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Fourier Analysis of DXRSX (Direxion Monthly Small Cap Bear)


DXRSX (Direxion Monthly Small Cap Bear) appears to have interesting cyclic behaviour every 75 weeks (222.2865*sine), 69 weeks (203.0299*sine), and 82 weeks (151.6801*sine).

DXRSX (Direxion Monthly Small Cap Bear) has an average price of 2,099.05 (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 12/1/1999 to 3/13/2017 for DXRSX (Direxion Monthly Small Cap Bear), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
02,099.048   0 
11,148.957 2,435.168 (1*2π)/902902 weeks
2145.0117 1,280.106 (2*2π)/902451 weeks
3-248.7832 799.8058 (3*2π)/902301 weeks
4-11.16938 426.8546 (4*2π)/902226 weeks
5-87.16258 257.2695 (5*2π)/902180 weeks
6213.2962 312.6929 (6*2π)/902150 weeks
7-24.91722 367.5651 (7*2π)/902129 weeks
8-10.86546 298.0913 (8*2π)/902113 weeks
9-92.71787 139.9564 (9*2π)/902100 weeks
1079.3231 130.2359 (10*2π)/90290 weeks
1174.63291 151.6801 (11*2π)/90282 weeks
1272.21892 222.2865 (12*2π)/90275 weeks
1335.84036 203.0299 (13*2π)/90269 weeks
14-50.93577 196.5457 (14*2π)/90264 weeks
155.10099 97.29887 (15*2π)/90260 weeks
16-10.11794 140.4352 (16*2π)/90256 weeks
1716.60671 63.59521 (17*2π)/90253 weeks
1849.06636 104.7252 (18*2π)/90250 weeks
1982.14378 133.6315 (19*2π)/90247 weeks
20-5.17743 170.005 (20*2π)/90245 weeks
215.8063 139.5515 (21*2π)/90243 weeks
22-63.78532 123.6032 (22*2π)/90241 weeks
23-11.24584 67.39852 (23*2π)/90239 weeks
24-47.98638 78.74298 (24*2π)/90238 weeks
2512.00693 8.23238 (25*2π)/90236 weeks
2647.3749 70.03549 (26*2π)/90235 weeks
2725.41491 94.53123 (27*2π)/90233 weeks
28-20.25845 73.07565 (28*2π)/90232 weeks
2940.28835 52.36818 (29*2π)/90231 weeks
30-13.99747 84.55668 (30*2π)/90230 weeks
3131.9451 39.36955 (31*2π)/90229 weeks
3216.76206 91.25322 (32*2π)/90228 weeks
33-2.90602 73.83733 (33*2π)/90227 weeks
34-28.337 53.68053 (34*2π)/90227 weeks
358.50017 16.39363 (35*2π)/90226 weeks
3626.55729 28.42326 (36*2π)/90225 weeks
3748.27077 46.66765 (37*2π)/90224 weeks
3834.92037 52.61433 (38*2π)/90224 weeks
3945.69963 89.10107 (39*2π)/90223 weeks
40-3.41814 66.34578 (40*2π)/90223 weeks
4125.35725 73.52197 (41*2π)/90222 weeks
42.49565 57.65371 (42*2π)/90221 weeks
436.98325 87.55428 (43*2π)/90221 weeks
44-17.34506 32.55449 (44*2π)/90221 weeks
456.75324 70.64726 (45*2π)/90220 weeks
46-16.1096 12.60304 (46*2π)/90220 weeks
4732.38906 50.3143 (47*2π)/90219 weeks
4823.06511 38.30396 (48*2π)/90219 weeks
492.77074 90.87693 (49*2π)/90218 weeks
50-8.61936 26.86218 (50*2π)/90218 weeks
51-11.81606 60.50799 (51*2π)/90218 weeks
5210.81775 7.96574 (52*2π)/90217 weeks
532.8882 55.93353 (53*2π)/90217 weeks
5432.88501 20.51314 (54*2π)/90217 weeks
55-1.3437 77.03091 (55*2π)/90216 weeks
5613.50906 38.59399 (56*2π)/90216 weeks
57-22.59128 60.69778 (57*2π)/90216 weeks
587.3602 28.69441 (58*2π)/90216 weeks
59-20.6096 49.10462 (59*2π)/90215 weeks
603.32895 23.66208 (60*2π)/90215 weeks
61-13.5069 35.30181 (61*2π)/90215 weeks
62.99646 28.02696 (62*2π)/90215 weeks
63-12.93589 19.52115 (63*2π)/90214 weeks
6411.60437 20.37843 (64*2π)/90214 weeks
65.01315 20.0744 (65*2π)/90214 weeks
6617.44185 26.30099 (66*2π)/90214 weeks
677.66763 27.26925 (67*2π)/90213 weeks
686.9704 44.58698 (68*2π)/90213 weeks
69-11.54095 22.21326 (69*2π)/90213 weeks
702.16467 21.68522 (70*2π)/90213 weeks
714.74514 20.15486 (71*2π)/90213 weeks
72.77783 25.60813 (72*2π)/90213 weeks
73.11776 11.6226 (73*2π)/90212 weeks
7413.9676 15.77071 (74*2π)/90212 weeks
755.48771 26.80511 (75*2π)/90212 weeks
762.31807 7.33398 (76*2π)/90212 weeks
7717.86139 12.42276 (77*2π)/90212 weeks
7823.59452 14.23544 (78*2π)/90212 weeks
7922.99528 30.16018 (79*2π)/90211 weeks
8018.45331 24.56643 (80*2π)/90211 weeks
8117.69461 41.17376 (81*2π)/90211 weeks
822.07201 35.2391 (82*2π)/90211 weeks
83-3.89837 30.64225 (83*2π)/90211 weeks
84-5.63277 12.30308 (84*2π)/90211 weeks
8515.48987 4.46238 (85*2π)/90211 weeks
8625.93414 28.60876 (86*2π)/90210 weeks
877.06316 29.02152 (87*2π)/90210 weeks
8812.59458 31.10984 (88*2π)/90210 weeks
89-4.61152 27.42602 (89*2π)/90210 weeks
904.24441 18.8549 (90*2π)/90210 weeks
913.10585 13.10433 (91*2π)/90210 weeks
9212.59905 21.77738 (92*2π)/90210 weeks
937.38475 13.03025 (93*2π)/90210 weeks
9413.11894 26.41937 (94*2π)/90210 weeks
951.91888 16.77283 (95*2π)/9029 weeks
967.27954 13.40942 (96*2π)/9029 weeks
9719.1843 10.21947 (97*2π)/9029 weeks
9819.09257 26.18838 (98*2π)/9029 weeks
9912.75749 26.01128 (99*2π)/9029 weeks
1007.06405 27.47771 (100*2π)/9029 weeks
101.10182 26.86413 (101*2π)/9029 weeks
102-1.66584 3.5254 (102*2π)/9029 weeks
10319.95736 12.39514 (103*2π)/9029 weeks
10419.51532 12.81348 (104*2π)/9029 weeks
10523.83934 31.54594 (105*2π)/9029 weeks
10611.84594 25.44982 (106*2π)/9029 weeks
1079.9625 38.35318 (107*2π)/9028 weeks
108-3.00609 19.14975 (108*2π)/9028 weeks
10911.731 24.85328 (109*2π)/9028 weeks
110-.48678 26.63142 (110*2π)/9028 weeks
1112.7013 17.30755 (111*2π)/9028 weeks
1125.69565 20.36943 (112*2π)/9028 weeks
1132.88448 20.83221 (113*2π)/9028 weeks
114-.41073 17.79291 (114*2π)/9028 weeks
1159.38091 10.76497 (115*2π)/9028 weeks
1161.74702 24.72643 (116*2π)/9028 weeks
11710.20921 5.67671 (117*2π)/9028 weeks
1187.6235 29.50179 (118*2π)/9028 weeks
1194.37882 13.75758 (119*2π)/9028 weeks
120-2.10355 24.06361 (120*2π)/9028 weeks
1216.27948 4.57577 (121*2π)/9027 weeks
1223.37597 21.37524 (122*2π)/9027 weeks
1236.01314 9.13537 (123*2π)/9027 weeks
1244.21109 12.5257 (124*2π)/9027 weeks
12514.45499 11.894 (125*2π)/9027 weeks
1264.70342 19.84547 (126*2π)/9027 weeks
12712.46585 14.68847 (127*2π)/9027 weeks
128-.10442 20.01803 (128*2π)/9027 weeks
1298.08681 17.57504 (129*2π)/9027 weeks
130-6.79862 10.52169 (130*2π)/9027 weeks
13111.91681 10.34478 (131*2π)/9027 weeks
132.08349 8.97973 (132*2π)/9027 weeks
13314.87295 14.06451 (133*2π)/9027 weeks
134-1.09146 10.03847 (134*2π)/9027 weeks
13511.00599 11.95971 (135*2π)/9027 weeks
1364.63362 3.88695 (136*2π)/9027 weeks
13717.11729 14.19721 (137*2π)/9027 weeks
1388.02157 9.24762 (138*2π)/9027 weeks
13912.07858 21.44563 (139*2π)/9026 weeks
1403.98907 4.02735 (140*2π)/9026 weeks
14113.07898 19.38734 (141*2π)/9026 weeks
1426.23987 3.82468 (142*2π)/9026 weeks
14313.61112 18.45417 (143*2π)/9026 weeks
1448.97043 2.86348 (144*2π)/9026 weeks
14520.95852 18.28143 (145*2π)/9026 weeks
14613.09618 17.65988 (146*2π)/9026 weeks
1479.16551 25.43601 (147*2π)/9026 weeks
1482.7641 16.11351 (148*2π)/9026 weeks
1495.77362 16.79135 (149*2π)/9026 weeks
1503.71801 14.51295 (150*2π)/9026 weeks
1513.60595 11.64854 (151*2π)/9026 weeks
1527.80655 10.53745 (152*2π)/9026 weeks
1538.27638 10.81941 (153*2π)/9026 weeks
15410.3438 12.66911 (154*2π)/9026 weeks
15511.39174 13.53043 (155*2π)/9026 weeks
15611.3798 17.04113 (156*2π)/9026 weeks
1576.38456 19.73256 (157*2π)/9026 weeks
1587.14427 15.39764 (158*2π)/9026 weeks
1592.71633 19.45999 (159*2π)/9026 weeks
1607.48242 11.99805 (160*2π)/9026 weeks
161.2363 24.21455 (161*2π)/9026 weeks
162-1.05629 8.03793 (162*2π)/9026 weeks
163-1.60939 14.44871 (163*2π)/9026 weeks
1645.40964 -.16772 (164*2π)/9026 weeks
16510.86535 14.4154 (165*2π)/9025 weeks
16610.36825 16.1078 (166*2π)/9025 weeks
167-3.51879 23.10157 (167*2π)/9025 weeks
168-4.46637 13.66503 (168*2π)/9025 weeks
169-14.79912 3.22033 (169*2π)/9025 weeks
1707.85815 -2.33036 (170*2π)/9025 weeks
171-1.94338 .78302 (171*2π)/9025 weeks
17216.57953 1.49689 (172*2π)/9025 weeks
1731.92562 6.28583 (173*2π)/9025 weeks
17415.57362 7.62453 (174*2π)/9025 weeks
175-.57451 7.51857 (175*2π)/9025 weeks
17610.59299 5.54713 (176*2π)/9025 weeks
1772.7018 .53153 (177*2π)/9025 weeks
17815.18658 8.42248 (178*2π)/9025 weeks
1793.12811 -.02929 (179*2π)/9025 weeks
18016.61347 6.91974 (180*2π)/9025 weeks
18110.3062 2.54395 (181*2π)/9025 weeks
18212.89562 10.94205 (182*2π)/9025 weeks
18315.23294 .11424 (183*2π)/9025 weeks
18414.82077 18.31394 (184*2π)/9025 weeks
18512.55161 2.53824 (185*2π)/9025 weeks
18615.42728 22.32367 (186*2π)/9025 weeks
1874.4728 6.12784 (187*2π)/9025 weeks
18811.53423 14.7763 (188*2π)/9025 weeks
1898.75433 6.43187 (189*2π)/9025 weeks
1909.77097 10.76345 (190*2π)/9025 weeks
19118.23116 8.34265 (191*2π)/9025 weeks
1928.08249 20.56504 (192*2π)/9025 weeks
19310.06787 10.1574 (193*2π)/9025 weeks
1946.24493 17.27897 (194*2π)/9025 weeks
1958.50854 9.30547 (195*2π)/9025 weeks
1969.69809 15.17637 (196*2π)/9025 weeks
1978.00661 19.97384 (197*2π)/9025 weeks
198-4.82999 14.053 (198*2π)/9025 weeks
1995.18425 9.85791 (199*2π)/9025 weeks
200-2.48323 6.68794 (200*2π)/9025 weeks
20110.89864 6.39858 (201*2π)/9024 weeks
2023.35679 9.09322 (202*2π)/9024 weeks
2039.78676 10.68892 (203*2π)/9024 weeks
2042.94877 10.82422 (204*2π)/9024 weeks
2053.98331 10.81279 (205*2π)/9024 weeks
2063.51581 4.61546 (206*2π)/9024 weeks
2079.20812 13.19874 (207*2π)/9024 weeks
208-3.15765 11.18885 (208*2π)/9024 weeks
209.99232 3.47104 (209*2π)/9024 weeks
2103.04938 4.66442 (210*2π)/9024 weeks
2111.44471 2.30193 (211*2π)/9024 weeks
2127.91741 -2.39458 (212*2π)/9024 weeks
21311.75686 4.1491 (213*2π)/9024 weeks
21410.97944 4.80033 (214*2π)/9024 weeks
21511.5048 9.75272 (215*2π)/9024 weeks
2164.87849 11.05969 (216*2π)/9024 weeks
2173.64724 1.39494 (217*2π)/9024 weeks
21813.73174 7.35188 (218*2π)/9024 weeks
2193.94302 6.27759 (219*2π)/9024 weeks
22012.68884 7.6125 (220*2π)/9024 weeks
2211.85956 7.73941 (221*2π)/9024 weeks
2229.96069 2.10625 (222*2π)/9024 weeks
2239.10019 4.79919 (223*2π)/9024 weeks
22413.4651 8.66489 (224*2π)/9024 weeks
2256.64186 8.13288 (225*2π)/9024 weeks
22611.39806 10.10915 (226*2π)/9024 weeks
2273.35533 10.80228 (227*2π)/9024 weeks
2285.44286 5.9048 (228*2π)/9024 weeks
2293.20798 4.50359 (229*2π)/9024 weeks
23011.56661 1.15793 (230*2π)/9024 weeks
23110.27961 9.39631 (231*2π)/9024 weeks
2327.12389 5.48379 (232*2π)/9024 weeks
23310.31118 6.79194 (233*2π)/9024 weeks
2348.26281 9.47407 (234*2π)/9024 weeks
2355.74541 4.08228 (235*2π)/9024 weeks
23611.75437 8.86196 (236*2π)/9024 weeks
2375.06436 6.80038 (237*2π)/9024 weeks
2387.68509 7.55687 (238*2π)/9024 weeks
2396.74282 3.97882 (239*2π)/9024 weeks
2407.35866 5.35083 (240*2π)/9024 weeks
24114.12696 1.09242 (241*2π)/9024 weeks
24211.92118 13.59884 (242*2π)/9024 weeks
2439.93617 7.65338 (243*2π)/9024 weeks
2446.4528 12.40248 (244*2π)/9024 weeks
2458.8493 6.41987 (245*2π)/9024 weeks
2466.89143 12.45172 (246*2π)/9024 weeks
2475.36629 10.16959 (247*2π)/9024 weeks
248.32325 5.66613 (248*2π)/9024 weeks
24910.27131 5.79768 (249*2π)/9024 weeks
2502.98923 7.16047 (250*2π)/9024 weeks
2519.03819 5.45751 (251*2π)/9024 weeks
2525.26479 8.00781 (252*2π)/9024 weeks
2535.76904 6.67884 (253*2π)/9024 weeks
2546.27163 3.49632 (254*2π)/9024 weeks
25510.75648 8.98524 (255*2π)/9024 weeks
2563.06774 10.46431 (256*2π)/9024 weeks
2571.66881 5.83708 (257*2π)/9024 weeks
2583.25013 .95489 (258*2π)/9023 weeks
2599.57623 2.23545 (259*2π)/9023 weeks
2609.48736 5.51232 (260*2π)/9023 weeks
2615.34734 8.49509 (261*2π)/9023 weeks
2626.72428 2.17807 (262*2π)/9023 weeks
2637.65987 7.32501 (263*2π)/9023 weeks
2645.31043 3.62896 (264*2π)/9023 weeks
2658.46435 4.66414 (265*2π)/9023 weeks
2667.6752 4.38019 (266*2π)/9023 weeks
2679.13415 6.63076 (267*2π)/9023 weeks
2686.83846 6.35288 (268*2π)/9023 weeks
2696.04968 7.4403 (269*2π)/9023 weeks
2706.24586 2.87171 (270*2π)/9023 weeks
2718.05844 6.80088 (271*2π)/9023 weeks
2728.49303 5.33495 (272*2π)/9023 weeks
2733.9733 11.72465 (273*2π)/9023 weeks
2742.677 1.28652 (274*2π)/9023 weeks
2753.71603 7.37738 (275*2π)/9023 weeks
2762.94908 -2.53475 (276*2π)/9023 weeks
2778.37519 2.86364 (277*2π)/9023 weeks
2788.2205 .87632 (278*2π)/9023 weeks
2795.59124 4.25814 (279*2π)/9023 weeks
2809.63914 -2.3918 (280*2π)/9023 weeks
28110.94828 3.375 (281*2π)/9023 weeks
28214.48526 2.20701 (282*2π)/9023 weeks
28310.77171 10.35306 (283*2π)/9023 weeks
2849.05247 7.78699 (284*2π)/9023 weeks
2853.06627 7.64327 (285*2π)/9023 weeks
2868.61929 2.64613 (286*2π)/9023 weeks
2875.82747 4.80205 (287*2π)/9023 weeks
28811.1391 5.16184 (288*2π)/9023 weeks
2893.01612 4.9721 (289*2π)/9023 weeks
29012.85775 2.51054 (290*2π)/9023 weeks
2915.24779 6.39353 (291*2π)/9023 weeks
29212.8918 3.07307 (292*2π)/9023 weeks
2938.88788 7.78866 (293*2π)/9023 weeks
29411.01775 11.79052 (294*2π)/9023 weeks
295-.2686 7.02633 (295*2π)/9023 weeks
2969.33217 6.40883 (296*2π)/9023 weeks
297.55427 5.78085 (297*2π)/9023 weeks
2987.15591 3.52212 (298*2π)/9023 weeks
2996.67637 1.5238 (299*2π)/9023 weeks
30011.21985 10.56795 (300*2π)/9023 weeks
301.52913 7.45887 (301*2π)/9023 weeks
3023.58817 5.82661 (302*2π)/9023 weeks
3033.15184 1.84544 (303*2π)/9023 weeks
3043.45014 6.12136 (304*2π)/9023 weeks
3052.46777 -.9548 (305*2π)/9023 weeks
3066.876 3.51174 (306*2π)/9023 weeks
3072.64321 1.78162 (307*2π)/9023 weeks
3083.8392 -.33109 (308*2π)/9023 weeks
3096.66924 -1.41317 (309*2π)/9023 weeks
3106.57124 -2.78275 (310*2π)/9023 weeks
31115.0186 -.0699 (311*2π)/9023 weeks
3128.71543 6.41718 (312*2π)/9023 weeks
3137.58358 4.08381 (313*2π)/9023 weeks
3144.97415 1.7185 (314*2π)/9023 weeks
31510.05608 2.53254 (315*2π)/9023 weeks
3164.27644 1.08891 (316*2π)/9023 weeks
31713.29633 .35132 (317*2π)/9023 weeks
3186.05088 6.19789 (318*2π)/9023 weeks
31910.60863 .41806 (319*2π)/9023 weeks
3204.85134 5.32435 (320*2π)/9023 weeks
32110.9859 -.79206 (321*2π)/9023 weeks
3227.81288 4.38182 (322*2π)/9023 weeks
32311.16632 2.28453 (323*2π)/9023 weeks
3245.39703 4.84221 (324*2π)/9023 weeks
32511.46766 -.52501 (325*2π)/9023 weeks
3269.0589 5.73788 (326*2π)/9023 weeks
32710.43353 1.42241 (327*2π)/9023 weeks
32811.3378 6.86932 (328*2π)/9023 weeks
3298.1033 4.94631 (329*2π)/9023 weeks
33010.01108 6.69633 (330*2π)/9023 weeks
3315.02799 9.17725 (331*2π)/9023 weeks
3323.91436 .23271 (332*2π)/9023 weeks
3338.36803 4.63629 (333*2π)/9023 weeks
3347.44387 -.17556 (334*2π)/9023 weeks
33512.26099 6.66367 (335*2π)/9023 weeks
3366.85085 3.52611 (336*2π)/9023 weeks
33711.60469 9.78364 (337*2π)/9023 weeks
3382.91882 7.03537 (338*2π)/9023 weeks
3394.87975 7.6332 (339*2π)/9023 weeks
3402.62539 2.94549 (340*2π)/9023 weeks
3413.01353 5.92778 (341*2π)/9023 weeks
3422.18393 -.97257 (342*2π)/9023 weeks
3434.79461 1.25421 (343*2π)/9023 weeks
3446.56377 -.67654 (344*2π)/9023 weeks
3455.72299 -.55981 (345*2π)/9023 weeks
34611.26082 .90271 (346*2π)/9023 weeks
3476.12588 2.30569 (347*2π)/9023 weeks
34810.02013 1.98404 (348*2π)/9023 weeks
3497.26409 -.37162 (349*2π)/9023 weeks
35015.88588 5.89365 (350*2π)/9023 weeks
3515.35764 7.4557 (351*2π)/9023 weeks
3528.21879 9.67622 (352*2π)/9023 weeks
353-.99328 4.91102 (353*2π)/9023 weeks
3543.16278 4.45614 (354*2π)/9023 weeks
355.82161 -1.65455 (355*2π)/9023 weeks
3564.46764 2.34913 (356*2π)/9023 weeks
3572.373 -3.42096 (357*2π)/9023 weeks
3584.97746 -2.78891 (358*2π)/9023 weeks
35910.50875 -4.7924 (359*2π)/9023 weeks
3608.95954 .80816 (360*2π)/9023 weeks
36110.3778 -.15782 (361*2π)/9022 weeks
3628.30441 .92285 (362*2π)/9022 weeks
3639.62836 2.32317 (363*2π)/9022 weeks
3646.17051 -.30688 (364*2π)/9022 weeks
36510.30142 .35904 (365*2π)/9022 weeks
3668.72926 -2.03128 (366*2π)/9022 weeks
36713.56474 2.86289 (367*2π)/9022 weeks
36810.88075 -.10979 (368*2π)/9022 weeks
36912.89457 8.91308 (369*2π)/9022 weeks
3706.49277 2.14656 (370*2π)/9022 weeks
37110.44549 7.37605 (371*2π)/9022 weeks
3724.50898 2.80435 (372*2π)/9022 weeks
3738.45776 3.2842 (373*2π)/9022 weeks
3748.86638 5.28706 (374*2π)/9022 weeks
375.49327 5.14058 (375*2π)/9022 weeks
3766.39275 -2.3449 (376*2π)/9022 weeks
3774.25422 -.68497 (377*2π)/9022 weeks
37813.85634 -4.66351 (378*2π)/9022 weeks
37912.57687 5.16832 (379*2π)/9022 weeks
38010.82295 5.96093 (380*2π)/9022 weeks
3816.12634 3.49959 (381*2π)/9022 weeks
38210.79689 6.92702 (382*2π)/9022 weeks
3831.75274 3.4336 (383*2π)/9022 weeks
3848.308 2.51027 (384*2π)/9022 weeks
3855.61385 -1.3048 (385*2π)/9022 weeks
38612.73001 5.73324 (386*2π)/9022 weeks
3875.56895 1.35336 (387*2π)/9022 weeks
38811.39822 8.30018 (388*2π)/9022 weeks
3893.35774 3.74363 (389*2π)/9022 weeks
3906.01654 7.34536 (390*2π)/9022 weeks
3912.25728 -.8772 (391*2π)/9022 weeks
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