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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 23 weeks (6.175*sine), 17 weeks (5.582*cosine), and 16 weeks (4.0514*cosine).

RUSS (Direxion Daily Russia Bear 3x S) has an average price of 65.7 (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 RUSS (Direxion Daily Russia Bear 3x S), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
065.70308   0 
110.5428 34.33974 (1*2π)/305305 weeks
28.1516 32.99805 (2*2π)/305153 weeks
33.35584 18.992 (3*2π)/305102 weeks
4-2.26129 18.11635 (4*2π)/30576 weeks
55.30787 12.72471 (5*2π)/30561 weeks
6-1.57283 9.78071 (6*2π)/30551 weeks
7-11.17321 17.57593 (7*2π)/30544 weeks
8-3.85555 .70055 (8*2π)/30538 weeks
9-9.69323 3.45981 (9*2π)/30534 weeks
10.12772 -1.16978 (10*2π)/30531 weeks
112.60957 -3.24362 (11*2π)/30528 weeks
12.94728 2.95312 (12*2π)/30525 weeks
13-.46438 6.17504 (13*2π)/30523 weeks
14-2.81907 .03839 (14*2π)/30522 weeks
15.39781 -1.19391 (15*2π)/30520 weeks
163.36084 -4.86379 (16*2π)/30519 weeks
172.2965 1.53046 (17*2π)/30518 weeks
185.58201 1.16014 (18*2π)/30517 weeks
194.05143 3.03598 (19*2π)/30516 weeks
203.20927 4.65525 (20*2π)/30515 weeks
211.59665 3.71049 (21*2π)/30515 weeks
22-.37709 3.53974 (22*2π)/30514 weeks
232.11762 4.5096 (23*2π)/30513 weeks
24-.65511 3.71458 (24*2π)/30513 weeks
25-2.83005 3.98851 (25*2π)/30512 weeks
26-1.42243 1.68643 (26*2π)/30512 weeks
27-3.37667 -1.88622 (27*2π)/30511 weeks
281.15347 -.1799 (28*2π)/30511 weeks
292.42154 -.49597 (29*2π)/30511 weeks
30.73007 .74394 (30*2π)/30510 weeks
312.43379 .56481 (31*2π)/30510 weeks
32.93565 1.68453 (32*2π)/30510 weeks
331.90045 .50856 (33*2π)/3059 weeks
342.41226 1.69244 (34*2π)/3059 weeks
352.33634 3.06619 (35*2π)/3059 weeks
361.19105 2.96619 (36*2π)/3058 weeks
37-.01658 4.32162 (37*2π)/3058 weeks
38-.73256 3.75283 (38*2π)/3058 weeks
39-2.59551 1.18368 (39*2π)/3058 weeks
40-.63698 2.31474 (40*2π)/3058 weeks
41-1.8414 .45755 (41*2π)/3057 weeks
42-1.49522 1.86114 (42*2π)/3057 weeks
43-1.69933 .33783 (43*2π)/3057 weeks
44-1.98055 -1.27308 (44*2π)/3057 weeks
45-2.12019 -1.61975 (45*2π)/3057 weeks
461.75787 -2.6919 (46*2π)/3057 weeks
47.81483 -1.64524 (47*2π)/3056 weeks
483.09211 .13606 (48*2π)/3056 weeks
491.50581 -.69396 (49*2π)/3056 weeks
501.78 .41278 (50*2π)/3056 weeks
511.98207 .85157 (51*2π)/3056 weeks
522.13711 .75072 (52*2π)/3056 weeks
531.41639 2.67994 (53*2π)/3056 weeks
541.86409 1.28243 (54*2π)/3056 weeks
55.02564 1.48985 (55*2π)/3056 weeks
56.14617 1.76793 (56*2π)/3055 weeks
57-.27152 1.79138 (57*2π)/3055 weeks
58.4156 1.31019 (58*2π)/3055 weeks
59.20608 .42994 (59*2π)/3055 weeks
60-.61938 .71371 (60*2π)/3055 weeks
61-.21293 1.20392 (61*2π)/3055 weeks
62-.48708 .44754 (62*2π)/3055 weeks
63.04646 -.18415 (63*2π)/3055 weeks
64.98422 -.95755 (64*2π)/3055 weeks
65.16824 1.01463 (65*2π)/3055 weeks
66.38817 .54406 (66*2π)/3055 weeks
67.24146 .35729 (67*2π)/3055 weeks
68.51162 .30775 (68*2π)/3054 weeks
69.44638 -.98358 (69*2π)/3054 weeks
70.80943 .70392 (70*2π)/3054 weeks
71.94202 .45549 (71*2π)/3054 weeks
72.54748 .43763 (72*2π)/3054 weeks
73.8474 .7429 (73*2π)/3054 weeks
74.99278 -.13025 (74*2π)/3054 weeks
75-.20338 1.11429 (75*2π)/3054 weeks
76.82253 1.09169 (76*2π)/3054 weeks
77-.29771 .12329 (77*2π)/3054 weeks
78.04318 .57902 (78*2π)/3054 weeks
79.03797 -.91411 (79*2π)/3054 weeks
80.09604 -.2881 (80*2π)/3054 weeks
811.23378 -.12296 (81*2π)/3054 weeks
821.13907 -.82488 (82*2π)/3054 weeks
831.51246 .68113 (83*2π)/3054 weeks
841.48177 .22901 (84*2π)/3054 weeks
85.46892 .4799 (85*2π)/3054 weeks
861.74912 1.20181 (86*2π)/3054 weeks
871.23744 .27627 (87*2π)/3054 weeks
88.64553 1.50153 (88*2π)/3053 weeks
89.59812 1.16034 (89*2π)/3053 weeks
90-.07201 .85762 (90*2π)/3053 weeks
91.01435 .41856 (91*2π)/3053 weeks
92.92726 .07312 (92*2π)/3053 weeks
93.17975 .76654 (93*2π)/3053 weeks
94.51812 .81348 (94*2π)/3053 weeks
95-.18038 -.33738 (95*2π)/3053 weeks
96.46807 .61563 (96*2π)/3053 weeks
971.14142 .42096 (97*2π)/3053 weeks
98.65967 .28109 (98*2π)/3053 weeks
99.18458 .99904 (99*2π)/3053 weeks
100.09556 .29565 (100*2π)/3053 weeks
101-.03589 .74975 (101*2π)/3053 weeks
102.72344 -.38769 (102*2π)/3053 weeks
103.21616 -.14024 (103*2π)/3053 weeks
104.87499 .32323 (104*2π)/3053 weeks
105.81992 .51023 (105*2π)/3053 weeks
106.79402 .28009 (106*2π)/3053 weeks
107.788 .65863 (107*2π)/3053 weeks
108.75208 1.0606 (108*2π)/3053 weeks
109.1594 1.02178 (109*2π)/3053 weeks
110-.10933 .82516 (110*2π)/3053 weeks
111-.4766 .94789 (111*2π)/3053 weeks
112-.57757 .07284 (112*2π)/3053 weeks
113-.26141 -.53703 (113*2π)/3053 weeks
114.37093 -.35749 (114*2π)/3053 weeks
115.33737 -.19942 (115*2π)/3053 weeks
116.45742 .24807 (116*2π)/3053 weeks
117.47832 .05014 (117*2π)/3053 weeks
118.05238 -.87972 (118*2π)/3053 weeks
1191.19803 .50835 (119*2π)/3053 weeks
1201.13425 .06358 (120*2π)/3053 weeks
121-.41462 .87855 (121*2π)/3053 weeks
122.59624 .56437 (122*2π)/3053 weeks
123-.48058 -.63306 (123*2π)/3052 weeks
124.30979 -.10173 (124*2π)/3052 weeks
125.77904 -.69799 (125*2π)/3052 weeks
126.33568 -.14811 (126*2π)/3052 weeks
1271.26716 .48693 (127*2π)/3052 weeks
128.80844 -.38512 (128*2π)/3052 weeks
129.31514 .44868 (129*2π)/3052 weeks
1301.46491 .15642 (130*2π)/3052 weeks
131.56621 .38207 (131*2π)/3052 weeks
1321.05578 1.05646 (132*2π)/3052 weeks
133-.05961 1.01779 (133*2π)/3052 weeks
134-.69924 1.16575 (134*2π)/3052 weeks
135-.39944 -.02913 (135*2π)/3052 weeks
136-.51931 -.64527 (136*2π)/3052 weeks
137-.15945 -.0009 (137*2π)/3052 weeks
138.29891 -.83292 (138*2π)/3052 weeks
139-.14732 -.31766 (139*2π)/3052 weeks
140.75801 -.55289 (140*2π)/3052 weeks
141.12013 -1.09951 (141*2π)/3052 weeks
1421.4146 -.4211 (142*2π)/3052 weeks
1431.29089 -.21231 (143*2π)/3052 weeks
144.99959 .37016 (144*2π)/3052 weeks
1451.19168 .74226 (145*2π)/3052 weeks
146.48598 -.13722 (146*2π)/3052 weeks
147.20242 .408 (147*2π)/3052 weeks
148.99139 .75179 (148*2π)/3052 weeks
149.46992 .5247 (149*2π)/3052 weeks
150.07799 .32105 (150*2π)/3052 weeks
151-.07527 .76306 (151*2π)/3052 weeks
152-.29397 .06464 (152*2π)/3052 weeks
153-.29397 -.06464 (153*2π)/3052 weeks
154-.07527 -.76306 (154*2π)/3052 weeks
155.07799 -.32105 (155*2π)/3052 weeks
156.46992 -.5247 (156*2π)/3052 weeks
157.99139 -.75179 (157*2π)/3052 weeks
158.20242 -.408 (158*2π)/3052 weeks
159.48598 .13722 (159*2π)/3052 weeks
1601.19168 -.74226 (160*2π)/3052 weeks
161.99959 -.37016 (161*2π)/3052 weeks
1621.29089 .21231 (162*2π)/3052 weeks
1631.4146 .4211 (163*2π)/3052 weeks
164.12013 1.09951 (164*2π)/3052 weeks
165.75801 .55289 (165*2π)/3052 weeks
166-.14732 .31766 (166*2π)/3052 weeks
167.29891 .83292 (167*2π)/3052 weeks
168-.15945 .0009 (168*2π)/3052 weeks
169-.51931 .64527 (169*2π)/3052 weeks
170-.39944 .02913 (170*2π)/3052 weeks
171-.69924 -1.16575 (171*2π)/3052 weeks
172-.05961 -1.01779 (172*2π)/3052 weeks
1731.05578 -1.05646 (173*2π)/3052 weeks
174.56621 -.38207 (174*2π)/3052 weeks
1751.46491 -.15642 (175*2π)/3052 weeks
176.31514 -.44868 (176*2π)/3052 weeks
177.80844 .38512 (177*2π)/3052 weeks
1781.26716 -.48693 (178*2π)/3052 weeks
179.33568 .14811 (179*2π)/3052 weeks
180.77904 .69799 (180*2π)/3052 weeks
181.30979 .10173 (181*2π)/3052 weeks
182-.48058 .63306 (182*2π)/3052 weeks
183.59624 -.56437 (183*2π)/3052 weeks
184-.41462 -.87855 (184*2π)/3052 weeks
1851.13425 -.06358 (185*2π)/3052 weeks
1861.19803 -.50835 (186*2π)/3052 weeks
187.05238 .87972 (187*2π)/3052 weeks
188.47832 -.05014 (188*2π)/3052 weeks
189.45742 -.24807 (189*2π)/3052 weeks
190.33737 .19942 (190*2π)/3052 weeks
191.37093 .35749 (191*2π)/3052 weeks
192-.26141 .53703 (192*2π)/3052 weeks
193-.57757 -.07284 (193*2π)/3052 weeks
194-.4766 -.94789 (194*2π)/3052 weeks
195-.10933 -.82516 (195*2π)/3052 weeks
196.1594 -1.02178 (196*2π)/3052 weeks
197.75208 -1.0606 (197*2π)/3052 weeks
198.788 -.65863 (198*2π)/3052 weeks
199.79402 -.28009 (199*2π)/3052 weeks
200.81992 -.51023 (200*2π)/3052 weeks
201.87499 -.32323 (201*2π)/3052 weeks
202.21616 .14024 (202*2π)/3052 weeks
203.72344 .38769 (203*2π)/3052 weeks
204-.03589 -.74975 (204*2π)/3051 weeks
205.09556 -.29565 (205*2π)/3051 weeks
206.18458 -.99904 (206*2π)/3051 weeks
207.65967 -.28109 (207*2π)/3051 weeks
2081.14142 -.42096 (208*2π)/3051 weeks
209.46807 -.61563 (209*2π)/3051 weeks
210-.18038 .33738 (210*2π)/3051 weeks
211.51812 -.81348 (211*2π)/3051 weeks
212.17975 -.76654 (212*2π)/3051 weeks
213.92726 -.07312 (213*2π)/3051 weeks
214.01435 -.41856 (214*2π)/3051 weeks
215-.07201 -.85762 (215*2π)/3051 weeks
216.59812 -1.16034 (216*2π)/3051 weeks
217.64553 -1.50153 (217*2π)/3051 weeks
2181.23744 -.27627 (218*2π)/3051 weeks
2191.74912 -1.20181 (219*2π)/3051 weeks
220.46892 -.4799 (220*2π)/3051 weeks
2211.48177 -.22901 (221*2π)/3051 weeks
2221.51246 -.68113 (222*2π)/3051 weeks
2231.13907 .82488 (223*2π)/3051 weeks
2241.23378 .12296 (224*2π)/3051 weeks
225.09604 .2881 (225*2π)/3051 weeks
226.03797 .91411 (226*2π)/3051 weeks
227.04318 -.57902 (227*2π)/3051 weeks
228-.29771 -.12329 (228*2π)/3051 weeks
229.82253 -1.09169 (229*2π)/3051 weeks
230-.20338 -1.11429 (230*2π)/3051 weeks
231.99278 .13025 (231*2π)/3051 weeks
232.8474 -.7429 (232*2π)/3051 weeks
233.54748 -.43763 (233*2π)/3051 weeks
234.94202 -.45549 (234*2π)/3051 weeks
235.80943 -.70392 (235*2π)/3051 weeks
236.44638 .98358 (236*2π)/3051 weeks
237.51162 -.30775 (237*2π)/3051 weeks
238.24146 -.35729 (238*2π)/3051 weeks
239.38817 -.54406 (239*2π)/3051 weeks
240.16824 -1.01463 (240*2π)/3051 weeks
241.98422 .95755 (241*2π)/3051 weeks
242.04646 .18415 (242*2π)/3051 weeks
243-.48708 -.44754 (243*2π)/3051 weeks
244-.21293 -1.20392 (244*2π)/3051 weeks
245-.61938 -.71371 (245*2π)/3051 weeks
246.20608 -.42994 (246*2π)/3051 weeks
247.4156 -1.31019 (247*2π)/3051 weeks
248-.27152 -1.79138 (248*2π)/3051 weeks
249.14617 -1.76793 (249*2π)/3051 weeks
250.02564 -1.48985 (250*2π)/3051 weeks
2511.86409 -1.28243 (251*2π)/3051 weeks
2521.41639 -2.67994 (252*2π)/3051 weeks
2532.13711 -.75072 (253*2π)/3051 weeks
2541.98207 -.85157 (254*2π)/3051 weeks
2551.78 -.41278 (255*2π)/3051 weeks
2561.50581 .69396 (256*2π)/3051 weeks
2573.09211 -.13606 (257*2π)/3051 weeks
258.81483 1.64524 (258*2π)/3051 weeks
2591.75787 2.6919 (259*2π)/3051 weeks
260-2.12019 1.61975 (260*2π)/3051 weeks
261-1.98055 1.27308 (261*2π)/3051 weeks
262-1.69933 -.33783 (262*2π)/3051 weeks
263-1.49522 -1.86114 (263*2π)/3051 weeks
264-1.8414 -.45755 (264*2π)/3051 weeks
265-.63698 -2.31474 (265*2π)/3051 weeks
266-2.59551 -1.18368 (266*2π)/3051 weeks
267-.73256 -3.75283 (267*2π)/3051 weeks
268-.01658 -4.32162 (268*2π)/3051 weeks
2691.19105 -2.96619 (269*2π)/3051 weeks
2702.33634 -3.06619 (270*2π)/3051 weeks
2712.41226 -1.69244 (271*2π)/3051 weeks
2721.90045 -.50856 (272*2π)/3051 weeks
273.93565 -1.68453 (273*2π)/3051 weeks
2742.43379 -.56481 (274*2π)/3051 weeks
275.73007 -.74394 (275*2π)/3051 weeks
2762.42154 .49597 (276*2π)/3051 weeks
2771.15347 .1799 (277*2π)/3051 weeks
278-3.37667 1.88622 (278*2π)/3051 weeks
279-1.42243 -1.68643 (279*2π)/3051 weeks
280-2.83005 -3.98851 (280*2π)/3051 weeks
281-.65511 -3.71458 (281*2π)/3051 weeks
2822.11762 -4.5096 (282*2π)/3051 weeks
283-.37709 -3.53974 (283*2π)/3051 weeks
2841.59665 -3.71049 (284*2π)/3051 weeks
2853.20927 -4.65525 (285*2π)/3051 weeks
2864.05143 -3.03598 (286*2π)/3051 weeks
2875.58201 -1.16014 (287*2π)/3051 weeks
2882.2965 -1.53046 (288*2π)/3051 weeks
2893.36084 4.86379 (289*2π)/3051 weeks
290.39781 1.19391 (290*2π)/3051 weeks
291-2.81907 -.03839 (291*2π)/3051 weeks
292-.46438 -6.17504 (292*2π)/3051 weeks
293.94728 -2.95312 (293*2π)/3051 weeks
2942.60957 3.24362 (294*2π)/3051 weeks
295.12772 1.16978 (295*2π)/3051 weeks
296-9.69323 -3.45981 (296*2π)/3051 weeks
297-3.85555 -.70055 (297*2π)/3051 weeks
298-11.17321 -17.57593 (298*2π)/3051 weeks
299-1.57283 -9.78071 (299*2π)/3051 weeks
3005.30787 -12.72471 (300*2π)/3051 weeks
301-2.26129 -18.11635 (301*2π)/3051 weeks
3023.35584 -18.992 (302*2π)/3051 weeks
3038.1516 -32.99805 (303*2π)/3051 weeks

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