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# Fourier Analysis of DXRSX (DIREXION MONTHLY SMALL CAP BEAR 2X FUND INVESTOR CLASS)

DXRSX (DIREXION MONTHLY SMALL CAP BEAR 2X FUND INVESTOR CLASS) appears to have interesting cyclic behaviour every 73 weeks (192.8228*sine), 68 weeks (192.688*sine), and 86 weeks (136.4989*sine).

DXRSX (DIREXION MONTHLY SMALL CAP BEAR 2X FUND INVESTOR CLASS) has an average price of 1,955.11 (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.

## Fourier Analysis

Using data from 1/3/2000 to 3/12/2018 for DXRSX (DIREXION MONTHLY SMALL CAP BEAR 2X FUND INVESTOR CLASS), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
01,955.11   0
11,233.715 2,309.461 (1*2π)/950950 weeks
2163.8591 1,245.582 (2*2π)/950475 weeks
3-188.6629 880.6122 (3*2π)/950317 weeks
4-63.62818 399.3972 (4*2π)/950238 weeks
5-109.0613 354.1883 (5*2π)/950190 weeks
6136.2439 169.8179 (6*2π)/950158 weeks
765.39704 396.6546 (7*2π)/950136 weeks
8-2.37285 267.6735 (8*2π)/950119 weeks
9-82.61005 263.4316 (9*2π)/950106 weeks
10-20.30219 76.67914 (10*2π)/95095 weeks
1152.40379 136.4989 (11*2π)/95086 weeks
1285.55749 132.6445 (12*2π)/95079 weeks
1350.78536 192.8228 (13*2π)/95073 weeks
1445.03232 192.688 (14*2π)/95068 weeks
15-51.26611 174.7034 (15*2π)/95063 weeks
167.47164 95.92535 (16*2π)/95059 weeks
17-16.02094 133.167 (17*2π)/95056 weeks
18-.59416 54.47991 (18*2π)/95053 weeks
1937.25152 79.51434 (19*2π)/95050 weeks
2082.2567 83.06277 (20*2π)/95048 weeks
2138.41681 158.6831 (21*2π)/95045 weeks
2227.49067 121.3054 (22*2π)/95043 weeks
23-14.23226 160.364 (23*2π)/95041 weeks
24-32.50453 83.48631 (24*2π)/95040 weeks
25-16.58768 113.5781 (25*2π)/95038 weeks
26-58.21626 47.26434 (26*2π)/95037 weeks
2716.97153 28.76233 (27*2π)/95035 weeks
2828.84024 61.072 (28*2π)/95034 weeks
2914.92851 91.68915 (29*2π)/95033 weeks
30-23.34655 50.21074 (30*2π)/95032 weeks
3137.06039 60.21942 (31*2π)/95031 weeks
32-20.68348 67.62785 (32*2π)/95030 weeks
3327.23342 34.21703 (33*2π)/95029 weeks
3421.90814 76.56905 (34*2π)/95028 weeks
359.03112 77.63566 (35*2π)/95027 weeks
36-28.62932 76.20979 (36*2π)/95026 weeks
37-23.18503 30.93972 (37*2π)/95026 weeks
38-10.53071 23.40336 (38*2π)/95025 weeks
3916.3738 15.20531 (39*2π)/95024 weeks
4012.49653 25.66384 (40*2π)/95024 weeks
4148.91497 25.05924 (41*2π)/95023 weeks
4217.21002 62.63744 (42*2π)/95023 weeks
4327.38766 29.74109 (43*2π)/95022 weeks
4418.2129 57.20337 (44*2π)/95022 weeks
4537.31547 37.2009 (45*2π)/95021 weeks
464.30005 78.48117 (46*2π)/95021 weeks
4716.04643 29.35207 (47*2π)/95020 weeks
481.50674 77.07903 (48*2π)/95020 weeks
49-9.60244 12.95159 (49*2π)/95019 weeks
5016.70326 39.77738 (50*2π)/95019 weeks
5131.20731 13.30604 (51*2π)/95019 weeks
5228.13055 77.39763 (52*2π)/95018 weeks
533.4711 31.45042 (53*2π)/95018 weeks
546.34225 69.01305 (54*2π)/95018 weeks
55-10.49534 13.10244 (55*2π)/95017 weeks
5613.48542 48.56499 (56*2π)/95017 weeks
57.58304 -1.25427 (57*2π)/95017 weeks
5840.85344 47.05349 (58*2π)/95016 weeks
5911.0183 21.51815 (59*2π)/95016 weeks
6034.88824 56.88803 (60*2π)/95016 weeks
611.62605 30.98423 (61*2π)/95016 weeks
6231.73602 49.87977 (62*2π)/95015 weeks
63.0216 40.1496 (63*2π)/95015 weeks
6421.56607 45.66785 (64*2π)/95015 weeks
654.57161 40.79404 (65*2π)/95015 weeks
6611.98861 51.96678 (66*2π)/95014 weeks
67-8.43132 37.07318 (67*2π)/95014 weeks
686.80356 38.46915 (68*2π)/95014 weeks
69-7.29568 29.04468 (69*2π)/95014 weeks
709.71988 28.24895 (70*2π)/95014 weeks
714.41675 20.68571 (71*2π)/95013 weeks
7225.35798 36.94649 (72*2π)/95013 weeks
731.41742 39.41748 (73*2π)/95013 weeks
747.12465 34.95133 (74*2π)/95013 weeks
754.82522 29.53862 (75*2π)/95013 weeks
7613.47317 37.26669 (76*2π)/95013 weeks
77-1.1248 39.67371 (77*2π)/95012 weeks
78.22969 29.78417 (78*2π)/95012 weeks
799.80337 31.50545 (79*2π)/95012 weeks
80-2.62232 45.79654 (80*2π)/95012 weeks
81-11.49521 28.67835 (81*2π)/95012 weeks
82-10.7224 26.24802 (82*2π)/95012 weeks
83-6.0024 12.17846 (83*2π)/95011 weeks
841.184 20.68256 (84*2π)/95011 weeks
85.48389 6.65404 (85*2π)/95011 weeks
8617.48758 16.82769 (86*2π)/95011 weeks
8713.78035 22.41679 (87*2π)/95011 weeks
8815.32392 34.28326 (88*2π)/95011 weeks
89-4.32283 36.9334 (89*2π)/95011 weeks
90-12.16272 17.72951 (90*2π)/95011 weeks
916.15692 7.53695 (91*2π)/95010 weeks
928.10566 19.03572 (92*2π)/95010 weeks
9312.25472 11.81229 (93*2π)/95010 weeks
9416.65794 27.92305 (94*2π)/95010 weeks
957.65062 24.36383 (95*2π)/95010 weeks
965.04228 29.49734 (96*2π)/95010 weeks
974.44337 18.09469 (97*2π)/95010 weeks
984.20552 27.32117 (98*2π)/95010 weeks
994.62779 14.65976 (99*2π)/95010 weeks
10012.09178 26.36166 (100*2π)/95010 weeks
1014.01538 27.96277 (101*2π)/9509 weeks
102-4.62362 27.20799 (102*2π)/9509 weeks
103-4.48101 13.18706 (103*2π)/9509 weeks
1044.32261 13.11433 (104*2π)/9509 weeks
1057.56748 12.98465 (105*2π)/9509 weeks
10612.40004 14.37718 (106*2π)/9509 weeks
10719.42212 29.53484 (107*2π)/9509 weeks
108-4.5173 33.81144 (108*2π)/9509 weeks
109-2.80676 23.81842 (109*2π)/9509 weeks
110-13.13203 18.51168 (110*2π)/9509 weeks
111.43965 7.43506 (111*2π)/9509 weeks
112-4.55013 11.52458 (112*2π)/9508 weeks
11310.60123 3.40363 (113*2π)/9508 weeks
1145.32259 21.0018 (114*2π)/9508 weeks
115.26955 8.53062 (115*2π)/9508 weeks
1169.81674 9.37791 (116*2π)/9508 weeks
1176.96151 15.74688 (117*2π)/9508 weeks
1184.15932 10.80566 (118*2π)/9508 weeks
1199.90218 10.71207 (119*2π)/9508 weeks
12011.09636 12.68227 (120*2π)/9508 weeks
1217.40303 20.97198 (121*2π)/9508 weeks
1224.82562 6.70078 (122*2π)/9508 weeks
12311.85153 23.87431 (123*2π)/9508 weeks
124-4.59803 6.58893 (124*2π)/9508 weeks
12514.86327 12.45988 (125*2π)/9508 weeks
1263.95433 7.54348 (126*2π)/9508 weeks
12720.31635 17.60665 (127*2π)/9507 weeks
128-.3363 14.68048 (128*2π)/9507 weeks
12915.80254 13.52682 (129*2π)/9507 weeks
1305.42375 15.89419 (130*2π)/9507 weeks
13111.05317 19.01353 (131*2π)/9507 weeks
132-1.61324 14.46745 (132*2π)/9507 weeks
13311.84626 11.738 (133*2π)/9507 weeks
134-1.84916 13.59521 (134*2π)/9507 weeks
13513.24877 8.15531 (135*2π)/9507 weeks
1361.99525 9.9939 (136*2π)/9507 weeks
13720.33159 10.21678 (137*2π)/9507 weeks
1382.75716 17.75005 (138*2π)/9507 weeks
13915.49545 10.33594 (139*2π)/9507 weeks
140.88057 17.28778 (140*2π)/9507 weeks
14115.8484 5.82601 (141*2π)/9507 weeks
1427.01449 17.65824 (142*2π)/9507 weeks
14317.15197 11.38198 (143*2π)/9507 weeks
1443.98619 22.94949 (144*2π)/9507 weeks
14510.8553 9.52759 (145*2π)/9507 weeks
1462.04332 19.30987 (146*2π)/9507 weeks
14715.1821 4.17914 (147*2π)/9506 weeks
1486.54515 24.14975 (148*2π)/9506 weeks
14912.25477 5.08534 (149*2π)/9506 weeks
15010.05713 25.69707 (150*2π)/9506 weeks
1519.68038 8.41065 (151*2π)/9506 weeks
15211.97831 30.01839 (152*2π)/9506 weeks
153-1.88878 17.02469 (153*2π)/9506 weeks
154.99057 19.94995 (154*2π)/9506 weeks
155-1.78772 7.77549 (155*2π)/9506 weeks
1566.67863 12.72372 (156*2π)/9506 weeks
1573.29015 10.13728 (157*2π)/9506 weeks
1585.81047 11.81203 (158*2π)/9506 weeks
1597.44813 8.58153 (159*2π)/9506 weeks
1608.32058 15.08338 (160*2π)/9506 weeks
1616.94651 11.28616 (161*2π)/9506 weeks
1627.7504 16.1455 (162*2π)/9506 weeks
1635.6032 14.32008 (163*2π)/9506 weeks
1645.05031 17.28956 (164*2π)/9506 weeks
165.21164 12.95082 (165*2π)/9506 weeks
1665.84283 13.30993 (166*2π)/9506 weeks
167-.66687 12.99789 (167*2π)/9506 weeks
1686.76874 10.86945 (168*2π)/9506 weeks
169-3.16465 16.04668 (169*2π)/9506 weeks
1702.48414 2.70981 (170*2π)/9506 weeks
1714.61166 11.9537 (171*2π)/9506 weeks
1726.67153 4.92345 (172*2π)/9506 weeks
1739.0843 18.46976 (173*2π)/9505 weeks
174-.97018 15.8639 (174*2π)/9505 weeks
175-6.86468 15.22981 (175*2π)/9505 weeks
176-7.31448 .93694 (176*2π)/9505 weeks
177-3.41281 .9749 (177*2π)/9505 weeks
1788.03115 -9.67645 (178*2π)/9505 weeks
17911.69335 10.18729 (179*2π)/9505 weeks
1806.82406 -.42385 (180*2π)/9505 weeks
18111.41485 14.10766 (181*2π)/9505 weeks
182.75584 2.60792 (182*2π)/9505 weeks
1838.93545 11.02635 (183*2π)/9505 weeks
184-1.53719 .14389 (184*2π)/9505 weeks
18510.67742 3.65621 (185*2π)/9505 weeks
1864.97339 -1.41394 (186*2π)/9505 weeks
18715.68103 6.97676 (187*2π)/9505 weeks
1883.89348 .62129 (188*2π)/9505 weeks
18918.63957 5.67983 (189*2π)/9505 weeks
1907.66656 5.46503 (190*2π)/9505 weeks
19115.15509 8.72421 (191*2π)/9505 weeks
1928.29266 2.58882 (192*2π)/9505 weeks
19319.5662 12.79406 (193*2π)/9505 weeks
1943.31027 7.03709 (194*2π)/9505 weeks
19520.2279 9.78757 (195*2π)/9505 weeks
1961.06377 13.70597 (196*2π)/9505 weeks
19714.03834 2.92276 (197*2π)/9505 weeks
1987.68118 10.83861 (198*2π)/9505 weeks
19914.17335 6.039 (199*2π)/9505 weeks
20010.31505 8.51551 (200*2π)/9505 weeks
20119.0957 12.2038 (201*2π)/9505 weeks
2024.33838 16.08587 (202*2π)/9505 weeks
20312.05953 7.72209 (203*2π)/9505 weeks
2047.59881 13.64325 (204*2π)/9505 weeks
20511.95815 8.05482 (205*2π)/9505 weeks
20612.1269 14.76035 (206*2π)/9505 weeks
20710.75214 18.43541 (207*2π)/9505 weeks
208-1.50538 16.0054 (208*2π)/9505 weeks
2097.24707 7.59151 (209*2π)/9505 weeks
2101.31294 12.52714 (210*2π)/9505 weeks
2119.53576 4.52421 (211*2π)/9505 weeks
2126.25683 14.34905 (212*2π)/9504 weeks
2137.89735 7.8391 (213*2π)/9504 weeks
2145.25145 14.25664 (214*2π)/9504 weeks
2155.70736 9.21597 (215*2π)/9504 weeks
2163.15158 10.85703 (216*2π)/9504 weeks
2179.38381 6.46685 (217*2π)/9504 weeks
2186.84085 17.33335 (218*2π)/9504 weeks
219-.86458 11.60989 (219*2π)/9504 weeks
2201.30936 7.61679 (220*2π)/9504 weeks
2213.94133 8.87216 (221*2π)/9504 weeks
222-1.4466 7.64312 (222*2π)/9504 weeks
2234.95689 1.45469 (223*2π)/9504 weeks
2245.97195 7.21695 (224*2π)/9504 weeks
2256.4556 5.54446 (225*2π)/9504 weeks
2265.39707 9.02538 (226*2π)/9504 weeks
2274.18001 8.08025 (227*2π)/9504 weeks
228-1.77417 5.28268 (228*2π)/9504 weeks
2299.59949 -2.35322 (229*2π)/9504 weeks
2306.92007 10.72437 (230*2π)/9504 weeks
2316.96306 .83335 (231*2π)/9504 weeks
2328.52199 12.0669 (232*2π)/9504 weeks
2332.08336 3.25158 (233*2π)/9504 weeks
2348.20668 5.48137 (234*2π)/9504 weeks
2357.39091 3.28911 (235*2π)/9504 weeks
2369.28852 9.72883 (236*2π)/9504 weeks
2374.66602 4.82599 (237*2π)/9504 weeks
2389.09442 8.85964 (238*2π)/9504 weeks
2393.35637 7.85996 (239*2π)/9504 weeks
2404.33808 5.6136 (240*2π)/9504 weeks
2413.73536 3.73094 (241*2π)/9504 weeks
2428.02091 1.00506 (242*2π)/9504 weeks
24311.56227 6.15982 (243*2π)/9504 weeks
2445.78956 9.05711 (244*2π)/9504 weeks
2457.29224 4.50789 (245*2π)/9504 weeks
2467.84669 8.94582 (246*2π)/9504 weeks
2472.64216 7.48485 (247*2π)/9504 weeks
2486.74632 2.73848 (248*2π)/9504 weeks
2496.31985 8.12099 (249*2π)/9504 weeks
2504.87673 4.52058 (250*2π)/9504 weeks
2514.43927 5.39377 (251*2π)/9504 weeks
2525.76408 3.41438 (252*2π)/9504 weeks
2532.89925 2.67988 (253*2π)/9504 weeks
25411.40423 -1.63291 (254*2π)/9504 weeks
2558.88069 8.33548 (255*2π)/9504 weeks
2568.61601 3.00654 (256*2π)/9504 weeks
2576.0887 7.40505 (257*2π)/9504 weeks
2587.81079 .8899 (258*2π)/9504 weeks
2599.36239 6.09958 (259*2π)/9504 weeks
2609.56453 4.70833 (260*2π)/9504 weeks
2614.07378 7.73787 (261*2π)/9504 weeks
26210.01427 -1.46185 (262*2π)/9504 weeks
2639.93243 8.82335 (263*2π)/9504 weeks
2648.82698 2.33917 (264*2π)/9504 weeks
26510.81336 8.35328 (265*2π)/9504 weeks
2668.29406 6.50284 (266*2π)/9504 weeks
2675.54598 7.9817 (267*2π)/9504 weeks
2688.74366 1.464 (268*2π)/9504 weeks
26911.27534 9.25013 (269*2π)/9504 weeks
2706.97948 8.8149 (270*2π)/9504 weeks
2713.22988 9.12327 (271*2π)/9504 weeks
2723.46294 1.50013 (272*2π)/9503 weeks
2738.18439 2.80327 (273*2π)/9503 weeks
27411.32312 2.12617 (274*2π)/9503 weeks
2759.61289 10.92691 (275*2π)/9503 weeks
2766.34143 3.56437 (276*2π)/9503 weeks
2779.9226 9.49627 (277*2π)/9503 weeks
2784.5642 7.14792 (278*2π)/9503 weeks
2795.8114 7.11386 (279*2π)/9503 weeks
2804.1424 4.7421 (280*2π)/9503 weeks
2815.92526 4.77772 (281*2π)/9503 weeks
2825.72148 3.63041 (282*2π)/9503 weeks
2836.59771 4.96187 (283*2π)/9503 weeks
2844.16569 2.87838 (284*2π)/9503 weeks
2857.62378 1.51656 (285*2π)/9503 weeks
2868.1384 .31431 (286*2π)/9503 weeks
28714.43722 2.8568 (287*2π)/9503 weeks
2889.96426 8.78225 (288*2π)/9503 weeks
28910.05135 5.31595 (289*2π)/9503 weeks
2908.95544 10.36932 (290*2π)/9503 weeks
2915.34783 6.39185 (291*2π)/9503 weeks
2927.90596 6.22265 (292*2π)/9503 weeks
2938.36193 6.84275 (293*2π)/9503 weeks
2946.34246 10.37593 (294*2π)/9503 weeks
2952.82928 6.58224 (295*2π)/9503 weeks
2964.19854 5.53764 (296*2π)/9503 weeks
2973.90074 3.05058 (297*2π)/9503 weeks
2988.00124 3.56311 (298*2π)/9503 weeks
2997.19379 6.07799 (299*2π)/9503 weeks
3006.08077 7.52251 (300*2π)/9503 weeks
3012.83534 5.70081 (301*2π)/9503 weeks
3024.00131 3.69099 (302*2π)/9503 weeks
3034.85311 1.71679 (303*2π)/9503 weeks
3048.38006 4.71892 (304*2π)/9503 weeks
3052.73447 4.60166 (305*2π)/9503 weeks
3068.26648 2.14522 (306*2π)/9503 weeks
3073.71371 6.67983 (307*2π)/9503 weeks
3085.00725 .66511 (308*2π)/9503 weeks
3095.81265 2.67093 (309*2π)/9503 weeks
31010.10594 2.55828 (310*2π)/9503 weeks
3113.72616 8.63464 (311*2π)/9503 weeks
3124.41766 .24128 (312*2π)/9503 weeks
3134.95636 6.2034 (313*2π)/9503 weeks
3141.95736 .63021 (314*2π)/9503 weeks
3152.35844 .0438 (315*2π)/9503 weeks
3167.51396 -6.53797 (316*2π)/9503 weeks
31712.54009 2.01752 (317*2π)/9503 weeks
3188.24528 1.37256 (318*2π)/9503 weeks
3198.66473 2.77019 (319*2π)/9503 weeks
3209.43434 .39445 (320*2π)/9503 weeks
3219.40348 4.76427 (321*2π)/9503 weeks
3226.46654 .45991 (322*2π)/9503 weeks
32312.13617 1.40519 (323*2π)/9503 weeks
32410.05557 4.41694 (324*2π)/9503 weeks
3259.16615 3.96438 (325*2π)/9503 weeks
3269.78329 4.73135 (326*2π)/9503 weeks
3275.41406 4.60647 (327*2π)/9503 weeks
3289.52983 -1.00284 (328*2π)/9503 weeks
32912.82922 3.67737 (329*2π)/9503 weeks
33012.57347 6.19436 (330*2π)/9503 weeks
3318.18886 9.35698 (331*2π)/9503 weeks
3327.94185 5.24019 (332*2π)/9503 weeks
3336.29146 9.91984 (333*2π)/9503 weeks
3341.50464 2.89956 (334*2π)/9503 weeks
3358.51084 2.11199 (335*2π)/9503 weeks
3364.37006 3.10943 (336*2π)/9503 weeks
33710.59749 .74989 (337*2π)/9503 weeks
3387.15424 4.58204 (338*2π)/9503 weeks
3399.89953 1.55989 (339*2π)/9503 weeks
34010.13397 4.87215 (340*2π)/9503 weeks
34112.00976 4.44392 (341*2π)/9503 weeks
3429.26577 11.40668 (342*2π)/9503 weeks
3434.78603 6.17392 (343*2π)/9503 weeks
3447.37066 9.15265 (344*2π)/9503 weeks
345.08773 6.05647 (345*2π)/9503 weeks
3465.94826 2.62996 (346*2π)/9503 weeks
3472.04348 4.02234 (347*2π)/9503 weeks
3485.96491 -1.18427 (348*2π)/9503 weeks
34910.61039 1.69053 (349*2π)/9503 weeks
3508.2845 6.35053 (350*2π)/9503 weeks
3517.64484 4.34406 (351*2π)/9503 weeks
3527.34799 8.18068 (352*2π)/9503 weeks
3533.30157 4.37505 (353*2π)/9503 weeks
3546.839 7.37265 (354*2π)/9503 weeks
355.00394 3.52383 (355*2π)/9503 weeks
3566.64868 3.35638 (356*2π)/9503 weeks
3571.39899 3.71462 (357*2π)/9503 weeks
3584.39753 2.74377 (358*2π)/9503 weeks
359.97619 .02008 (359*2π)/9503 weeks
3606.842 .23444 (360*2π)/9503 weeks
3612.57437 .11339 (361*2π)/9503 weeks
3627.1803 -2.24937 (362*2π)/9503 weeks
3637.52621 -.81187 (363*2π)/9503 weeks
3649.27148 -.1426 (364*2π)/9503 weeks
3659.7926 .04262 (365*2π)/9503 weeks
36612.54067 2.73559 (366*2π)/9503 weeks
36711.31156 6.37664 (367*2π)/9503 weeks
3687.10453 10.41494 (368*2π)/9503 weeks
3691.55229 5.05615 (369*2π)/9503 weeks
3704.17495 4.79836 (370*2π)/9503 weeks
3711.57635 1.1524 (371*2π)/9503 weeks
3725.77144 2.16172 (372*2π)/9503 weeks
3733.01794 1.17703 (373*2π)/9503 weeks
3744.82353 1.90461 (374*2π)/9503 weeks
3752.16847 -1.09249 (375*2π)/9503 weeks
3766.84365 -2.0013 (376*2π)/9503 weeks
3777.14334 .35818 (377*2π)/9503 weeks
3785.27162 .87436 (378*2π)/9503 weeks
3795.59851 -.86487 (379*2π)/9503 weeks
3805.42273 -2.17233 (380*2π)/9503 weeks
3818.74772 -2.0545 (381*2π)/9502 weeks
3826.76457 -2.27126 (382*2π)/9502 weeks
38312.11813 -2.99208 (383*2π)/9502 weeks
38410.79193 .71166 (384*2π)/9502 weeks
38512.96854 .63181 (385*2π)/9502 weeks
3869.77244 5.03259 (386*2π)/9502 weeks
38710.40335 1.9314 (387*2π)/9502 weeks
3886.87298 6.53628 (388*2π)/9502 weeks
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