.9657 -7.52251 (259*2π)/3481 weeks
2604.53467 -7.93117 (260*2π)/3481 weeks
2614.23327 -5.90361 (261*2π)/3481 weeks
2623.8605 -6.27178 (262*2π)/3481 weeks
2631.31248 -5.37143 (263*2π)/3481 weeks
2641.98828 -9.30031 (264*2π)/3481 weeks
2654.01994 -8.81778 (265*2π)/3481 weeks
2664.51264 -9.1096 (266*2π)/3481 weeks
2676.15318 -8.95625 (267*2π)/3481 weeks
2685.54659 -7.43045 (268*2π)/3481 weeks
2696.31866 -9.8621 (269*2π)/3481 weeks
2708.84106 -7.32951 (270*2π)/3481 weeks
2717.7937 -5.53781 (271*2π)/3481 weeks
2727.31458 -5.89184 (272*2π)/3481 weeks
2737.68721 -4.13204 (273*2π)/3481 weeks
2744.60965 -2.7215 (274*2π)/3481 weeks
2753.98707 -7.31776 (275*2π)/3481 weeks
2767.36461 -6.38116 (276*2π)/3481 weeks
2777.46976 -4.35904 (277*2π)/3481 weeks
2785.89979 -3.07281 (278*2π)/3481 weeks
2794.42118 -4.31171 (279*2π)/3481 weeks
2804.388 -4.21927 (280*2π)/3481 weeks
2814.93739 -4.53679 (281*2π)/3481 weeks
2823.77209 -2.98482 (282*2π)/3481 weeks
2832.16404 -3.01951 (283*2π)/3481 weeks
2841.50985 -4.4314 (284*2π)/3481 weeks
285.43752 -5.79934 (285*2π)/3481 weeks
286.1722 -5.89237 (286*2π)/3481 weeks
2871.11825 -7.23683 (287*2π)/3481 weeks
288-1.80574 -6.17447 (288*2π)/3481 weeks
289-1.82056 -10.05156 (289*2π)/3481 weeks
290-1.41985 -9.15729 (290*2π)/3481 weeks
291-2.93125 -12.17199 (291*2π)/3481 weeks
292-.32041 -14.60175 (292*2π)/3481 weeks
293-1.99538 -14.15275 (293*2π)/3481 weeks
294.07941 -20.14292 (294*2π)/3481 weeks
2952.67772 -19.93808 (295*2π)/3481 weeks
2967.96232 -24.40024 (296*2π)/3481 weeks
29713.45666 -17.92553 (297*2π)/3481 weeks
29811.68096 -16.22459 (298*2π)/3481 weeks
29914.22071 -15.26488 (299*2π)/3481 weeks
30012.18849 -13.2305 (300*2π)/3481 weeks
30115.17781 -14.98829 (301*2π)/3481 weeks
30215.16881 -10.39733 (302*2π)/3481 weeks
30314.62281 -12.31057 (303*2π)/3481 weeks
30418.61523 -6.8858 (304*2π)/3481 weeks
30514.15707 -2.207 (305*2π)/3481 weeks
30610.54545 -2.65427 (306*2π)/3481 weeks
30710.56522 -3.34292 (307*2π)/3481 weeks
3086.62848 -2.00205 (308*2π)/3481 weeks
3095.26428 -4.81514 (309*2π)/3481 weeks
3103.51586 -6.85532 (310*2π)/3481 weeks
3117.36194 -7.68783 (311*2π)/3481 weeks
3123.84239 -3.9139 (312*2π)/3481 weeks
3132.48319 -8.93451 (313*2π)/3481 weeks
3143.03994 -6.3976 (314*2π)/3481 weeks
315-1.00808 -9.39739 (315*2π)/3481 weeks
316-1.6889 -11.62816 (316*2π)/3481 weeks
3174.14986 -18.05975 (317*2π)/3481 weeks
3184.96033 -8.55013 (318*2π)/3481 weeks
3192.62528 -13.79544 (319*2π)/3481 weeks
3203.22129 -8.36083 (320*2π)/3481 weeks
321-2.06689 -9.21455 (321*2π)/3481 weeks
322-4.76219 -13.76091 (322*2π)/3481 weeks
323-3.14467 -14.86209 (323*2π)/3481 weeks
324-6.65033 -14.14311 (324*2π)/3481 weeks
325-13.43369 -17.77366 (325*2π)/3481 weeks
326-15.40174 -25.44047 (326*2π)/3481 weeks
327-15.95076 -35.43432 (327*2π)/3481 weeks
328-4.81002 -42.07043 (328*2π)/3481 weeks
329-6.74874 -39.2356 (329*2π)/3481 weeks
330-1.94809 -55.12753 (330*2π)/3481 weeks
33110.4357 -52.68084 (331*2π)/3481 weeks
33215.64315 -48.82112 (332*2π)/3481 weeks
33316.02602 -34.82811 (333*2π)/3481 weeks
334-1.80271 -44.5547 (334*2π)/3481 weeks
335.66003 -58.45927 (335*2π)/3481 weeks
3369.02533 -73.56487 (336*2π)/3481 weeks
33728.22579 -81.4657 (337*2π)/3481 weeks
33835.15316 -65.79346 (338*2π)/3481 weeks
33945.70392 -87.43687 (339*2π)/3481 weeks
34077.27491 -50.70844 (340*2π)/3481 weeks
34144.05586 -48.91526 (341*2π)/3481 weeks
34248.37422 -63.00504 (342*2π)/3481 weeks
34362.09777 -78.5985 (343*2π)/3481 weeks
34468.69767 -72.47851 (344*2π)/3481 weeks
34585.76659 -91.16454 (345*2π)/3481 weeks
34690.28488 -67.39425 (346*2π)/3481 weeks



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