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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 30 weeks (179.9402*sine), 27 weeks (140.4808*sine), and 23 weeks (47.0062*cosine).

RUSL (Direxion Daily Russia Bull 3x S) has an average price of 555.34 (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 1/17/2017 for RUSL (Direxion Daily Russia Bull 3x S), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0555.3369   0 
1237.3556 444.8078 (1*2π)/296296 weeks
2251.5239 182.5992 (2*2π)/296148 weeks
3167.8963 194.2562 (3*2π)/29699 weeks
4162.6073 180.9473 (4*2π)/29674 weeks
5112.3472 154.15 (5*2π)/29659 weeks
6103.5421 115.0132 (6*2π)/29649 weeks
7187.3249 155.9187 (7*2π)/29642 weeks
877.54176 186.6816 (8*2π)/29637 weeks
992.34373 179.8424 (9*2π)/29633 weeks
1030.81382 179.9402 (10*2π)/29630 weeks
111.92654 140.4808 (11*2π)/29627 weeks
12-3.37739 100.2717 (12*2π)/29625 weeks
1347.00623 94.76632 (13*2π)/29623 weeks
1431.95398 118.4966 (14*2π)/29621 weeks
159.84627 130.7787 (15*2π)/29620 weeks
16-21.49701 98.26389 (16*2π)/29619 weeks
17-12.30134 100.4057 (17*2π)/29617 weeks
18-39.4609 79.74827 (18*2π)/29616 weeks
19-35.79622 55.32524 (19*2π)/29616 weeks
20-23.51385 34.84922 (20*2π)/29615 weeks
21-9.74955 33.83932 (21*2π)/29614 weeks
22-11.71562 34.35934 (22*2π)/29613 weeks
23-5.20531 22.12096 (23*2π)/29613 weeks
2410.28302 22.72297 (24*2π)/29612 weeks
251.17025 28.08571 (25*2π)/29612 weeks
2618.97059 34.08577 (26*2π)/29611 weeks
27-5.43013 32.63049 (27*2π)/29611 weeks
28-2.40107 23.46662 (28*2π)/29611 weeks
297.92225 15.9791 (29*2π)/29610 weeks
303.1018 18.99717 (30*2π)/29610 weeks
3115.6161 11.56454 (31*2π)/29610 weeks
3210.33158 20.68758 (32*2π)/2969 weeks
3311.77959 12.00177 (33*2π)/2969 weeks
3414.95655 5.51829 (34*2π)/2969 weeks
3524.43629 9.64923 (35*2π)/2968 weeks
3627.29053 6.45829 (36*2π)/2968 weeks
3740.35284 9.42213 (37*2π)/2968 weeks
3840.31823 28.601 (38*2π)/2968 weeks
3934.93627 24.2871 (39*2π)/2968 weeks
4035.6503 35.87534 (40*2π)/2967 weeks
4130.22995 30.92866 (41*2π)/2967 weeks
4231.18009 39.55205 (42*2π)/2967 weeks
4329.64563 38.9767 (43*2π)/2967 weeks
4425.95872 56.26502 (44*2π)/2967 weeks
456.47572 48.41365 (45*2π)/2967 weeks
46-.85231 47.58626 (46*2π)/2966 weeks
47-1.9843 32.19138 (47*2π)/2966 weeks
48-4.25885 34.14629 (48*2π)/2966 weeks
49-5.64377 23.91711 (49*2π)/2966 weeks
50-2.26435 24.41527 (50*2π)/2966 weeks
51-4.20546 14.96014 (51*2π)/2966 weeks
522.27154 17.68055 (52*2π)/2966 weeks
532.03949 13.64899 (53*2π)/2966 weeks
541.64713 10.98533 (54*2π)/2965 weeks
553.50658 8.80804 (55*2π)/2965 weeks
568.48614 7.47613 (56*2π)/2965 weeks
5711.89509 10.99228 (57*2π)/2965 weeks
5811.01288 10.0435 (58*2π)/2965 weeks
5910.62482 8.71966 (59*2π)/2965 weeks
6016.35809 8.82306 (60*2π)/2965 weeks
6117.89766 14.08335 (61*2π)/2965 weeks
6210.76723 18.41772 (62*2π)/2965 weeks
6311.93981 6.61725 (63*2π)/2965 weeks
6418.91842 11.39658 (64*2π)/2965 weeks
6516.9801 13.62195 (65*2π)/2965 weeks
6620.42444 15.3439 (66*2π)/2964 weeks
6717.6561 23.38615 (67*2π)/2964 weeks
6813.0156 17.91682 (68*2π)/2964 weeks
6914.22626 21.86404 (69*2π)/2964 weeks
7010.24887 21.47368 (70*2π)/2964 weeks
718.65673 22.2629 (71*2π)/2964 weeks
721.58447 16.62211 (72*2π)/2964 weeks
739.62143 14.08752 (73*2π)/2964 weeks
7410.18544 13.99225 (74*2π)/2964 weeks
759.87977 19.42561 (75*2π)/2964 weeks
767.57871 17.7381 (76*2π)/2964 weeks
774.68782 20.15893 (77*2π)/2964 weeks
782.56798 17.3646 (78*2π)/2964 weeks
791.61503 17.35041 (79*2π)/2964 weeks
80-4.78909 15.29338 (80*2π)/2964 weeks
81-1.8449 7.17562 (81*2π)/2964 weeks
821.0073 7.67492 (82*2π)/2964 weeks
83-.18998 8.03793 (83*2π)/2964 weeks
84.57187 5.70864 (84*2π)/2964 weeks
85-1.5035 1.48108 (85*2π)/2963 weeks
863.42631 -.36324 (86*2π)/2963 weeks
874.72495 -1.93431 (87*2π)/2963 weeks
8810.49947 .74363 (88*2π)/2963 weeks
895.3681 1.49323 (89*2π)/2963 weeks
907.79796 -2.06091 (90*2π)/2963 weeks
9112.57753 -3.082 (91*2π)/2963 weeks
9214.44907 3.66258 (92*2π)/2963 weeks
939.5904 3.78199 (93*2π)/2963 weeks
948.32634 .13704 (94*2π)/2963 weeks
9511.70172 1.03203 (95*2π)/2963 weeks
9613.58732 -.23306 (96*2π)/2963 weeks
9712.93067 2.70888 (97*2π)/2963 weeks
9815.22764 .0017 (98*2π)/2963 weeks
9915.05208 6.79625 (99*2π)/2963 weeks
10013.06587 6.357 (100*2π)/2963 weeks
1019.21388 6.12493 (101*2π)/2963 weeks
1029.73658 2.82408 (102*2π)/2963 weeks
1038.14924 2.9682 (103*2π)/2963 weeks
1049.50024 -.74975 (104*2π)/2963 weeks
10513.28383 -3.29575 (105*2π)/2963 weeks
10615.34007 1.25062 (106*2π)/2963 weeks
10715.96517 -.32895 (107*2π)/2963 weeks
10817.86523 1.9074 (108*2π)/2963 weeks
10919.26849 6.62724 (109*2π)/2963 weeks
11014.18989 7.71327 (110*2π)/2963 weeks
11112.59013 6.85293 (111*2π)/2963 weeks
11213.32111 6.41505 (112*2π)/2963 weeks
11310.99444 5.58523 (113*2π)/2963 weeks
11414.57401 7.94985 (114*2π)/2963 weeks
1154.6078 7.75263 (115*2π)/2963 weeks
1167.93869 1.26789 (116*2π)/2963 weeks
11711.10626 -1.7846 (117*2π)/2963 weeks
11812.73276 3.52665 (118*2π)/2963 weeks
11914.12672 2.37142 (119*2π)/2962 weeks
12011.80846 4.4323 (120*2π)/2962 weeks
12111.54428 3.83924 (121*2π)/2962 weeks
12210.07556 3.99791 (122*2π)/2962 weeks
1239.26312 1.93425 (123*2π)/2962 weeks
12410.16304 3.04442 (124*2π)/2962 weeks
12511.03394 1.06557 (125*2π)/2962 weeks
1268.67091 2.26323 (126*2π)/2962 weeks
12710.4729 -.35049 (127*2π)/2962 weeks
1288.45216 -1.17584 (128*2π)/2962 weeks
12913.47881 -5.78941 (129*2π)/2962 weeks
13017.53835 -2.76592 (130*2π)/2962 weeks
13118.34255 1.38204 (131*2π)/2962 weeks
13215.60039 3.29493 (132*2π)/2962 weeks
13317.62327 3.41869 (133*2π)/2962 weeks
13414.56806 6.54863 (134*2π)/2962 weeks
13513.35219 7.41128 (135*2π)/2962 weeks
1369.96731 5.33424 (136*2π)/2962 weeks
13710.32998 7.54991 (137*2π)/2962 weeks
1385.54094 3.15224 (138*2π)/2962 weeks
1397.05928 .96838 (139*2π)/2962 weeks
1408.11368 -1.15759 (140*2π)/2962 weeks
1419.99976 -2.61225 (141*2π)/2962 weeks
14211.32425 .80887 (142*2π)/2962 weeks
1438.01205 .67352 (143*2π)/2962 weeks
14410.07554 -4.17086 (144*2π)/2962 weeks
14512.69668 -3.50557 (145*2π)/2962 weeks
14612.04625 -2.68904 (146*2π)/2962 weeks
14716.04502 -2.55671 (147*2π)/2962 weeks
14815.70366   (148*2π)/2962 weeks
14916.04502 2.55671 (149*2π)/2962 weeks
15012.04625 2.68904 (150*2π)/2962 weeks
15112.69668 3.50557 (151*2π)/2962 weeks
15210.07554 4.17086 (152*2π)/2962 weeks
1538.01205 -.67352 (153*2π)/2962 weeks
15411.32425 -.80887 (154*2π)/2962 weeks
1559.99976 2.61225 (155*2π)/2962 weeks
1568.11368 1.15759 (156*2π)/2962 weeks
1577.05928 -.96838 (157*2π)/2962 weeks
1585.54094 -3.15224 (158*2π)/2962 weeks
15910.32998 -7.54991 (159*2π)/2962 weeks
1609.96731 -5.33424 (160*2π)/2962 weeks
16113.35219 -7.41128 (161*2π)/2962 weeks
16214.56806 -6.54863 (162*2π)/2962 weeks
16317.62327 -3.41869 (163*2π)/2962 weeks
16415.60039 -3.29493 (164*2π)/2962 weeks
16518.34255 -1.38204 (165*2π)/2962 weeks
16617.53835 2.76592 (166*2π)/2962 weeks
16713.47881 5.78941 (167*2π)/2962 weeks
1688.45216 1.17584 (168*2π)/2962 weeks
16910.4729 .35049 (169*2π)/2962 weeks
1708.67091 -2.26323 (170*2π)/2962 weeks
17111.03394 -1.06557 (171*2π)/2962 weeks
17210.16304 -3.04442 (172*2π)/2962 weeks
1739.26312 -1.93425 (173*2π)/2962 weeks
17410.07556 -3.99791 (174*2π)/2962 weeks
17511.54428 -3.83924 (175*2π)/2962 weeks
17611.80846 -4.4323 (176*2π)/2962 weeks
17714.12672 -2.37142 (177*2π)/2962 weeks
17812.73276 -3.52665 (178*2π)/2962 weeks
17911.10626 1.7846 (179*2π)/2962 weeks
1807.93869 -1.26789 (180*2π)/2962 weeks
1814.6078 -7.75263 (181*2π)/2962 weeks
18214.57401 -7.94985 (182*2π)/2962 weeks
18310.99444 -5.58523 (183*2π)/2962 weeks
18413.32111 -6.41505 (184*2π)/2962 weeks
18512.59013 -6.85293 (185*2π)/2962 weeks
18614.18989 -7.71327 (186*2π)/2962 weeks
18719.26849 -6.62724 (187*2π)/2962 weeks
18817.86523 -1.9074 (188*2π)/2962 weeks
18915.96517 .32895 (189*2π)/2962 weeks
19015.34007 -1.25062 (190*2π)/2962 weeks
19113.28383 3.29575 (191*2π)/2962 weeks
1929.50024 .74975 (192*2π)/2962 weeks
1938.14924 -2.9682 (193*2π)/2962 weeks
1949.73658 -2.82408 (194*2π)/2962 weeks
1959.21388 -6.12493 (195*2π)/2962 weeks
19613.06587 -6.357 (196*2π)/2962 weeks
19715.05208 -6.79625 (197*2π)/2962 weeks
19815.22764 -.0017 (198*2π)/2961 weeks
19912.93067 -2.70888 (199*2π)/2961 weeks
20013.58732 .23306 (200*2π)/2961 weeks
20111.70172 -1.03203 (201*2π)/2961 weeks
2028.32634 -.13704 (202*2π)/2961 weeks
2039.5904 -3.78199 (203*2π)/2961 weeks
20414.44907 -3.66258 (204*2π)/2961 weeks
20512.57753 3.082 (205*2π)/2961 weeks
2067.79796 2.06091 (206*2π)/2961 weeks
2075.3681 -1.49323 (207*2π)/2961 weeks
20810.49947 -.74363 (208*2π)/2961 weeks
2094.72495 1.93431 (209*2π)/2961 weeks
2103.42631 .36324 (210*2π)/2961 weeks
211-1.5035 -1.48108 (211*2π)/2961 weeks
212.57187 -5.70864 (212*2π)/2961 weeks
213-.18998 -8.03793 (213*2π)/2961 weeks
2141.0073 -7.67492 (214*2π)/2961 weeks
215-1.8449 -7.17562 (215*2π)/2961 weeks
216-4.78909 -15.29338 (216*2π)/2961 weeks
2171.61503 -17.35041 (217*2π)/2961 weeks
2182.56798 -17.3646 (218*2π)/2961 weeks
2194.68782 -20.15893 (219*2π)/2961 weeks
2207.57871 -17.7381 (220*2π)/2961 weeks
2219.87977 -19.42561 (221*2π)/2961 weeks
22210.18544 -13.99225 (222*2π)/2961 weeks
2239.62143 -14.08752 (223*2π)/2961 weeks
2241.58447 -16.62211 (224*2π)/2961 weeks
2258.65673 -22.2629 (225*2π)/2961 weeks
22610.24887 -21.47368 (226*2π)/2961 weeks
22714.22626 -21.86404 (227*2π)/2961 weeks
22813.0156 -17.91682 (228*2π)/2961 weeks
22917.6561 -23.38615 (229*2π)/2961 weeks
23020.42444 -15.3439 (230*2π)/2961 weeks
23116.9801 -13.62195 (231*2π)/2961 weeks
23218.91842 -11.39658 (232*2π)/2961 weeks
23311.93981 -6.61725 (233*2π)/2961 weeks
23410.76723 -18.41772 (234*2π)/2961 weeks
23517.89766 -14.08335 (235*2π)/2961 weeks
23616.35809 -8.82306 (236*2π)/2961 weeks
23710.62482 -8.71966 (237*2π)/2961 weeks
23811.01288 -10.0435 (238*2π)/2961 weeks
23911.89509 -10.99228 (239*2π)/2961 weeks
2408.48614 -7.47613 (240*2π)/2961 weeks
2413.50658 -8.80804 (241*2π)/2961 weeks
2421.64713 -10.98533 (242*2π)/2961 weeks
2432.03949 -13.64899 (243*2π)/2961 weeks
2442.27154 -17.68055 (244*2π)/2961 weeks
245-4.20546 -14.96014 (245*2π)/2961 weeks
246-2.26435 -24.41527 (246*2π)/2961 weeks
247-5.64377 -23.91711 (247*2π)/2961 weeks
248-4.25885 -34.14629 (248*2π)/2961 weeks
249-1.9843 -32.19138 (249*2π)/2961 weeks
250-.85231 -47.58626 (250*2π)/2961 weeks
2516.47572 -48.41365 (251*2π)/2961 weeks
25225.95872 -56.26502 (252*2π)/2961 weeks
25329.64563 -38.9767 (253*2π)/2961 weeks
25431.18009 -39.55205 (254*2π)/2961 weeks
25530.22995 -30.92866 (255*2π)/2961 weeks
25635.6503 -35.87534 (256*2π)/2961 weeks
25734.93627 -24.2871 (257*2π)/2961 weeks
25840.31823 -28.601 (258*2π)/2961 weeks
25940.35284 -9.42213 (259*2π)/2961 weeks
26027.29053 -6.45829 (260*2π)/2961 weeks
26124.43629 -9.64923 (261*2π)/2961 weeks
26214.95655 -5.51829 (262*2π)/2961 weeks
26311.77959 -12.00177 (263*2π)/2961 weeks
26410.33158 -20.68758 (264*2π)/2961 weeks
26515.6161 -11.56454 (265*2π)/2961 weeks
2663.1018 -18.99717 (266*2π)/2961 weeks
2677.92225 -15.9791 (267*2π)/2961 weeks
268-2.40107 -23.46662 (268*2π)/2961 weeks
269-5.43013 -32.63049 (269*2π)/2961 weeks
27018.97059 -34.08577 (270*2π)/2961 weeks
2711.17025 -28.08571 (271*2π)/2961 weeks
27210.28302 -22.72297 (272*2π)/2961 weeks
273-5.20531 -22.12096 (273*2π)/2961 weeks
274-11.71562 -34.35934 (274*2π)/2961 weeks
275-9.74955 -33.83932 (275*2π)/2961 weeks
276-23.51385 -34.84922 (276*2π)/2961 weeks
277-35.79622 -55.32524 (277*2π)/2961 weeks
278-39.4609 -79.74827 (278*2π)/2961 weeks
279-12.30134 -100.4057 (279*2π)/2961 weeks
280-21.49701 -98.26389 (280*2π)/2961 weeks
2819.84627 -130.7787 (281*2π)/2961 weeks
28231.95398 -118.4966 (282*2π)/2961 weeks
28347.00623 -94.76632 (283*2π)/2961 weeks
284-3.37739 -100.2717 (284*2π)/2961 weeks
2851.92654 -140.4808 (285*2π)/2961 weeks
28630.81382 -179.9402 (286*2π)/2961 weeks
28792.34373 -179.8424 (287*2π)/2961 weeks
28877.54176 -186.6816 (288*2π)/2961 weeks
289187.3249 -155.9187 (289*2π)/2961 weeks
290103.5421 -115.0132 (290*2π)/2961 weeks
291112.3472 -154.15 (291*2π)/2961 weeks
292162.6073 -180.9473 (292*2π)/2961 weeks
293167.8963 -194.2562 (293*2π)/2961 weeks
294251.5239 -182.5992 (294*2π)/2961 weeks

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