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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 30 weeks (82.4734*sine), 34 weeks (74.3219*sine), and 34 weeks (42.8002*cosine).

RUSL (DIREXION DAILY RUSSIA BULL 3X SHARES DIREXION DAILY RUSSIA BULL 3X SHARES) has an average price of 250.43 (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 10/16/2017 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
0250.428   0 
1141.2196 217.8911 (1*2π)/335335 weeks
2100.0112 70.75534 (2*2π)/335168 weeks
384.6833 94.35457 (3*2π)/335112 weeks
472.18934 74.8956 (4*2π)/33584 weeks
558.18859 81.83901 (5*2π)/33567 weeks
649.42803 65.40388 (6*2π)/33556 weeks
750.71626 45.34616 (7*2π)/33548 weeks
882.44924 74.30583 (8*2π)/33542 weeks
936.2056 84.19077 (9*2π)/33537 weeks
1042.80017 74.32188 (10*2π)/33534 weeks
1119.55219 82.47344 (11*2π)/33530 weeks
123.34842 69.59148 (12*2π)/33528 weeks
13-.71008 54.86007 (13*2π)/33526 weeks
145.20343 35.87012 (14*2π)/33524 weeks
1520.37676 47.52431 (15*2π)/33522 weeks
1613.55289 52.95678 (16*2π)/33521 weeks
174.10017 57.55976 (17*2π)/33520 weeks
18-10.19717 45.00148 (18*2π)/33519 weeks
19-3.97175 42.55992 (19*2π)/33518 weeks
20-15.79683 40.69379 (20*2π)/33517 weeks
21-16.79039 28.4859 (21*2π)/33516 weeks
22-14.90363 20.27449 (22*2π)/33515 weeks
23-7.66437 15.05551 (23*2π)/33515 weeks
24-3.52857 15.57813 (24*2π)/33514 weeks
25-5.13689 14.75122 (25*2π)/33513 weeks
26-2.27908 9.83616 (26*2π)/33513 weeks
273.60522 9.13198 (27*2π)/33512 weeks
281.99437 14.46324 (28*2π)/33512 weeks
296.54858 9.77624 (29*2π)/33512 weeks
302.0357 19.15161 (30*2π)/33511 weeks
31-1.05863 11.48717 (31*2π)/33511 weeks
32-.96117 8.49629 (32*2π)/33510 weeks
334.0427 7.71531 (33*2π)/33510 weeks
341.23474 8.07581 (34*2π)/33510 weeks
356.40854 4.72179 (35*2π)/33510 weeks
365.77141 9.41713 (36*2π)/3359 weeks
374.31799 5.56373 (37*2π)/3359 weeks
385.21829 4.2508 (38*2π)/3359 weeks
399.49406 2.21736 (39*2π)/3359 weeks
4010.23059 4.32605 (40*2π)/3358 weeks
4112.99908 2.90569 (41*2π)/3358 weeks
4218.55975 5.07935 (42*2π)/3358 weeks
4318.03317 12.77309 (43*2π)/3358 weeks
4415.11593 10.86159 (44*2π)/3358 weeks
4517.11988 14.47355 (45*2π)/3357 weeks
4612.56708 14.67879 (46*2π)/3357 weeks
4715.04362 15.29786 (47*2π)/3357 weeks
4812.38091 17.37676 (48*2π)/3357 weeks
4913.98841 18.42071 (49*2π)/3357 weeks
509.13961 25.71651 (50*2π)/3357 weeks
512.89599 21.1512 (51*2π)/3357 weeks
52.07098 21.24708 (52*2π)/3356 weeks
53-1.73845 14.74758 (53*2π)/3356 weeks
54-.52894 15.53479 (54*2π)/3356 weeks
55-2.93336 12.34548 (55*2π)/3356 weeks
56-.77609 9.72405 (56*2π)/3356 weeks
57-2.34746 9.92604 (57*2π)/3356 weeks
58-.6418 5.83208 (58*2π)/3356 weeks
59.44412 7.8604 (59*2π)/3356 weeks
60.81837 6.06862 (60*2π)/3356 weeks
61.42905 5.16946 (61*2π)/3355 weeks
621.39913 4.54765 (62*2π)/3355 weeks
633.28863 3.36954 (63*2π)/3355 weeks
645.18504 3.66637 (64*2π)/3355 weeks
654.60897 4.92064 (65*2π)/3355 weeks
665.04492 4.60184 (66*2π)/3355 weeks
675.11768 3.35642 (67*2π)/3355 weeks
687.33812 3.98062 (68*2π)/3355 weeks
697.86951 6.10122 (69*2π)/3355 weeks
705.5925 8.28693 (70*2π)/3355 weeks
713.71571 3.82053 (71*2π)/3355 weeks
727.87076 4.01067 (72*2π)/3355 weeks
738.02517 6.21878 (73*2π)/3355 weeks
748.07373 5.83806 (74*2π)/3355 weeks
759.33855 7.5194 (75*2π)/3354 weeks
766.98252 10.46046 (76*2π)/3354 weeks
775.90008 7.88117 (77*2π)/3354 weeks
786.52101 9.51659 (78*2π)/3354 weeks
794.78643 9.59343 (79*2π)/3354 weeks
804.31286 9.38649 (80*2π)/3354 weeks
811.70648 9.48434 (81*2π)/3354 weeks
822.31309 5.18013 (82*2π)/3354 weeks
833.86335 6.69429 (83*2π)/3354 weeks
844.96736 6.55016 (84*2π)/3354 weeks
854.05422 8.69596 (85*2π)/3354 weeks
863.37991 7.88429 (86*2π)/3354 weeks
872.51249 8.98165 (87*2π)/3354 weeks
881.28189 7.8078 (88*2π)/3354 weeks
891.03695 7.41052 (89*2π)/3354 weeks
90-.43904 7.74842 (90*2π)/3354 weeks
91-2.43313 4.63466 (91*2π)/3354 weeks
92-.25901 3.06878 (92*2π)/3354 weeks
93.42731 3.43725 (93*2π)/3354 weeks
94-.16462 3.48897 (94*2π)/3354 weeks
95.30857 2.43593 (95*2π)/3354 weeks
96-.80873 1.15842 (96*2π)/3353 weeks
971.05514 -.47363 (97*2π)/3353 weeks
981.56508 -.41328 (98*2π)/3353 weeks
993.26954 -1.24053 (99*2π)/3353 weeks
1003.77288 1.45034 (100*2π)/3353 weeks
1012.28945 .11879 (101*2π)/3353 weeks
1023.54504 -.8998 (102*2π)/3353 weeks
1035.5731 -1.30332 (103*2π)/3353 weeks
1046.55233 1.3196 (104*2π)/3353 weeks
1054.40525 1.95216 (105*2π)/3353 weeks
1063.56551 1.01859 (106*2π)/3353 weeks
1075.07927 -.22865 (107*2π)/3353 weeks
1084.91195 .09795 (108*2π)/3353 weeks
1096.31584 .48156 (109*2π)/3353 weeks
1105.4366 1.06183 (110*2π)/3353 weeks
1116.96127 .15917 (111*2π)/3353 weeks
1126.74759 3.03266 (112*2π)/3353 weeks
1135.80852 2.71295 (113*2π)/3353 weeks
1144.5253 3.12853 (114*2π)/3353 weeks
1153.90119 1.64763 (115*2π)/3353 weeks
1164.47785 1.64328 (116*2π)/3353 weeks
1173.59442 .41666 (117*2π)/3353 weeks
1184.4228 -.63256 (118*2π)/3353 weeks
1196.37065 -1.41593 (119*2π)/3353 weeks
1206.70851 .48797 (120*2π)/3353 weeks
1216.82954 -.22618 (121*2π)/3353 weeks
1227.71411 .69536 (122*2π)/3353 weeks
1238.59031 1.90921 (123*2π)/3353 weeks
1246.94179 3.83237 (124*2π)/3353 weeks
1256.01647 3.30204 (125*2π)/3353 weeks
1265.51505 2.74579 (126*2π)/3353 weeks
1275.76391 3.11037 (127*2π)/3353 weeks
1284.97018 2.3019 (128*2π)/3353 weeks
1296.49771 3.41575 (129*2π)/3353 weeks
1302.46972 4.06456 (130*2π)/3353 weeks
1313.04204 .56447 (131*2π)/3353 weeks
1323.74464 -.22092 (132*2π)/3353 weeks
1336.36579 .43011 (133*2π)/3353 weeks
1345.08504 1.01385 (134*2π)/3353 weeks
1356.19484 1.81636 (135*2π)/3352 weeks
1365.18678 1.95768 (136*2π)/3352 weeks
1375.19175 1.75164 (137*2π)/3352 weeks
1384.5759 1.79065 (138*2π)/3352 weeks
1394.0924 1.10213 (139*2π)/3352 weeks
1404.94114 1.0057 (140*2π)/3352 weeks
1414.22249 .37857 (141*2π)/3352 weeks
1424.76229 1.05652 (142*2π)/3352 weeks
1433.57964 .13661 (143*2π)/3352 weeks
1444.51518 .09466 (144*2π)/3352 weeks
1453.6192 -.78517 (145*2π)/3352 weeks
1465.95663 -2.50097 (146*2π)/3352 weeks
1477.58675 -1.37282 (147*2π)/3352 weeks
1488.13026 .22376 (148*2π)/3352 weeks
1497.3731 1.53834 (149*2π)/3352 weeks
1507.02656 .96318 (150*2π)/3352 weeks
1517.48474 2.6143 (151*2π)/3352 weeks
1526.18678 2.83487 (152*2π)/3352 weeks
1535.52984 3.53109 (153*2π)/3352 weeks
1544.5243 2.33631 (154*2π)/3352 weeks
1554.77699 3.3036 (155*2π)/3352 weeks
1562.44403 1.85158 (156*2π)/3352 weeks
1573.10881 .5522 (157*2π)/3352 weeks
1583.21871 -.19709 (158*2π)/3352 weeks
1593.83786 -.64525 (159*2π)/3352 weeks
1605.25429 -.8113 (160*2π)/3352 weeks
1614.68798 .44952 (161*2π)/3352 weeks
1623.276 .01208 (162*2π)/3352 weeks
1634.51218 -1.78725 (163*2π)/3352 weeks
1645.52115 -1.56235 (164*2π)/3352 weeks
1655.48705 -.87514 (165*2π)/3352 weeks
1666.61032 -1.69431 (166*2π)/3352 weeks
1677.08906 -.25977 (167*2π)/3352 weeks
1687.08906 .25977 (168*2π)/3352 weeks
1696.61032 1.69431 (169*2π)/3352 weeks
1705.48705 .87514 (170*2π)/3352 weeks
1715.52115 1.56235 (171*2π)/3352 weeks
1724.51218 1.78725 (172*2π)/3352 weeks
1733.276 -.01208 (173*2π)/3352 weeks
1744.68798 -.44952 (174*2π)/3352 weeks
1755.25429 .8113 (175*2π)/3352 weeks
1763.83786 .64525 (176*2π)/3352 weeks
1773.21871 .19709 (177*2π)/3352 weeks
1783.10881 -.5522 (178*2π)/3352 weeks
1792.44403 -1.85158 (179*2π)/3352 weeks
1804.77699 -3.3036 (180*2π)/3352 weeks
1814.5243 -2.33631 (181*2π)/3352 weeks
1825.52984 -3.53109 (182*2π)/3352 weeks
1836.18678 -2.83487 (183*2π)/3352 weeks
1847.48474 -2.6143 (184*2π)/3352 weeks
1857.02656 -.96318 (185*2π)/3352 weeks
1867.3731 -1.53834 (186*2π)/3352 weeks
1878.13026 -.22376 (187*2π)/3352 weeks
1887.58675 1.37282 (188*2π)/3352 weeks
1895.95663 2.50097 (189*2π)/3352 weeks
1903.6192 .78517 (190*2π)/3352 weeks
1914.51518 -.09466 (191*2π)/3352 weeks
1923.57964 -.13661 (192*2π)/3352 weeks
1934.76229 -1.05652 (193*2π)/3352 weeks
1944.22249 -.37857 (194*2π)/3352 weeks
1954.94114 -1.0057 (195*2π)/3352 weeks
1964.0924 -1.10213 (196*2π)/3352 weeks
1974.5759 -1.79065 (197*2π)/3352 weeks
1985.19175 -1.75164 (198*2π)/3352 weeks
1995.18678 -1.95768 (199*2π)/3352 weeks
2006.19484 -1.81636 (200*2π)/3352 weeks
2015.08504 -1.01385 (201*2π)/3352 weeks
2026.36579 -.43011 (202*2π)/3352 weeks
2033.74464 .22092 (203*2π)/3352 weeks
2043.04204 -.56447 (204*2π)/3352 weeks
2052.46972 -4.06456 (205*2π)/3352 weeks
2066.49771 -3.41575 (206*2π)/3352 weeks
2074.97018 -2.3019 (207*2π)/3352 weeks
2085.76391 -3.11037 (208*2π)/3352 weeks
2095.51505 -2.74579 (209*2π)/3352 weeks
2106.01647 -3.30204 (210*2π)/3352 weeks
2116.94179 -3.83237 (211*2π)/3352 weeks
2128.59031 -1.90921 (212*2π)/3352 weeks
2137.71411 -.69536 (213*2π)/3352 weeks
2146.82954 .22618 (214*2π)/3352 weeks
2156.70851 -.48797 (215*2π)/3352 weeks
2166.37065 1.41593 (216*2π)/3352 weeks
2174.4228 .63256 (217*2π)/3352 weeks
2183.59442 -.41666 (218*2π)/3352 weeks
2194.47785 -1.64328 (219*2π)/3352 weeks
2203.90119 -1.64763 (220*2π)/3352 weeks
2214.5253 -3.12853 (221*2π)/3352 weeks
2225.80852 -2.71295 (222*2π)/3352 weeks
2236.74759 -3.03266 (223*2π)/3352 weeks
2246.96127 -.15917 (224*2π)/3351 weeks
2255.4366 -1.06183 (225*2π)/3351 weeks
2266.31584 -.48156 (226*2π)/3351 weeks
2274.91195 -.09795 (227*2π)/3351 weeks
2285.07927 .22865 (228*2π)/3351 weeks
2293.56551 -1.01859 (229*2π)/3351 weeks
2304.40525 -1.95216 (230*2π)/3351 weeks
2316.55233 -1.3196 (231*2π)/3351 weeks
2325.5731 1.30332 (232*2π)/3351 weeks
2333.54504 .8998 (233*2π)/3351 weeks
2342.28945 -.11879 (234*2π)/3351 weeks
2353.77288 -1.45034 (235*2π)/3351 weeks
2363.26954 1.24053 (236*2π)/3351 weeks
2371.56508 .41328 (237*2π)/3351 weeks
2381.05514 .47363 (238*2π)/3351 weeks
239-.80873 -1.15842 (239*2π)/3351 weeks
240.30857 -2.43593 (240*2π)/3351 weeks
241-.16462 -3.48897 (241*2π)/3351 weeks
242.42731 -3.43725 (242*2π)/3351 weeks
243-.25901 -3.06878 (243*2π)/3351 weeks
244-2.43313 -4.63466 (244*2π)/3351 weeks
245-.43904 -7.74842 (245*2π)/3351 weeks
2461.03695 -7.41052 (246*2π)/3351 weeks
2471.28189 -7.8078 (247*2π)/3351 weeks
2482.51249 -8.98165 (248*2π)/3351 weeks
2493.37991 -7.88429 (249*2π)/3351 weeks
2504.05422 -8.69596 (250*2π)/3351 weeks
2514.96736 -6.55016 (251*2π)/3351 weeks
2523.86335 -6.69429 (252*2π)/3351 weeks
2532.31309 -5.18013 (253*2π)/3351 weeks
2541.70648 -9.48434 (254*2π)/3351 weeks
2554.31286 -9.38649 (255*2π)/3351 weeks
2564.78643 -9.59343 (256*2π)/3351 weeks
2576.52101 -9.51659 (257*2π)/3351 weeks
2585.90008 -7.88117 (258*2π)/3351 weeks
2596.98252 -10.46046 (259*2π)/3351 weeks
2609.33855 -7.5194 (260*2π)/3351 weeks
2618.07373 -5.83806 (261*2π)/3351 weeks
2628.02517 -6.21878 (262*2π)/3351 weeks
2637.87076 -4.01067 (263*2π)/3351 weeks
2643.71571 -3.82053 (264*2π)/3351 weeks
2655.5925 -8.28693 (265*2π)/3351 weeks
2667.86951 -6.10122 (266*2π)/3351 weeks
2677.33812 -3.98062 (267*2π)/3351 weeks
2685.11768 -3.35642 (268*2π)/3351 weeks
2695.04492 -4.60184 (269*2π)/3351 weeks
2704.60897 -4.92064 (270*2π)/3351 weeks
2715.18504 -3.66637 (271*2π)/3351 weeks
2723.28863 -3.36954 (272*2π)/3351 weeks
2731.39913 -4.54765 (273*2π)/3351 weeks
274.42905 -5.16946 (274*2π)/3351 weeks
275.81837 -6.06862 (275*2π)/3351 weeks
276.44412 -7.8604 (276*2π)/3351 weeks
277-.6418 -5.83208 (277*2π)/3351 weeks
278-2.34746 -9.92604 (278*2π)/3351 weeks
279-.77609 -9.72405 (279*2π)/3351 weeks
280-2.93336 -12.34548 (280*2π)/3351 weeks
281-.52894 -15.53479 (281*2π)/3351 weeks
282-1.73845 -14.74758 (282*2π)/3351 weeks
283.07098 -21.24708 (283*2π)/3351 weeks
2842.89599 -21.1512 (284*2π)/3351 weeks
2859.13961 -25.71651 (285*2π)/3351 weeks
28613.98841 -18.42071 (286*2π)/3351 weeks
28712.38091 -17.37676 (287*2π)/3351 weeks
28815.04362 -15.29786 (288*2π)/3351 weeks
28912.56708 -14.67879 (289*2π)/3351 weeks
29017.11988 -14.47355 (290*2π)/3351 weeks
29115.11593 -10.86159 (291*2π)/3351 weeks
29218.03317 -12.77309 (292*2π)/3351 weeks
29318.55975 -5.07935 (293*2π)/3351 weeks
29412.99908 -2.90569 (294*2π)/3351 weeks
29510.23059 -4.32605 (295*2π)/3351 weeks
2969.49406 -2.21736 (296*2π)/3351 weeks
2975.21829 -4.2508 (297*2π)/3351 weeks
2984.31799 -5.56373 (298*2π)/3351 weeks
2995.77141 -9.41713 (299*2π)/3351 weeks
3006.40854 -4.72179 (300*2π)/3351 weeks
3011.23474 -8.07581 (301*2π)/3351 weeks
3024.0427 -7.71531 (302*2π)/3351 weeks
303-.96117 -8.49629 (303*2π)/3351 weeks
304-1.05863 -11.48717 (304*2π)/3351 weeks
3052.0357 -19.15161 (305*2π)/3351 weeks
3066.54858 -9.77624 (306*2π)/3351 weeks
3071.99437 -14.46324 (307*2π)/3351 weeks
3083.60522 -9.13198 (308*2π)/3351 weeks
309-2.27908 -9.83616 (309*2π)/3351 weeks
310-5.13689 -14.75122 (310*2π)/3351 weeks
311-3.52857 -15.57813 (311*2π)/3351 weeks
312-7.66437 -15.05551 (312*2π)/3351 weeks
313-14.90363 -20.27449 (313*2π)/3351 weeks
314-16.79039 -28.4859 (314*2π)/3351 weeks
315-15.79683 -40.69379 (315*2π)/3351 weeks
316-3.97175 -42.55992 (316*2π)/3351 weeks
317-10.19717 -45.00148 (317*2π)/3351 weeks
3184.10017 -57.55976 (318*2π)/3351 weeks
31913.55289 -52.95678 (319*2π)/3351 weeks
32020.37676 -47.52431 (320*2π)/3351 weeks
3215.20343 -35.87012 (321*2π)/3351 weeks
322-.71008 -54.86007 (322*2π)/3351 weeks
3233.34842 -69.59148 (323*2π)/3351 weeks
32419.55219 -82.47344 (324*2π)/3351 weeks
32542.80017 -74.32188 (325*2π)/3351 weeks
32636.2056 -84.19077 (326*2π)/3351 weeks
32782.44924 -74.30583 (327*2π)/3351 weeks
32850.71626 -45.34616 (328*2π)/3351 weeks
32949.42803 -65.40388 (329*2π)/3351 weeks
33058.18859 -81.83901 (330*2π)/3351 weeks
33172.18934 -74.8956 (331*2π)/3351 weeks
33284.6833 -94.35457 (332*2π)/3351 weeks
333100.0112 -70.75534 (333*2π)/3351 weeks



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