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Fourier Analysis of RUSS (DIREXION DAILY RUSSIA BEAR 3X SHARES DIREXION DAILY RUSSIA BEAR 3X SHARES)


RUSS (DIREXION DAILY RUSSIA BEAR 3X SHARES DIREXION DAILY RUSSIA BEAR 3X SHARES) appears to have interesting cyclic behaviour every 34 weeks (44.4395*cosine), 19 weeks (27.3148*cosine), and 17 weeks (25.2506*cosine).

RUSS (DIREXION DAILY RUSSIA BEAR 3X SHARES DIREXION DAILY RUSSIA BEAR 3X SHARES) has an average price of 299.52 (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 11/6/2017 for RUSS (DIREXION DAILY RUSSIA BEAR 3X SHARES DIREXION DAILY RUSSIA BEAR 3X SHARES), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0299.5172   0 
149.22049 191.918 (1*2π)/338338 weeks
267.12283 155.8489 (2*2π)/338169 weeks
314.18497 93.65417 (3*2π)/338113 weeks
412.52676 87.3232 (4*2π)/33885 weeks
5-6.1519 41.81036 (5*2π)/33868 weeks
6-.87375 77.11107 (6*2π)/33856 weeks
710.60507 55.87352 (7*2π)/33848 weeks
8-67.90553 53.13423 (8*2π)/33842 weeks
9-11.98968 9.4887 (9*2π)/33838 weeks
10-44.4395 14.38315 (10*2π)/33834 weeks
11-.28786 -8.2981 (11*2π)/33831 weeks
121.4607 -15.44662 (12*2π)/33828 weeks
1311.1044 17.58354 (13*2π)/33826 weeks
1411.46452 18.70693 (14*2π)/33824 weeks
15-17.86111 11.19976 (15*2π)/33823 weeks
16-8.76527 -6.42624 (16*2π)/33821 weeks
17-2.33699 -4.41225 (17*2π)/33820 weeks
1827.31476 -12.50882 (18*2π)/33819 weeks
199.19588 2.37441 (19*2π)/33818 weeks
2025.25056 6.67939 (20*2π)/33817 weeks
2118.23924 13.35235 (21*2π)/33816 weeks
2216.05909 19.74222 (22*2π)/33815 weeks
235.51253 18.33269 (23*2π)/33815 weeks
243.1102 21.4976 (24*2π)/33814 weeks
257.58775 10.85943 (25*2π)/33814 weeks
26-.42503 23.32876 (26*2π)/33813 weeks
27-1.39834 18.7619 (27*2π)/33813 weeks
28-15.0176 11.57937 (28*2π)/33812 weeks
29-7.49335 9.59119 (29*2π)/33812 weeks
30-13.18252 -10.31699 (30*2π)/33811 weeks
315.68998 -1.26096 (31*2π)/33811 weeks
329.43139 -4.0224 (32*2π)/33811 weeks
334.40804 5.40115 (33*2π)/33810 weeks
348.49507 -.0475 (34*2π)/33810 weeks
358.25003 8.86208 (35*2π)/33810 weeks
364.29186 3.15938 (36*2π)/3389 weeks
3710.80876 4.92304 (37*2π)/3389 weeks
3811.0659 8.59071 (38*2π)/3389 weeks
399.27836 15.21449 (39*2π)/3389 weeks
405.59035 13.63864 (40*2π)/3388 weeks
41.04643 19.48649 (41*2π)/3388 weeks
42-2.70804 16.75804 (42*2π)/3388 weeks
43-13.15627 9.64594 (43*2π)/3388 weeks
44-.7605 6.83933 (44*2π)/3388 weeks
45-10.18299 7.53201 (45*2π)/3388 weeks
46-2.00703 3.8568 (46*2π)/3387 weeks
47-10.58571 4.24586 (47*2π)/3387 weeks
48-9.28741 1.70686 (48*2π)/3387 weeks
49-6.19507 -5.7803 (49*2π)/3387 weeks
50-9.6367 -9.84993 (50*2π)/3387 weeks
518.41363 -11.78868 (51*2π)/3387 weeks
523.3272 -6.36378 (52*2π)/3387 weeks
5314.86779 -3.40743 (53*2π)/3386 weeks
544.50141 -.20307 (54*2π)/3386 weeks
5510.05127 1.44688 (55*2π)/3386 weeks
569.876 1.61408 (56*2π)/3386 weeks
577.8326 3.43477 (57*2π)/3386 weeks
5811.4462 4.96756 (58*2π)/3386 weeks
592.43288 10.53026 (59*2π)/3386 weeks
608.65403 8.10955 (60*2π)/3386 weeks
61.60995 6.44877 (61*2π)/3386 weeks
62.69061 8.33581 (62*2π)/3385 weeks
63.48045 8.34129 (63*2π)/3385 weeks
641.39024 3.76588 (64*2π)/3385 weeks
65-2.48482 3.19851 (65*2π)/3385 weeks
66.31329 6.80513 (66*2π)/3385 weeks
67.81327 1.9987 (67*2π)/3385 weeks
68-2.58337 3.29683 (68*2π)/3385 weeks
69-3.05619 1.16608 (69*2π)/3385 weeks
70.0869 -.55899 (70*2π)/3385 weeks
715.56962 -3.54032 (71*2π)/3385 weeks
72.85013 4.7513 (72*2π)/3385 weeks
732.38311 2.26848 (73*2π)/3385 weeks
741.1348 1.5865 (74*2π)/3385 weeks
751.84216 -.06917 (75*2π)/3385 weeks
76-1.30026 .17175 (76*2π)/3384 weeks
777.29883 -.59938 (77*2π)/3384 weeks
782.95456 1.30168 (78*2π)/3384 weeks
793.35835 2.66882 (79*2π)/3384 weeks
802.73923 1.42393 (80*2π)/3384 weeks
813.22032 3.93143 (81*2π)/3384 weeks
824.35642 -.80914 (82*2π)/3384 weeks
83.25315 6.47575 (83*2π)/3384 weeks
844.19407 2.60072 (84*2π)/3384 weeks
85-2.04261 2.8287 (85*2π)/3384 weeks
861.27827 1.28176 (86*2π)/3384 weeks
87-2.84532 -.10719 (87*2π)/3384 weeks
883.56666 -1.75369 (88*2π)/3384 weeks
891.41367 -4.07236 (89*2π)/3384 weeks
904.42722 .27804 (90*2π)/3384 weeks
916.07642 -3.49492 (91*2π)/3384 weeks
926.79963 2.90681 (92*2π)/3384 weeks
936.27472 .94319 (93*2π)/3384 weeks
942.76706 3.72377 (94*2π)/3384 weeks
958.98372 1.66494 (95*2π)/3384 weeks
962.02893 2.97603 (96*2π)/3384 weeks
976.87087 5.92397 (97*2π)/3383 weeks
981.96622 5.10261 (98*2π)/3383 weeks
991.48393 5.61935 (99*2π)/3383 weeks
100-.06107 3.34281 (100*2π)/3383 weeks
101-.18203 1.49018 (101*2π)/3383 weeks
1024.64926 .56724 (102*2π)/3383 weeks
103.85693 3.94509 (103*2π)/3383 weeks
1042.68645 2.67138 (104*2π)/3383 weeks
105-2.04962 1.36298 (105*2π)/3383 weeks
1064.36375 1.06763 (106*2π)/3383 weeks
1072.73215 -.62106 (107*2π)/3383 weeks
1082.16876 3.73036 (108*2π)/3383 weeks
1094.39445 2.86855 (109*2π)/3383 weeks
110.14873 3.70304 (110*2π)/3383 weeks
111.81665 .88616 (111*2π)/3383 weeks
112-.46107 3.23577 (112*2π)/3383 weeks
1132.79066 -1.97083 (113*2π)/3383 weeks
114.84811 .10404 (114*2π)/3383 weeks
1154.41687 .95932 (115*2π)/3383 weeks
1163.74745 1.2627 (116*2π)/3383 weeks
1172.65669 1.91774 (117*2π)/3383 weeks
1183.82979 2.50853 (118*2π)/3383 weeks
1193.91235 3.19295 (119*2π)/3383 weeks
1202.34133 5.59454 (120*2π)/3383 weeks
121.65348 4.35547 (121*2π)/3383 weeks
122-.27863 3.8406 (122*2π)/3383 weeks
123-2.22809 4.19368 (123*2π)/3383 weeks
124-2.47103 .43673 (124*2π)/3383 weeks
125-2.16105 -1.80855 (125*2π)/3383 weeks
1261.20841 -2.28991 (126*2π)/3383 weeks
1271.7241 -.32834 (127*2π)/3383 weeks
1282.64873 -.79825 (128*2π)/3383 weeks
1291.01487 .32302 (129*2π)/3383 weeks
130.7514 1.27624 (130*2π)/3383 weeks
1312.92801 -4.92489 (131*2π)/3383 weeks
1324.32123 2.94714 (132*2π)/3383 weeks
1335.15213 .18938 (133*2π)/3383 weeks
134-1.02291 5.0464 (134*2π)/3383 weeks
1352.61256 .64762 (135*2π)/3383 weeks
136-3.4896 .16724 (136*2π)/3382 weeks
1372.20802 -1.42082 (137*2π)/3382 weeks
138.67819 -2.49741 (138*2π)/3382 weeks
1394.7854 -.03747 (139*2π)/3382 weeks
1402.9563 -2.8573 (140*2π)/3382 weeks
1413.57846 3.13657 (141*2π)/3382 weeks
1424.707 -1.02126 (142*2π)/3382 weeks
1431.39519 1.51803 (143*2π)/3382 weeks
1446.55552 .31748 (144*2π)/3382 weeks
1452.21588 2.34237 (145*2π)/3382 weeks
1465.38154 3.30074 (146*2π)/3382 weeks
147.55862 6.21327 (147*2π)/3382 weeks
148.2148 4.87213 (148*2π)/3382 weeks
149-4.68037 1.5753 (149*2π)/3382 weeks
150-2.36851 .48417 (150*2π)/3382 weeks
151-.07903 -3.0416 (151*2π)/3382 weeks
152-1.78612 -.52166 (152*2π)/3382 weeks
1531.92318 -3.58004 (153*2π)/3382 weeks
154-.63386 -.95868 (154*2π)/3382 weeks
1553.21379 -3.54802 (155*2π)/3382 weeks
156.02636 -2.65301 (156*2π)/3382 weeks
1576.17633 -4.27478 (157*2π)/3382 weeks
1585.51127 -1.16108 (158*2π)/3382 weeks
1596.0955 .8297 (159*2π)/3382 weeks
1604.47909 .53159 (160*2π)/3382 weeks
1613.14072 4.69929 (161*2π)/3382 weeks
1623.71086 -.43661 (162*2π)/3382 weeks
1631.10807 1.13433 (163*2π)/3382 weeks
1644.36517 3.41236 (164*2π)/3382 weeks
1652.11087 2.01365 (165*2π)/3382 weeks
166.06635 2.49636 (166*2π)/3382 weeks
1671.20588 2.91012 (167*2π)/3382 weeks
168-1.5508 1.3476 (168*2π)/3382 weeks
169-1.18416   (169*2π)/3382 weeks
170-1.5508 -1.3476 (170*2π)/3382 weeks
1711.20588 -2.91012 (171*2π)/3382 weeks
172.06635 -2.49636 (172*2π)/3382 weeks
1732.11087 -2.01365 (173*2π)/3382 weeks
1744.36517 -3.41236 (174*2π)/3382 weeks
1751.10807 -1.13433 (175*2π)/3382 weeks
1763.71086 .43661 (176*2π)/3382 weeks
1773.14072 -4.69929 (177*2π)/3382 weeks
1784.47909 -.53159 (178*2π)/3382 weeks
1796.0955 -.8297 (179*2π)/3382 weeks
1805.51127 1.16108 (180*2π)/3382 weeks
1816.17633 4.27478 (181*2π)/3382 weeks
182.02636 2.65301 (182*2π)/3382 weeks
1833.21379 3.54802 (183*2π)/3382 weeks
184-.63386 .95868 (184*2π)/3382 weeks
1851.92318 3.58004 (185*2π)/3382 weeks
186-1.78612 .52166 (186*2π)/3382 weeks
187-.07903 3.0416 (187*2π)/3382 weeks
188-2.36851 -.48417 (188*2π)/3382 weeks
189-4.68037 -1.5753 (189*2π)/3382 weeks
190.2148 -4.87213 (190*2π)/3382 weeks
191.55862 -6.21327 (191*2π)/3382 weeks
1925.38154 -3.30074 (192*2π)/3382 weeks
1932.21588 -2.34237 (193*2π)/3382 weeks
1946.55552 -.31748 (194*2π)/3382 weeks
1951.39519 -1.51803 (195*2π)/3382 weeks
1964.707 1.02126 (196*2π)/3382 weeks
1973.57846 -3.13657 (197*2π)/3382 weeks
1982.9563 2.8573 (198*2π)/3382 weeks
1994.7854 .03747 (199*2π)/3382 weeks
200.67819 2.49741 (200*2π)/3382 weeks
2012.20802 1.42082 (201*2π)/3382 weeks
202-3.4896 -.16724 (202*2π)/3382 weeks
2032.61256 -.64762 (203*2π)/3382 weeks
204-1.02291 -5.0464 (204*2π)/3382 weeks
2055.15213 -.18938 (205*2π)/3382 weeks
2064.32123 -2.94714 (206*2π)/3382 weeks
2072.92801 4.92489 (207*2π)/3382 weeks
208.7514 -1.27624 (208*2π)/3382 weeks
2091.01487 -.32302 (209*2π)/3382 weeks
2102.64873 .79825 (210*2π)/3382 weeks
2111.7241 .32834 (211*2π)/3382 weeks
2121.20841 2.28991 (212*2π)/3382 weeks
213-2.16105 1.80855 (213*2π)/3382 weeks
214-2.47103 -.43673 (214*2π)/3382 weeks
215-2.22809 -4.19368 (215*2π)/3382 weeks
216-.27863 -3.8406 (216*2π)/3382 weeks
217.65348 -4.35547 (217*2π)/3382 weeks
2182.34133 -5.59454 (218*2π)/3382 weeks
2193.91235 -3.19295 (219*2π)/3382 weeks
2203.82979 -2.50853 (220*2π)/3382 weeks
2212.65669 -1.91774 (221*2π)/3382 weeks
2223.74745 -1.2627 (222*2π)/3382 weeks
2234.41687 -.95932 (223*2π)/3382 weeks
224.84811 -.10404 (224*2π)/3382 weeks
2252.79066 1.97083 (225*2π)/3382 weeks
226-.46107 -3.23577 (226*2π)/3381 weeks
227.81665 -.88616 (227*2π)/3381 weeks
228.14873 -3.70304 (228*2π)/3381 weeks
2294.39445 -2.86855 (229*2π)/3381 weeks
2302.16876 -3.73036 (230*2π)/3381 weeks
2312.73215 .62106 (231*2π)/3381 weeks
2324.36375 -1.06763 (232*2π)/3381 weeks
233-2.04962 -1.36298 (233*2π)/3381 weeks
2342.68645 -2.67138 (234*2π)/3381 weeks
235.85693 -3.94509 (235*2π)/3381 weeks
2364.64926 -.56724 (236*2π)/3381 weeks
237-.18203 -1.49018 (237*2π)/3381 weeks
238-.06107 -3.34281 (238*2π)/3381 weeks
2391.48393 -5.61935 (239*2π)/3381 weeks
2401.96622 -5.10261 (240*2π)/3381 weeks
2416.87087 -5.92397 (241*2π)/3381 weeks
2422.02893 -2.97603 (242*2π)/3381 weeks
2438.98372 -1.66494 (243*2π)/3381 weeks
2442.76706 -3.72377 (244*2π)/3381 weeks
2456.27472 -.94319 (245*2π)/3381 weeks
2466.79963 -2.90681 (246*2π)/3381 weeks
2476.07642 3.49492 (247*2π)/3381 weeks
2484.42722 -.27804 (248*2π)/3381 weeks
2491.41367 4.07236 (249*2π)/3381 weeks
2503.56666 1.75369 (250*2π)/3381 weeks
251-2.84532 .10719 (251*2π)/3381 weeks
2521.27827 -1.28176 (252*2π)/3381 weeks
253-2.04261 -2.8287 (253*2π)/3381 weeks
2544.19407 -2.60072 (254*2π)/3381 weeks
255.25315 -6.47575 (255*2π)/3381 weeks
2564.35642 .80914 (256*2π)/3381 weeks
2573.22032 -3.93143 (257*2π)/3381 weeks
2582.73923 -1.42393 (258*2π)/3381 weeks
2593.35835 -2.66882 (259*2π)/3381 weeks
2602.95456 -1.30168 (260*2π)/3381 weeks
2617.29883 .59938 (261*2π)/3381 weeks
262-1.30026 -.17175 (262*2π)/3381 weeks
2631.84216 .06917 (263*2π)/3381 weeks
2641.1348 -1.5865 (264*2π)/3381 weeks
2652.38311 -2.26848 (265*2π)/3381 weeks
266.85013 -4.7513 (266*2π)/3381 weeks
2675.56962 3.54032 (267*2π)/3381 weeks
268.0869 .55899 (268*2π)/3381 weeks
269-3.05619 -1.16608 (269*2π)/3381 weeks
270-2.58337 -3.29683 (270*2π)/3381 weeks
271.81327 -1.9987 (271*2π)/3381 weeks
272.31329 -6.80513 (272*2π)/3381 weeks
273-2.48482 -3.19851 (273*2π)/3381 weeks
2741.39024 -3.76588 (274*2π)/3381 weeks
275.48045 -8.34129 (275*2π)/3381 weeks
276.69061 -8.33581 (276*2π)/3381 weeks
277.60995 -6.44877 (277*2π)/3381 weeks
2788.65403 -8.10955 (278*2π)/3381 weeks
2792.43288 -10.53026 (279*2π)/3381 weeks
28011.4462 -4.96756 (280*2π)/3381 weeks
2817.8326 -3.43477 (281*2π)/3381 weeks
2829.876 -1.61408 (282*2π)/3381 weeks
28310.05127 -1.44688 (283*2π)/3381 weeks
2844.50141 .20307 (284*2π)/3381 weeks
28514.86779 3.40743 (285*2π)/3381 weeks
2863.3272 6.36378 (286*2π)/3381 weeks
2878.41363 11.78868 (287*2π)/3381 weeks
288-9.6367 9.84993 (288*2π)/3381 weeks
289-6.19507 5.7803 (289*2π)/3381 weeks
290-9.28741 -1.70686 (290*2π)/3381 weeks
291-10.58571 -4.24586 (291*2π)/3381 weeks
292-2.00703 -3.8568 (292*2π)/3381 weeks
293-10.18299 -7.53201 (293*2π)/3381 weeks
294-.7605 -6.83933 (294*2π)/3381 weeks
295-13.15627 -9.64594 (295*2π)/3381 weeks
296-2.70804 -16.75804 (296*2π)/3381 weeks
297.04643 -19.48649 (297*2π)/3381 weeks
2985.59035 -13.63864 (298*2π)/3381 weeks
2999.27836 -15.21449 (299*2π)/3381 weeks
30011.0659 -8.59071 (300*2π)/3381 weeks
30110.80876 -4.92304 (301*2π)/3381 weeks
3024.29186 -3.15938 (302*2π)/3381 weeks
3038.25003 -8.86208 (303*2π)/3381 weeks
3048.49507 .0475 (304*2π)/3381 weeks
3054.40804 -5.40115 (305*2π)/3381 weeks
3069.43139 4.0224 (306*2π)/3381 weeks
3075.68998 1.26096 (307*2π)/3381 weeks
308-13.18252 10.31699 (308*2π)/3381 weeks
309-7.49335 -9.59119 (309*2π)/3381 weeks
310-15.0176 -11.57937 (310*2π)/3381 weeks
311-1.39834 -18.7619 (311*2π)/3381 weeks
312-.42503 -23.32876 (312*2π)/3381 weeks
3137.58775 -10.85943 (313*2π)/3381 weeks
3143.1102 -21.4976 (314*2π)/3381 weeks
3155.51253 -18.33269 (315*2π)/3381 weeks
31616.05909 -19.74222 (316*2π)/3381 weeks
31718.23924 -13.35235 (317*2π)/3381 weeks
31825.25056 -6.67939 (318*2π)/3381 weeks
3199.19588 -2.37441 (319*2π)/3381 weeks
32027.31476 12.50882 (320*2π)/3381 weeks
321-2.33699 4.41225 (321*2π)/3381 weeks
322-8.76527 6.42624 (322*2π)/3381 weeks
323-17.86111 -11.19976 (323*2π)/3381 weeks
32411.46452 -18.70693 (324*2π)/3381 weeks
32511.1044 -17.58354 (325*2π)/3381 weeks
3261.4607 15.44662 (326*2π)/3381 weeks
327-.28786 8.2981 (327*2π)/3381 weeks
328-44.4395 -14.38315 (328*2π)/3381 weeks
329-11.98968 -9.4887 (329*2π)/3381 weeks
330-67.90553 -53.13423 (330*2π)/3381 weeks
33110.60507 -55.87352 (331*2π)/3381 weeks
332-.87375 -77.11107 (332*2π)/3381 weeks
333-6.1519 -41.81036 (333*2π)/3381 weeks
33412.52676 -87.3232 (334*2π)/3381 weeks
33514.18497 -93.65417 (335*2π)/3381 weeks
33667.12283 -155.8489 (336*2π)/3381 weeks



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