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Fourier Analysis of RUSS (Direxion Daily Russia Bear 3x S)


RUSS (Direxion Daily Russia Bear 3x S) appears to have interesting cyclic behaviour every 19 weeks (6.5211*cosine), 27 weeks (5.2079*cosine), and 16 weeks (4.5764*cosine).

RUSS (Direxion Daily Russia Bear 3x S) has an average price of 67.51 (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 RUSS (Direxion Daily Russia Bear 3x S), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
067.51206   0 
111.32092 33.19084 (1*2π)/296296 weeks
26.70983 32.75614 (2*2π)/296148 weeks
33.57503 19.15214 (3*2π)/29699 weeks
4-3.6183 16.64429 (4*2π)/29674 weeks
54.54883 15.79741 (5*2π)/29659 weeks
61.21917 10.64057 (6*2π)/29649 weeks
7-15.3186 12.1891 (7*2π)/29642 weeks
8-2.08614 3.74932 (8*2π)/29637 weeks
9-9.29401 -1.7555 (9*2π)/29633 weeks
10-1.44304 .13017 (10*2π)/29630 weeks
115.20795 .52564 (11*2π)/29627 weeks
122.08177 2.35418 (12*2π)/29625 weeks
13-3.97963 3.79079 (13*2π)/29623 weeks
14-2.04077 -1.46769 (14*2π)/29621 weeks
15-.96435 -1.76976 (15*2π)/29620 weeks
166.5211 .33478 (16*2π)/29619 weeks
173.81132 -.9561 (17*2π)/29617 weeks
184.57639 2.92479 (18*2π)/29616 weeks
193.9403 3.95443 (19*2π)/29616 weeks
201.42242 4.57269 (20*2π)/29615 weeks
21.78939 4.94823 (21*2π)/29614 weeks
222.20855 2.83496 (22*2π)/29613 weeks
23-.77452 4.61741 (23*2π)/29613 weeks
24-1.57458 4.82442 (24*2π)/29612 weeks
25-1.8398 1.19763 (25*2π)/29612 weeks
26-4.12456 -.17408 (26*2π)/29611 weeks
271.58583 -.87564 (27*2π)/29611 weeks
282.01689 -1.02531 (28*2π)/29611 weeks
29.86325 1.05898 (29*2π)/29610 weeks
302.39746 .37669 (30*2π)/29610 weeks
311.07309 1.84678 (31*2π)/29610 weeks
321.92174 .51848 (32*2π)/2969 weeks
332.50441 1.76134 (33*2π)/2969 weeks
342.37904 3.23305 (34*2π)/2969 weeks
351.32415 3.07599 (35*2π)/2968 weeks
36-.26464 4.32573 (36*2π)/2968 weeks
37-1.04413 4.01307 (37*2π)/2968 weeks
38-2.06949 .71122 (38*2π)/2968 weeks
39-1.24141 2.56459 (39*2π)/2968 weeks
40-1.19975 .31064 (40*2π)/2967 weeks
41-2.26291 1.45963 (41*2π)/2967 weeks
42-2.06265 .48156 (42*2π)/2967 weeks
43-1.29818 -1.23969 (43*2π)/2967 weeks
44-1.55545 -3.2372 (44*2π)/2967 weeks
451.82583 -1.27 (45*2π)/2967 weeks
462.10659 -2.22656 (46*2π)/2966 weeks
471.52384 .79966 (47*2π)/2966 weeks
482.46842 .00824 (48*2π)/2966 weeks
492.16675 .32491 (49*2π)/2966 weeks
501.86265 .74656 (50*2π)/2966 weeks
512.66276 1.75715 (51*2π)/2966 weeks
52.56653 1.10411 (52*2π)/2966 weeks
53.47067 2.6907 (53*2π)/2966 weeks
54.72369 1.87086 (54*2π)/2965 weeks
55.34174 1.75993 (55*2π)/2965 weeks
56.23221 .73094 (56*2π)/2965 weeks
57-.45548 .5887 (57*2π)/2965 weeks
58-.48664 1.32236 (58*2π)/2965 weeks
59.19054 1.12154 (59*2π)/2965 weeks
60-.44209 .4646 (60*2π)/2965 weeks
61-.06158 -.30358 (61*2π)/2965 weeks
62.58716 -1.04683 (62*2π)/2965 weeks
63.37413 1.18913 (63*2π)/2965 weeks
64.44441 .53534 (64*2π)/2965 weeks
65.2622 .36192 (65*2π)/2965 weeks
66.52702 .31988 (66*2π)/2964 weeks
67.59814 -1.03567 (67*2π)/2964 weeks
68.72792 .6619 (68*2π)/2964 weeks
69.93582 .5329 (69*2π)/2964 weeks
70.57574 .38291 (70*2π)/2964 weeks
71.65699 .87172 (71*2π)/2964 weeks
721.48456 .24939 (72*2π)/2964 weeks
73-.22196 .43847 (73*2π)/2964 weeks
74.23041 1.39047 (74*2π)/2964 weeks
75.07854 .01206 (75*2π)/2964 weeks
76-.46353 .42138 (76*2π)/2964 weeks
77.7543 -.58882 (77*2π)/2964 weeks
78.50146 -.96167 (78*2π)/2964 weeks
79.68499 -.06039 (79*2π)/2964 weeks
801.97997 -.33467 (80*2π)/2964 weeks
811.01147 .39761 (81*2π)/2964 weeks
821.35557 1.0055 (82*2π)/2964 weeks
831.58398 -.14831 (83*2π)/2964 weeks
84.49892 .86567 (84*2π)/2964 weeks
851.44219 1.47297 (85*2π)/2963 weeks
86.55284 1.03758 (86*2π)/2963 weeks
87.05325 1.1901 (87*2π)/2963 weeks
88.02335 .54403 (88*2π)/2963 weeks
89.46468 -.12069 (89*2π)/2963 weeks
90.47274 1.02384 (90*2π)/2963 weeks
91.58867 .57585 (91*2π)/2963 weeks
92-.48272 .1332 (92*2π)/2963 weeks
93.8127 .58809 (93*2π)/2963 weeks
941.11703 .13512 (94*2π)/2963 weeks
95.52234 .31447 (95*2π)/2963 weeks
96.28214 1.08714 (96*2π)/2963 weeks
97.06845 .33355 (97*2π)/2963 weeks
98-.00371 .78155 (98*2π)/2963 weeks
99.75664 -.38107 (99*2π)/2963 weeks
100.26005 -.20027 (100*2π)/2963 weeks
101.85233 .34461 (101*2π)/2963 weeks
102.77933 .5617 (102*2π)/2963 weeks
103.89056 .34494 (103*2π)/2963 weeks
104.81071 .68483 (104*2π)/2963 weeks
105.63346 1.18839 (105*2π)/2963 weeks
106.12221 1.02736 (106*2π)/2963 weeks
107-.07574 .80023 (107*2π)/2963 weeks
108-.76859 .69911 (108*2π)/2963 weeks
109-.59383 -.03674 (109*2π)/2963 weeks
110.04544 -.56335 (110*2π)/2963 weeks
111.43859 -.19193 (111*2π)/2963 weeks
112.58602 -.21002 (112*2π)/2963 weeks
113.18745 .02264 (113*2π)/2963 weeks
114-.02636 .19136 (114*2π)/2963 weeks
1151.38696 -.71498 (115*2π)/2963 weeks
116.48024 .20304 (116*2π)/2963 weeks
117.80291 1.34056 (117*2π)/2963 weeks
118.2632 -.20637 (118*2π)/2963 weeks
119-.78025 .36782 (119*2π)/2962 weeks
120.54212 -.34686 (120*2π)/2962 weeks
121.30471 -.68584 (121*2π)/2962 weeks
122.68345 .17019 (122*2π)/2962 weeks
1231.48708 -.14364 (123*2π)/2962 weeks
124.37344 -.24035 (124*2π)/2962 weeks
125.66588 .67835 (125*2π)/2962 weeks
1261.34744 -.19368 (126*2π)/2962 weeks
127.54116 .56053 (127*2π)/2962 weeks
1281.15584 .94989 (128*2π)/2962 weeks
129-.04825 1.13312 (129*2π)/2962 weeks
130-.62088 1.25641 (130*2π)/2962 weeks
131-.41475 -.03365 (131*2π)/2962 weeks
132-.50533 -.67151 (132*2π)/2962 weeks
133-.21634 -.01477 (133*2π)/2962 weeks
134.41239 -.78443 (134*2π)/2962 weeks
135-.18661 -.48467 (135*2π)/2962 weeks
136.73107 -.36439 (136*2π)/2962 weeks
137.44955 -1.34967 (137*2π)/2962 weeks
1381.32965 -.27304 (138*2π)/2962 weeks
1391.41917 -.06998 (139*2π)/2962 weeks
140.94646 .2416 (140*2π)/2962 weeks
141.68047 1.02782 (141*2π)/2962 weeks
1421.04081 .16359 (142*2π)/2962 weeks
143.53246 -.13873 (143*2π)/2962 weeks
144.416 .83591 (144*2π)/2962 weeks
145.28316 .76069 (145*2π)/2962 weeks
146.38333 .45554 (146*2π)/2962 weeks
147-.41964 .3941 (147*2π)/2962 weeks
148-.23547   (148*2π)/2962 weeks
149-.41964 -.3941 (149*2π)/2962 weeks
150.38333 -.45554 (150*2π)/2962 weeks
151.28316 -.76069 (151*2π)/2962 weeks
152.416 -.83591 (152*2π)/2962 weeks
153.53246 .13873 (153*2π)/2962 weeks
1541.04081 -.16359 (154*2π)/2962 weeks
155.68047 -1.02782 (155*2π)/2962 weeks
156.94646 -.2416 (156*2π)/2962 weeks
1571.41917 .06998 (157*2π)/2962 weeks
1581.32965 .27304 (158*2π)/2962 weeks
159.44955 1.34967 (159*2π)/2962 weeks
160.73107 .36439 (160*2π)/2962 weeks
161-.18661 .48467 (161*2π)/2962 weeks
162.41239 .78443 (162*2π)/2962 weeks
163-.21634 .01477 (163*2π)/2962 weeks
164-.50533 .67151 (164*2π)/2962 weeks
165-.41475 .03365 (165*2π)/2962 weeks
166-.62088 -1.25641 (166*2π)/2962 weeks
167-.04825 -1.13312 (167*2π)/2962 weeks
1681.15584 -.94989 (168*2π)/2962 weeks
169.54116 -.56053 (169*2π)/2962 weeks
1701.34744 .19368 (170*2π)/2962 weeks
171.66588 -.67835 (171*2π)/2962 weeks
172.37344 .24035 (172*2π)/2962 weeks
1731.48708 .14364 (173*2π)/2962 weeks
174.68345 -.17019 (174*2π)/2962 weeks
175.30471 .68584 (175*2π)/2962 weeks
176.54212 .34686 (176*2π)/2962 weeks
177-.78025 -.36782 (177*2π)/2962 weeks
178.2632 .20637 (178*2π)/2962 weeks
179.80291 -1.34056 (179*2π)/2962 weeks
180.48024 -.20304 (180*2π)/2962 weeks
1811.38696 .71498 (181*2π)/2962 weeks
182-.02636 -.19136 (182*2π)/2962 weeks
183.18745 -.02264 (183*2π)/2962 weeks
184.58602 .21002 (184*2π)/2962 weeks
185.43859 .19193 (185*2π)/2962 weeks
186.04544 .56335 (186*2π)/2962 weeks
187-.59383 .03674 (187*2π)/2962 weeks
188-.76859 -.69911 (188*2π)/2962 weeks
189-.07574 -.80023 (189*2π)/2962 weeks
190.12221 -1.02736 (190*2π)/2962 weeks
191.63346 -1.18839 (191*2π)/2962 weeks
192.81071 -.68483 (192*2π)/2962 weeks
193.89056 -.34494 (193*2π)/2962 weeks
194.77933 -.5617 (194*2π)/2962 weeks
195.85233 -.34461 (195*2π)/2962 weeks
196.26005 .20027 (196*2π)/2962 weeks
197.75664 .38107 (197*2π)/2962 weeks
198-.00371 -.78155 (198*2π)/2961 weeks
199.06845 -.33355 (199*2π)/2961 weeks
200.28214 -1.08714 (200*2π)/2961 weeks
201.52234 -.31447 (201*2π)/2961 weeks
2021.11703 -.13512 (202*2π)/2961 weeks
203.8127 -.58809 (203*2π)/2961 weeks
204-.48272 -.1332 (204*2π)/2961 weeks
205.58867 -.57585 (205*2π)/2961 weeks
206.47274 -1.02384 (206*2π)/2961 weeks
207.46468 .12069 (207*2π)/2961 weeks
208.02335 -.54403 (208*2π)/2961 weeks
209.05325 -1.1901 (209*2π)/2961 weeks
210.55284 -1.03758 (210*2π)/2961 weeks
2111.44219 -1.47297 (211*2π)/2961 weeks
212.49892 -.86567 (212*2π)/2961 weeks
2131.58398 .14831 (213*2π)/2961 weeks
2141.35557 -1.0055 (214*2π)/2961 weeks
2151.01147 -.39761 (215*2π)/2961 weeks
2161.97997 .33467 (216*2π)/2961 weeks
217.68499 .06039 (217*2π)/2961 weeks
218.50146 .96167 (218*2π)/2961 weeks
219.7543 .58882 (219*2π)/2961 weeks
220-.46353 -.42138 (220*2π)/2961 weeks
221.07854 -.01206 (221*2π)/2961 weeks
222.23041 -1.39047 (222*2π)/2961 weeks
223-.22196 -.43847 (223*2π)/2961 weeks
2241.48456 -.24939 (224*2π)/2961 weeks
225.65699 -.87172 (225*2π)/2961 weeks
226.57574 -.38291 (226*2π)/2961 weeks
227.93582 -.5329 (227*2π)/2961 weeks
228.72792 -.6619 (228*2π)/2961 weeks
229.59814 1.03567 (229*2π)/2961 weeks
230.52702 -.31988 (230*2π)/2961 weeks
231.2622 -.36192 (231*2π)/2961 weeks
232.44441 -.53534 (232*2π)/2961 weeks
233.37413 -1.18913 (233*2π)/2961 weeks
234.58716 1.04683 (234*2π)/2961 weeks
235-.06158 .30358 (235*2π)/2961 weeks
236-.44209 -.4646 (236*2π)/2961 weeks
237.19054 -1.12154 (237*2π)/2961 weeks
238-.48664 -1.32236 (238*2π)/2961 weeks
239-.45548 -.5887 (239*2π)/2961 weeks
240.23221 -.73094 (240*2π)/2961 weeks
241.34174 -1.75993 (241*2π)/2961 weeks
242.72369 -1.87086 (242*2π)/2961 weeks
243.47067 -2.6907 (243*2π)/2961 weeks
244.56653 -1.10411 (244*2π)/2961 weeks
2452.66276 -1.75715 (245*2π)/2961 weeks
2461.86265 -.74656 (246*2π)/2961 weeks
2472.16675 -.32491 (247*2π)/2961 weeks
2482.46842 -.00824 (248*2π)/2961 weeks
2491.52384 -.79966 (249*2π)/2961 weeks
2502.10659 2.22656 (250*2π)/2961 weeks
2511.82583 1.27 (251*2π)/2961 weeks
252-1.55545 3.2372 (252*2π)/2961 weeks
253-1.29818 1.23969 (253*2π)/2961 weeks
254-2.06265 -.48156 (254*2π)/2961 weeks
255-2.26291 -1.45963 (255*2π)/2961 weeks
256-1.19975 -.31064 (256*2π)/2961 weeks
257-1.24141 -2.56459 (257*2π)/2961 weeks
258-2.06949 -.71122 (258*2π)/2961 weeks
259-1.04413 -4.01307 (259*2π)/2961 weeks
260-.26464 -4.32573 (260*2π)/2961 weeks
2611.32415 -3.07599 (261*2π)/2961 weeks
2622.37904 -3.23305 (262*2π)/2961 weeks
2632.50441 -1.76134 (263*2π)/2961 weeks
2641.92174 -.51848 (264*2π)/2961 weeks
2651.07309 -1.84678 (265*2π)/2961 weeks
2662.39746 -.37669 (266*2π)/2961 weeks
267.86325 -1.05898 (267*2π)/2961 weeks
2682.01689 1.02531 (268*2π)/2961 weeks
2691.58583 .87564 (269*2π)/2961 weeks
270-4.12456 .17408 (270*2π)/2961 weeks
271-1.8398 -1.19763 (271*2π)/2961 weeks
272-1.57458 -4.82442 (272*2π)/2961 weeks
273-.77452 -4.61741 (273*2π)/2961 weeks
2742.20855 -2.83496 (274*2π)/2961 weeks
275.78939 -4.94823 (275*2π)/2961 weeks
2761.42242 -4.57269 (276*2π)/2961 weeks
2773.9403 -3.95443 (277*2π)/2961 weeks
2784.57639 -2.92479 (278*2π)/2961 weeks
2793.81132 .9561 (279*2π)/2961 weeks
2806.5211 -.33478 (280*2π)/2961 weeks
281-.96435 1.76976 (281*2π)/2961 weeks
282-2.04077 1.46769 (282*2π)/2961 weeks
283-3.97963 -3.79079 (283*2π)/2961 weeks
2842.08177 -2.35418 (284*2π)/2961 weeks
2855.20795 -.52564 (285*2π)/2961 weeks
286-1.44304 -.13017 (286*2π)/2961 weeks
287-9.29401 1.7555 (287*2π)/2961 weeks
288-2.08614 -3.74932 (288*2π)/2961 weeks
289-15.3186 -12.1891 (289*2π)/2961 weeks
2901.21917 -10.64057 (290*2π)/2961 weeks
2914.54883 -15.79741 (291*2π)/2961 weeks
292-3.6183 -16.64429 (292*2π)/2961 weeks
2933.57503 -19.15214 (293*2π)/2961 weeks
2946.70983 -32.75614 (294*2π)/2961 weeks

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