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Fourier Analysis of RUSL (Direxion Daily Russia Bull 3x S)


RUSL (Direxion Daily Russia Bull 3x S) appears to have interesting cyclic behaviour every 31 weeks (182.423*sine), 28 weeks (150.2503*sine), and 31 weeks (42.3604*cosine).

RUSL (Direxion Daily Russia Bull 3x S) has an average price of 541.82 (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 3/20/2017 for RUSL (Direxion Daily Russia Bull 3x S), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0541.82   0 
1249.0104 445.2587 (1*2π)/305305 weeks
2242.2294 169.6461 (2*2π)/305153 weeks
3167.8144 193.3948 (3*2π)/305102 weeks
4162.0942 170.2288 (4*2π)/30576 weeks
5110.0151 155.4829 (5*2π)/30561 weeks
699.00889 123.4874 (6*2π)/30551 weeks
7176.5216 117.6923 (7*2π)/30544 weeks
892.78513 198.606 (8*2π)/30538 weeks
990.85185 158.2067 (9*2π)/30534 weeks
1042.36036 182.423 (10*2π)/30531 weeks
114.78329 150.2503 (11*2π)/30528 weeks
12-4.03895 115.1601 (12*2π)/30525 weeks
1327.28679 76.62932 (13*2π)/30523 weeks
1435.74574 112.2148 (14*2π)/30522 weeks
1520.94826 122.2152 (15*2π)/30520 weeks
16-16.85213 120.192 (16*2π)/30519 weeks
17-9.44019 90.15487 (17*2π)/30518 weeks
18-28.18847 96.35799 (18*2π)/30517 weeks
19-37.01634 65.61526 (19*2π)/30516 weeks
20-32.73256 45.50903 (20*2π)/30515 weeks
21-15.98639 33.25277 (21*2π)/30515 weeks
22-7.59966 35.39789 (22*2π)/30514 weeks
23-11.3841 29.54741 (23*2π)/30513 weeks
24-1.21228 20.60529 (24*2π)/30513 weeks
2511.94844 27.85346 (25*2π)/30512 weeks
263.68062 22.38987 (26*2π)/30512 weeks
2714.94389 39.6828 (27*2π)/30511 weeks
28-4.19696 28.20671 (28*2π)/30511 weeks
29-2.29649 21.14708 (29*2π)/30511 weeks
308.93234 16.88829 (30*2π)/30510 weeks
312.85676 17.33967 (31*2π)/30510 weeks
3216.04998 12.25487 (32*2π)/30510 weeks
339.96819 20.16829 (33*2π)/3059 weeks
3411.70769 11.94034 (34*2π)/3059 weeks
3514.44363 5.88978 (35*2π)/3059 weeks
3624.19688 9.24056 (36*2π)/3058 weeks
3726.00935 6.67302 (37*2π)/3058 weeks
3837.74505 7.97012 (38*2π)/3058 weeks
3941.86108 25.71137 (39*2π)/3058 weeks
4032.53984 24.07 (40*2π)/3058 weeks
4137.22006 32.38036 (41*2π)/3057 weeks
4227.76496 31.37353 (42*2π)/3057 weeks
4332.58564 36.31716 (43*2π)/3057 weeks
4427.34075 37.55021 (44*2π)/3057 weeks
4530.95149 47.88448 (45*2π)/3057 weeks
468.57378 52.65235 (46*2π)/3057 weeks
475.33693 46.91608 (47*2π)/3056 weeks
48-5.72715 36.17996 (48*2π)/3056 weeks
49.19165 33.75433 (49*2π)/3056 weeks
50-6.35555 28.04894 (50*2π)/3056 weeks
51-1.49013 21.63091 (51*2π)/3056 weeks
52-5.45613 20.97186 (52*2π)/3056 weeks
531.20019 13.13054 (53*2π)/3056 weeks
54-.22624 15.8624 (54*2π)/3056 weeks
551.8942 14.02499 (55*2π)/3056 weeks
563.38157 10.24905 (56*2π)/3055 weeks
575.33192 7.11602 (57*2π)/3055 weeks
589.8036 7.09818 (58*2π)/3055 weeks
5910.59697 11.0901 (59*2π)/3055 weeks
6011.09637 10.02278 (60*2π)/3055 weeks
6111.30084 7.4735 (61*2π)/3055 weeks
6216.5545 9.19363 (62*2π)/3055 weeks
6317.22687 14.41121 (63*2π)/3055 weeks
649.10255 17.04906 (64*2π)/3055 weeks
6512.73579 6.27401 (65*2π)/3055 weeks
6618.46876 11.34424 (66*2π)/3055 weeks
6716.5724 13.13409 (67*2π)/3055 weeks
6819.88475 14.83959 (68*2π)/3054 weeks
6917.64935 22.51666 (69*2π)/3054 weeks
7012.35848 17.6089 (70*2π)/3054 weeks
7114.37423 20.85839 (71*2π)/3054 weeks
7210.33435 21.01641 (72*2π)/3054 weeks
739.17571 21.12975 (73*2π)/3054 weeks
742.06209 18.53462 (74*2π)/3054 weeks
758.76182 12.14746 (75*2π)/3054 weeks
768.83417 13.60154 (76*2π)/3054 weeks
7711.22243 17.56658 (77*2π)/3054 weeks
787.02682 17.38798 (78*2π)/3054 weeks
796.67483 19.23502 (79*2π)/3054 weeks
802.76768 17.27526 (80*2π)/3054 weeks
812.22797 16.21892 (81*2π)/3054 weeks
82-1.39562 16.92294 (82*2π)/3054 weeks
83-4.63544 8.72425 (83*2π)/3054 weeks
84.24305 6.69856 (84*2π)/3054 weeks
85.89998 7.50964 (85*2π)/3054 weeks
86-.85271 5.53194 (86*2π)/3054 weeks
87-1.27818 5.16126 (87*2π)/3054 weeks
88.37919 -.63177 (88*2π)/3053 weeks
893.28663 -.28041 (89*2π)/3053 weeks
906.26514 -2.63247 (90*2π)/3053 weeks
918.69671 3.06027 (91*2π)/3053 weeks
925.14591 .00362 (92*2π)/3053 weeks
938.08169 -2.20618 (93*2π)/3053 weeks
9413.56875 -1.81177 (94*2π)/3053 weeks
9512.92408 4.64524 (95*2π)/3053 weeks
969.08429 3.48589 (96*2π)/3053 weeks
978.73961 -.50493 (97*2π)/3053 weeks
9811.07676 1.05071 (98*2π)/3053 weeks
9913.46845 .06808 (99*2π)/3053 weeks
10012.38434 2.60199 (100*2π)/3053 weeks
10114.91238 .07423 (101*2π)/3053 weeks
10214.65425 6.6014 (102*2π)/3053 weeks
10312.6997 6.08292 (103*2π)/3053 weeks
1049.11884 6.18812 (104*2π)/3053 weeks
1059.13632 2.80332 (105*2π)/3053 weeks
1068.28957 3.37573 (106*2π)/3053 weeks
1078.87202 -.46519 (107*2π)/3053 weeks
10811.55555 -3.03049 (108*2π)/3053 weeks
10915.54424 .5573 (109*2π)/3053 weeks
11014.46007 -.20821 (110*2π)/3053 weeks
11117.04417 1.48126 (111*2π)/3053 weeks
11219.03372 4.27928 (112*2π)/3053 weeks
11314.80718 8.21468 (113*2π)/3053 weeks
11412.92867 7.10638 (114*2π)/3053 weeks
11512.50321 5.61179 (115*2π)/3053 weeks
11611.34817 6.83685 (116*2π)/3053 weeks
11712.85444 4.5233 (117*2π)/3053 weeks
1189.42116 11.00861 (118*2π)/3053 weeks
1195.09891 2.42887 (119*2π)/3053 weeks
1207.90117 .47686 (120*2π)/3053 weeks
12113.85511 .25088 (121*2π)/3053 weeks
12211.21367 2.18049 (122*2π)/3053 weeks
12313.29726 4.25875 (123*2π)/3052 weeks
12411.1235 4.11492 (124*2π)/3052 weeks
12511.07032 4.24601 (125*2π)/3052 weeks
1269.55176 3.71297 (126*2π)/3052 weeks
1279.83735 1.4354 (127*2π)/3052 weeks
1289.13208 2.56386 (128*2π)/3052 weeks
12911.00078 1.72876 (129*2π)/3052 weeks
1308.04604 1.51536 (130*2π)/3052 weeks
13110.2553 .08987 (131*2π)/3052 weeks
1328.13485 -1.62584 (132*2π)/3052 weeks
13313.69395 -5.29462 (133*2π)/3052 weeks
13417.26863 -2.39326 (134*2π)/3052 weeks
13517.91562 1.50127 (135*2π)/3052 weeks
13615.30393 3.30199 (136*2π)/3052 weeks
13717.16238 3.15587 (137*2π)/3052 weeks
13814.50473 6.46246 (138*2π)/3052 weeks
13913.41161 6.93581 (139*2π)/3052 weeks
1409.70544 5.70789 (140*2π)/3052 weeks
14110.97872 6.60038 (141*2π)/3052 weeks
1425.28962 4.25135 (142*2π)/3052 weeks
1436.83876 1.18251 (143*2π)/3052 weeks
1447.35108 -.75601 (144*2π)/3052 weeks
1458.74418 -1.92363 (145*2π)/3052 weeks
14611.90368 -.13984 (146*2π)/3052 weeks
1479.38852 1.16028 (147*2π)/3052 weeks
1487.83957 -3.3696 (148*2π)/3052 weeks
14911.33005 -3.63926 (149*2π)/3052 weeks
15012.54105 -1.95383 (150*2π)/3052 weeks
15113.71887 -3.99262 (151*2π)/3052 weeks
15215.52046 -.67308 (152*2π)/3052 weeks
15315.52046 .67308 (153*2π)/3052 weeks
15413.71887 3.99262 (154*2π)/3052 weeks
15512.54105 1.95383 (155*2π)/3052 weeks
15611.33005 3.63926 (156*2π)/3052 weeks
1577.83957 3.3696 (157*2π)/3052 weeks
1589.38852 -1.16028 (158*2π)/3052 weeks
15911.90368 .13984 (159*2π)/3052 weeks
1608.74418 1.92363 (160*2π)/3052 weeks
1617.35108 .75601 (161*2π)/3052 weeks
1626.83876 -1.18251 (162*2π)/3052 weeks
1635.28962 -4.25135 (163*2π)/3052 weeks
16410.97872 -6.60038 (164*2π)/3052 weeks
1659.70544 -5.70789 (165*2π)/3052 weeks
16613.41161 -6.93581 (166*2π)/3052 weeks
16714.50473 -6.46246 (167*2π)/3052 weeks
16817.16238 -3.15587 (168*2π)/3052 weeks
16915.30393 -3.30199 (169*2π)/3052 weeks
17017.91562 -1.50127 (170*2π)/3052 weeks
17117.26863 2.39326 (171*2π)/3052 weeks
17213.69395 5.29462 (172*2π)/3052 weeks
1738.13485 1.62584 (173*2π)/3052 weeks
17410.2553 -.08987 (174*2π)/3052 weeks
1758.04604 -1.51536 (175*2π)/3052 weeks
17611.00078 -1.72876 (176*2π)/3052 weeks
1779.13208 -2.56386 (177*2π)/3052 weeks
1789.83735 -1.4354 (178*2π)/3052 weeks
1799.55176 -3.71297 (179*2π)/3052 weeks
18011.07032 -4.24601 (180*2π)/3052 weeks
18111.1235 -4.11492 (181*2π)/3052 weeks
18213.29726 -4.25875 (182*2π)/3052 weeks
18311.21367 -2.18049 (183*2π)/3052 weeks
18413.85511 -.25088 (184*2π)/3052 weeks
1857.90117 -.47686 (185*2π)/3052 weeks
1865.09891 -2.42887 (186*2π)/3052 weeks
1879.42116 -11.00861 (187*2π)/3052 weeks
18812.85444 -4.5233 (188*2π)/3052 weeks
18911.34817 -6.83685 (189*2π)/3052 weeks
19012.50321 -5.61179 (190*2π)/3052 weeks
19112.92867 -7.10638 (191*2π)/3052 weeks
19214.80718 -8.21468 (192*2π)/3052 weeks
19319.03372 -4.27928 (193*2π)/3052 weeks
19417.04417 -1.48126 (194*2π)/3052 weeks
19514.46007 .20821 (195*2π)/3052 weeks
19615.54424 -.5573 (196*2π)/3052 weeks
19711.55555 3.03049 (197*2π)/3052 weeks
1988.87202 .46519 (198*2π)/3052 weeks
1998.28957 -3.37573 (199*2π)/3052 weeks
2009.13632 -2.80332 (200*2π)/3052 weeks
2019.11884 -6.18812 (201*2π)/3052 weeks
20212.6997 -6.08292 (202*2π)/3052 weeks
20314.65425 -6.6014 (203*2π)/3052 weeks
20414.91238 -.07423 (204*2π)/3051 weeks
20512.38434 -2.60199 (205*2π)/3051 weeks
20613.46845 -.06808 (206*2π)/3051 weeks
20711.07676 -1.05071 (207*2π)/3051 weeks
2088.73961 .50493 (208*2π)/3051 weeks
2099.08429 -3.48589 (209*2π)/3051 weeks
21012.92408 -4.64524 (210*2π)/3051 weeks
21113.56875 1.81177 (211*2π)/3051 weeks
2128.08169 2.20618 (212*2π)/3051 weeks
2135.14591 -.00362 (213*2π)/3051 weeks
2148.69671 -3.06027 (214*2π)/3051 weeks
2156.26514 2.63247 (215*2π)/3051 weeks
2163.28663 .28041 (216*2π)/3051 weeks
217.37919 .63177 (217*2π)/3051 weeks
218-1.27818 -5.16126 (218*2π)/3051 weeks
219-.85271 -5.53194 (219*2π)/3051 weeks
220.89998 -7.50964 (220*2π)/3051 weeks
221.24305 -6.69856 (221*2π)/3051 weeks
222-4.63544 -8.72425 (222*2π)/3051 weeks
223-1.39562 -16.92294 (223*2π)/3051 weeks
2242.22797 -16.21892 (224*2π)/3051 weeks
2252.76768 -17.27526 (225*2π)/3051 weeks
2266.67483 -19.23502 (226*2π)/3051 weeks
2277.02682 -17.38798 (227*2π)/3051 weeks
22811.22243 -17.56658 (228*2π)/3051 weeks
2298.83417 -13.60154 (229*2π)/3051 weeks
2308.76182 -12.14746 (230*2π)/3051 weeks
2312.06209 -18.53462 (231*2π)/3051 weeks
2329.17571 -21.12975 (232*2π)/3051 weeks
23310.33435 -21.01641 (233*2π)/3051 weeks
23414.37423 -20.85839 (234*2π)/3051 weeks
23512.35848 -17.6089 (235*2π)/3051 weeks
23617.64935 -22.51666 (236*2π)/3051 weeks
23719.88475 -14.83959 (237*2π)/3051 weeks
23816.5724 -13.13409 (238*2π)/3051 weeks
23918.46876 -11.34424 (239*2π)/3051 weeks
24012.73579 -6.27401 (240*2π)/3051 weeks
2419.10255 -17.04906 (241*2π)/3051 weeks
24217.22687 -14.41121 (242*2π)/3051 weeks
24316.5545 -9.19363 (243*2π)/3051 weeks
24411.30084 -7.4735 (244*2π)/3051 weeks
24511.09637 -10.02278 (245*2π)/3051 weeks
24610.59697 -11.0901 (246*2π)/3051 weeks
2479.8036 -7.09818 (247*2π)/3051 weeks
2485.33192 -7.11602 (248*2π)/3051 weeks
2493.38157 -10.24905 (249*2π)/3051 weeks
2501.8942 -14.02499 (250*2π)/3051 weeks
251-.22624 -15.8624 (251*2π)/3051 weeks
2521.20019 -13.13054 (252*2π)/3051 weeks
253-5.45613 -20.97186 (253*2π)/3051 weeks
254-1.49013 -21.63091 (254*2π)/3051 weeks
255-6.35555 -28.04894 (255*2π)/3051 weeks
256.19165 -33.75433 (256*2π)/3051 weeks
257-5.72715 -36.17996 (257*2π)/3051 weeks
2585.33693 -46.91608 (258*2π)/3051 weeks
2598.57378 -52.65235 (259*2π)/3051 weeks
26030.95149 -47.88448 (260*2π)/3051 weeks
26127.34075 -37.55021 (261*2π)/3051 weeks
26232.58564 -36.31716 (262*2π)/3051 weeks
26327.76496 -31.37353 (263*2π)/3051 weeks
26437.22006 -32.38036 (264*2π)/3051 weeks
26532.53984 -24.07 (265*2π)/3051 weeks
26641.86108 -25.71137 (266*2π)/3051 weeks
26737.74505 -7.97012 (267*2π)/3051 weeks
26826.00935 -6.67302 (268*2π)/3051 weeks
26924.19688 -9.24056 (269*2π)/3051 weeks
27014.44363 -5.88978 (270*2π)/3051 weeks
27111.70769 -11.94034 (271*2π)/3051 weeks
2729.96819 -20.16829 (272*2π)/3051 weeks
27316.04998 -12.25487 (273*2π)/3051 weeks
2742.85676 -17.33967 (274*2π)/3051 weeks
2758.93234 -16.88829 (275*2π)/3051 weeks
276-2.29649 -21.14708 (276*2π)/3051 weeks
277-4.19696 -28.20671 (277*2π)/3051 weeks
27814.94389 -39.6828 (278*2π)/3051 weeks
2793.68062 -22.38987 (279*2π)/3051 weeks
28011.94844 -27.85346 (280*2π)/3051 weeks
281-1.21228 -20.60529 (281*2π)/3051 weeks
282-11.3841 -29.54741 (282*2π)/3051 weeks
283-7.59966 -35.39789 (283*2π)/3051 weeks
284-15.98639 -33.25277 (284*2π)/3051 weeks
285-32.73256 -45.50903 (285*2π)/3051 weeks
286-37.01634 -65.61526 (286*2π)/3051 weeks
287-28.18847 -96.35799 (287*2π)/3051 weeks
288-9.44019 -90.15487 (288*2π)/3051 weeks
289-16.85213 -120.192 (289*2π)/3051 weeks
29020.94826 -122.2152 (290*2π)/3051 weeks
29135.74574 -112.2148 (291*2π)/3051 weeks
29227.28679 -76.62932 (292*2π)/3051 weeks
293-4.03895 -115.1601 (293*2π)/3051 weeks
2944.78329 -150.2503 (294*2π)/3051 weeks
29542.36036 -182.423 (295*2π)/3051 weeks
29690.85185 -158.2067 (296*2π)/3051 weeks
29792.78513 -198.606 (297*2π)/3051 weeks
298176.5216 -117.6923 (298*2π)/3051 weeks
29999.00889 -123.4874 (299*2π)/3051 weeks
300110.0151 -155.4829 (300*2π)/3051 weeks
301162.0942 -170.2288 (301*2π)/3051 weeks
302167.8144 -193.3948 (302*2π)/3051 weeks
303242.2294 -169.6461 (303*2π)/3051 weeks

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