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Fourier Analysis of RUSS (Direxion Daily Russia Bear 3X ETF)


RUSS (Direxion Daily Russia Bear 3X ETF) appears to have interesting cyclic behaviour every 33 weeks (41.4362*cosine), 18 weeks (23.685*cosine), and 17 weeks (21.6437*cosine).

RUSS (Direxion Daily Russia Bear 3X ETF) has an average price of 276.14 (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 6/4/2018 for RUSS (Direxion Daily Russia Bear 3X ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0276.1426   0 
154.72471 205.4734 (1*2π)/368368 weeks
280.11854 136.7043 (2*2π)/368184 weeks
310.54441 96.34327 (3*2π)/368123 weeks
415.10291 77.45001 (4*2π)/36892 weeks
5-15.27552 66.80653 (5*2π)/36874 weeks
622.23982 51.92295 (6*2π)/36861 weeks
7-14.40593 50.37564 (7*2π)/36853 weeks
8-1.9031 77.17797 (8*2π)/36846 weeks
9-58.08422 18.76536 (9*2π)/36841 weeks
10-8.60296 17.72065 (10*2π)/36837 weeks
11-41.43618 5.59805 (11*2π)/36833 weeks
12.34819 -6.63703 (12*2π)/36831 weeks
13-1.30856 -13.25223 (13*2π)/36828 weeks
1415.41447 14.03886 (14*2π)/36826 weeks
159.88393 10.73767 (15*2π)/36825 weeks
16-12.87293 20.32109 (16*2π)/36823 weeks
17-11.13831 -.97794 (17*2π)/36822 weeks
181.02747 -6.22211 (18*2π)/36820 weeks
19.4515 -17.34753 (19*2π)/36819 weeks
2023.68502 5.49779 (20*2π)/36818 weeks
2112.11277 -2.9563 (21*2π)/36818 weeks
2221.64373 9.64798 (22*2π)/36817 weeks
2316.78413 13.01546 (23*2π)/36816 weeks
2414.24438 18.51446 (24*2π)/36815 weeks
255.23226 17.25847 (25*2π)/36815 weeks
264.71779 20.04719 (26*2π)/36814 weeks
273.23205 9.03602 (27*2π)/36814 weeks
285.17849 21.81965 (28*2π)/36813 weeks
29-2.3739 15.35806 (29*2π)/36813 weeks
30-9.1744 18.57164 (30*2π)/36812 weeks
31-8.48382 4.70164 (31*2π)/36812 weeks
32-14.03375 7.16047 (32*2π)/36812 weeks
33-2.39276 -12.48074 (33*2π)/36811 weeks
342.60151 -.14653 (34*2π)/36811 weeks
3510.18604 -1.69088 (35*2π)/36811 weeks
363.76604 4.73995 (36*2π)/36810 weeks
377.42613 .06503 (37*2π)/36810 weeks
388.59995 7.71074 (38*2π)/36810 weeks
393.27204 4.51772 (39*2π)/3689 weeks
408.98471 3.05676 (40*2π)/3689 weeks
4110.10335 7.22215 (41*2π)/3689 weeks
4210.62723 11.48641 (42*2π)/3689 weeks
435.12173 13.84551 (43*2π)/3689 weeks
446.30019 15.30925 (44*2π)/3688 weeks
45-2.34191 15.56316 (45*2π)/3688 weeks
46-4.28191 16.0094 (46*2π)/3688 weeks
47-11.28675 5.7981 (47*2π)/3688 weeks
48-.98719 7.25089 (48*2π)/3688 weeks
49-9.17946 6.82605 (49*2π)/3688 weeks
50-2.40257 2.77307 (50*2π)/3687 weeks
51-9.24186 5.5118 (51*2π)/3687 weeks
52-7.24506 1.74716 (52*2π)/3687 weeks
53-9.03591 -4.67351 (53*2π)/3687 weeks
54-7.0302 -3.62599 (54*2π)/3687 weeks
55-.79235 -15.16923 (55*2π)/3687 weeks
567.01089 -4.56658 (56*2π)/3687 weeks
575.93314 -8.78338 (57*2π)/3686 weeks
5812.10202 1.78999 (58*2π)/3686 weeks
595.22002 -2.27471 (59*2π)/3686 weeks
608.8314 1.94257 (60*2π)/3686 weeks
618.95668 1.54959 (61*2π)/3686 weeks
627.36677 3.15707 (62*2π)/3686 weeks
639.82415 3.89747 (63*2π)/3686 weeks
645.12478 11.09465 (64*2π)/3686 weeks
656.39915 3.91077 (65*2π)/3686 weeks
66.81177 9.98657 (66*2π)/3686 weeks
673.37653 6.76184 (67*2π)/3685 weeks
681.04369 5.84059 (68*2π)/3685 weeks
69-2.33143 5.87203 (69*2π)/3685 weeks
701.61207 5.6112 (70*2π)/3685 weeks
71-.79312 1.77477 (71*2π)/3685 weeks
72-1.13027 5.94153 (72*2π)/3685 weeks
731.15977 2.27075 (73*2π)/3685 weeks
74-2.57778 3.33146 (74*2π)/3685 weeks
75-2.46004 1.53487 (75*2π)/3685 weeks
76.20555 -.66439 (76*2π)/3685 weeks
771.51254 -3.88037 (77*2π)/3685 weeks
785.22186 4.6855 (78*2π)/3685 weeks
791.20753 1.00333 (79*2π)/3685 weeks
80.86824 1.85312 (80*2π)/3685 weeks
81.76915 1.38548 (81*2π)/3685 weeks
822.22087 1.12641 (82*2π)/3684 weeks
83-.52007 -2.50553 (83*2π)/3684 weeks
846.53081 1.35038 (84*2π)/3684 weeks
852.75801 .89138 (85*2π)/3684 weeks
863.3382 2.41748 (86*2π)/3684 weeks
872.28816 1.60768 (87*2π)/3684 weeks
883.74946 2.79738 (88*2π)/3684 weeks
891.59715 -.10646 (89*2π)/3684 weeks
904.4244 6.10096 (90*2π)/3684 weeks
91.97353 .2455 (91*2π)/3684 weeks
92.92976 5.57423 (92*2π)/3684 weeks
93-.79459 .22253 (93*2π)/3684 weeks
94.68107 2.21377 (94*2π)/3684 weeks
95-2.18096 -2.21627 (95*2π)/3684 weeks
962.91234 -.62397 (96*2π)/3684 weeks
972.23035 -3.92441 (97*2π)/3684 weeks
983.77498 .24019 (98*2π)/3684 weeks
995.167 -3.40041 (99*2π)/3684 weeks
1007.086 2.40236 (100*2π)/3684 weeks
1014.65104 .64404 (101*2π)/3684 weeks
1025.09259 4.23192 (102*2π)/3684 weeks
1034.4381 -.88359 (103*2π)/3684 weeks
1044.96103 6.03178 (104*2π)/3684 weeks
1055.39902 1.24168 (105*2π)/3684 weeks
1063.68804 6.54008 (106*2π)/3683 weeks
1072.35774 4.15135 (107*2π)/3683 weeks
108.6673 5.12453 (108*2π)/3683 weeks
109-.14156 2.67737 (109*2π)/3683 weeks
110.02704 1.31151 (110*2π)/3683 weeks
1113.83735 .30338 (111*2π)/3683 weeks
1121.38976 3.90363 (112*2π)/3683 weeks
1132.14312 1.92257 (113*2π)/3683 weeks
114-1.02982 3.45915 (114*2π)/3683 weeks
1152.63009 -1.75281 (115*2π)/3683 weeks
1161.08508 1.9905 (116*2π)/3683 weeks
1174.75648 1.56119 (117*2π)/3683 weeks
1181.76421 1.63821 (118*2π)/3683 weeks
1192.99164 4.35192 (119*2π)/3683 weeks
120.09113 2.62393 (120*2π)/3683 weeks
1211.38011 1.04599 (121*2π)/3683 weeks
122-.87931 2.66174 (122*2π)/3683 weeks
1232.63741 -2.01186 (123*2π)/3683 weeks
124.80025 .86453 (124*2π)/3683 weeks
1254.12435 -.19288 (125*2π)/3683 weeks
1263.25657 1.17923 (126*2π)/3683 weeks
1272.7821 2.27325 (127*2π)/3683 weeks
1283.57222 1.26018 (128*2π)/3683 weeks
1293.32233 2.64668 (129*2π)/3683 weeks
1303.44833 3.63251 (130*2π)/3683 weeks
1311.2422 4.79451 (131*2π)/3683 weeks
132.25645 4.18351 (132*2π)/3683 weeks
133-.28294 3.29131 (133*2π)/3683 weeks
134-2.18872 3.80411 (134*2π)/3683 weeks
135-2.47894 .4062 (135*2π)/3683 weeks
136-2.04931 -1.52965 (136*2π)/3683 weeks
137.67852 -2.06596 (137*2π)/3683 weeks
1381.73545 -.7355 (138*2π)/3683 weeks
1391.78251 -.97502 (139*2π)/3683 weeks
1401.77888 1.08602 (140*2π)/3683 weeks
1411.85068 -.25164 (141*2π)/3683 weeks
142-1.01814 -.79158 (142*2π)/3683 weeks
1435.72878 -2.6146 (143*2π)/3683 weeks
1442.30348 1.97126 (144*2π)/3683 weeks
1455.46364 1.82342 (145*2π)/3683 weeks
146-1.72309 3.57808 (146*2π)/3683 weeks
1472.65847 .74592 (147*2π)/3683 weeks
148-3.30584 .96686 (148*2π)/3682 weeks
1491.91428 -2.21642 (149*2π)/3682 weeks
150.50019 -1.15525 (150*2π)/3682 weeks
1514.09027 -2.20001 (151*2π)/3682 weeks
1521.43235 -.47659 (152*2π)/3682 weeks
1535.99215 .12254 (153*2π)/3682 weeks
154.85952 .13121 (154*2π)/3682 weeks
1554.9428 1.59418 (155*2π)/3682 weeks
1561.22551 -.36312 (156*2π)/3682 weeks
1576.07639 1.85138 (157*2π)/3682 weeks
1582.30412 1.80402 (158*2π)/3682 weeks
1594.7618 3.17474 (159*2π)/3682 weeks
160.96386 5.75935 (160*2π)/3682 weeks
161.28647 4.24733 (161*2π)/3682 weeks
162-4.26841 2.93374 (162*2π)/3682 weeks
163-1.46364 .2134 (163*2π)/3682 weeks
164-2.51692 -2.2427 (164*2π)/3682 weeks
165.71614 -.34817 (165*2π)/3682 weeks
166-1.21605 -2.97275 (166*2π)/3682 weeks
1672.1805 -1.34728 (167*2π)/3682 weeks
168-.57861 -2.86744 (168*2π)/3682 weeks
1693.10103 -1.84377 (169*2π)/3682 weeks
170.06618 -3.69258 (170*2π)/3682 weeks
1716.03332 -3.44558 (171*2π)/3682 weeks
1724.87522 -1.05133 (172*2π)/3682 weeks
1735.83252 .21808 (173*2π)/3682 weeks
1743.82644 1.01443 (174*2π)/3682 weeks
1754.742 3.29119 (175*2π)/3682 weeks
176.99942 -.03713 (176*2π)/3682 weeks
1772.73208 2.93137 (177*2π)/3682 weeks
1783.65658 -.40001 (178*2π)/3682 weeks
1791.78331 3.41965 (179*2π)/3682 weeks
1801.86925 2.69802 (180*2π)/3682 weeks
181.37589 1.33808 (181*2π)/3682 weeks
182.5401 3.21869 (182*2π)/3682 weeks
183-1.53024 .92147 (183*2π)/3682 weeks
184-.85026   (184*2π)/3682 weeks
185-1.53024 -.92147 (185*2π)/3682 weeks
186.5401 -3.21869 (186*2π)/3682 weeks
187.37589 -1.33808 (187*2π)/3682 weeks
1881.86925 -2.69802 (188*2π)/3682 weeks
1891.78331 -3.41965 (189*2π)/3682 weeks
1903.65658 .40001 (190*2π)/3682 weeks
1912.73208 -2.93137 (191*2π)/3682 weeks
192.99942 .03713 (192*2π)/3682 weeks
1934.742 -3.29119 (193*2π)/3682 weeks
1943.82644 -1.01443 (194*2π)/3682 weeks
1955.83252 -.21808 (195*2π)/3682 weeks
1964.87522 1.05133 (196*2π)/3682 weeks
1976.03332 3.44558 (197*2π)/3682 weeks
198.06618 3.69258 (198*2π)/3682 weeks
1993.10103 1.84377 (199*2π)/3682 weeks
200-.57861 2.86744 (200*2π)/3682 weeks
2012.1805 1.34728 (201*2π)/3682 weeks
202-1.21605 2.97275 (202*2π)/3682 weeks
203.71614 .34817 (203*2π)/3682 weeks
204-2.51692 2.2427 (204*2π)/3682 weeks
205-1.46364 -.2134 (205*2π)/3682 weeks
206-4.26841 -2.93374 (206*2π)/3682 weeks
207.28647 -4.24733 (207*2π)/3682 weeks
208.96386 -5.75935 (208*2π)/3682 weeks
2094.7618 -3.17474 (209*2π)/3682 weeks
2102.30412 -1.80402 (210*2π)/3682 weeks
2116.07639 -1.85138 (211*2π)/3682 weeks
2121.22551 .36312 (212*2π)/3682 weeks
2134.9428 -1.59418 (213*2π)/3682 weeks
214.85952 -.13121 (214*2π)/3682 weeks
2155.99215 -.12254 (215*2π)/3682 weeks
2161.43235 .47659 (216*2π)/3682 weeks
2174.09027 2.20001 (217*2π)/3682 weeks
218.50019 1.15525 (218*2π)/3682 weeks
2191.91428 2.21642 (219*2π)/3682 weeks
220-3.30584 -.96686 (220*2π)/3682 weeks
2212.65847 -.74592 (221*2π)/3682 weeks
222-1.72309 -3.57808 (222*2π)/3682 weeks
2235.46364 -1.82342 (223*2π)/3682 weeks
2242.30348 -1.97126 (224*2π)/3682 weeks
2255.72878 2.6146 (225*2π)/3682 weeks
226-1.01814 .79158 (226*2π)/3682 weeks
2271.85068 .25164 (227*2π)/3682 weeks
2281.77888 -1.08602 (228*2π)/3682 weeks
2291.78251 .97502 (229*2π)/3682 weeks
2301.73545 .7355 (230*2π)/3682 weeks
231.67852 2.06596 (231*2π)/3682 weeks
232-2.04931 1.52965 (232*2π)/3682 weeks
233-2.47894 -.4062 (233*2π)/3682 weeks
234-2.18872 -3.80411 (234*2π)/3682 weeks
235-.28294 -3.29131 (235*2π)/3682 weeks
236.25645 -4.18351 (236*2π)/3682 weeks
2371.2422 -4.79451 (237*2π)/3682 weeks
2383.44833 -3.63251 (238*2π)/3682 weeks
2393.32233 -2.64668 (239*2π)/3682 weeks
2403.57222 -1.26018 (240*2π)/3682 weeks
2412.7821 -2.27325 (241*2π)/3682 weeks
2423.25657 -1.17923 (242*2π)/3682 weeks
2434.12435 .19288 (243*2π)/3682 weeks
244.80025 -.86453 (244*2π)/3682 weeks
2452.63741 2.01186 (245*2π)/3682 weeks
246-.87931 -2.66174 (246*2π)/3681 weeks
2471.38011 -1.04599 (247*2π)/3681 weeks
248.09113 -2.62393 (248*2π)/3681 weeks
2492.99164 -4.35192 (249*2π)/3681 weeks
2501.76421 -1.63821 (250*2π)/3681 weeks
2514.75648 -1.56119 (251*2π)/3681 weeks
2521.08508 -1.9905 (252*2π)/3681 weeks
2532.63009 1.75281 (253*2π)/3681 weeks
254-1.02982 -3.45915 (254*2π)/3681 weeks
2552.14312 -1.92257 (255*2π)/3681 weeks
2561.38976 -3.90363 (256*2π)/3681 weeks
2573.83735 -.30338 (257*2π)/3681 weeks
258.02704 -1.31151 (258*2π)/3681 weeks
259-.14156 -2.67737 (259*2π)/3681 weeks
260.6673 -5.12453 (260*2π)/3681 weeks
2612.35774 -4.15135 (261*2π)/3681 weeks
2623.68804 -6.54008 (262*2π)/3681 weeks
2635.39902 -1.24168 (263*2π)/3681 weeks
2644.96103 -6.03178 (264*2π)/3681 weeks
2654.4381 .88359 (265*2π)/3681 weeks
2665.09259 -4.23192 (266*2π)/3681 weeks
2674.65104 -.64404 (267*2π)/3681 weeks
2687.086 -2.40236 (268*2π)/3681 weeks
2695.167 3.40041 (269*2π)/3681 weeks
2703.77498 -.24019 (270*2π)/3681 weeks
2712.23035 3.92441 (271*2π)/3681 weeks
2722.91234 .62397 (272*2π)/3681 weeks
273-2.18096 2.21627 (273*2π)/3681 weeks
274.68107 -2.21377 (274*2π)/3681 weeks
275-.79459 -.22253 (275*2π)/3681 weeks
276.92976 -5.57423 (276*2π)/3681 weeks
277.97353 -.2455 (277*2π)/3681 weeks
2784.4244 -6.10096 (278*2π)/3681 weeks
2791.59715 .10646 (279*2π)/3681 weeks
2803.74946 -2.79738 (280*2π)/3681 weeks
2812.28816 -1.60768 (281*2π)/3681 weeks
2823.3382 -2.41748 (282*2π)/3681 weeks
2832.75801 -.89138 (283*2π)/3681 weeks
2846.53081 -1.35038 (284*2π)/3681 weeks
285-.52007 2.50553 (285*2π)/3681 weeks
2862.22087 -1.12641 (286*2π)/3681 weeks
287.76915 -1.38548 (287*2π)/3681 weeks
288.86824 -1.85312 (288*2π)/3681 weeks
2891.20753 -1.00333 (289*2π)/3681 weeks
2905.22186 -4.6855 (290*2π)/3681 weeks
2911.51254 3.88037 (291*2π)/3681 weeks
292.20555 .66439 (292*2π)/3681 weeks
293-2.46004 -1.53487 (293*2π)/3681 weeks
294-2.57778 -3.33146 (294*2π)/3681 weeks
2951.15977 -2.27075 (295*2π)/3681 weeks
296-1.13027 -5.94153 (296*2π)/3681 weeks
297-.79312 -1.77477 (297*2π)/3681 weeks
2981.61207 -5.6112 (298*2π)/3681 weeks
299-2.33143 -5.87203 (299*2π)/3681 weeks
3001.04369 -5.84059 (300*2π)/3681 weeks
3013.37653 -6.76184 (301*2π)/3681 weeks
302.81177 -9.98657 (302*2π)/3681 weeks
3036.39915 -3.91077 (303*2π)/3681 weeks
3045.12478 -11.09465 (304*2π)/3681 weeks
3059.82415 -3.89747 (305*2π)/3681 weeks
3067.36677 -3.15707 (306*2π)/3681 weeks
3078.95668 -1.54959 (307*2π)/3681 weeks
3088.8314 -1.94257 (308*2π)/3681 weeks
3095.22002 2.27471 (309*2π)/3681 weeks
31012.10202 -1.78999 (310*2π)/3681 weeks
3115.93314 8.78338 (311*2π)/3681 weeks
3127.01089 4.56658 (312*2π)/3681 weeks
313-.79235 15.16923 (313*2π)/3681 weeks
314-7.0302 3.62599 (314*2π)/3681 weeks
315-9.03591 4.67351 (315*2π)/3681 weeks
316-7.24506 -1.74716 (316*2π)/3681 weeks
317-9.24186 -5.5118 (317*2π)/3681 weeks
318-2.40257 -2.77307 (318*2π)/3681 weeks
319-9.17946 -6.82605 (319*2π)/3681 weeks
320-.98719 -7.25089 (320*2π)/3681 weeks
321-11.28675 -5.7981 (321*2π)/3681 weeks
322-4.28191 -16.0094 (322*2π)/3681 weeks
323-2.34191 -15.56316 (323*2π)/3681 weeks
3246.30019 -15.30925 (324*2π)/3681 weeks
3255.12173 -13.84551 (325*2π)/3681 weeks
32610.62723 -11.48641 (326*2π)/3681 weeks
32710.10335 -7.22215 (327*2π)/3681 weeks
3288.98471 -3.05676 (328*2π)/3681 weeks
3293.27204 -4.51772 (329*2π)/3681 weeks
3308.59995 -7.71074 (330*2π)/3681 weeks
3317.42613 -.06503 (331*2π)/3681 weeks
3323.76604 -4.73995 (332*2π)/3681 weeks
33310.18604 1.69088 (333*2π)/3681 weeks
3342.60151 .14653 (334*2π)/3681 weeks
335-2.39276 12.48074 (335*2π)/3681 weeks
336-14.03375 -7.16047 (336*2π)/3681 weeks
337-8.48382 -4.70164 (337*2π)/3681 weeks
338-9.1744 -18.57164 (338*2π)/3681 weeks
339-2.3739 -15.35806 (339*2π)/3681 weeks
3405.17849 -21.81965 (340*2π)/3681 weeks
3413.23205 -9.03602 (341*2π)/3681 weeks
3424.71779 -20.04719 (342*2π)/3681 weeks
3435.23226 -17.25847 (343*2π)/3681 weeks
34414.24438 -18.51446 (344*2π)/3681 weeks
34516.78413 -13.01546 (345*2π)/3681 weeks
34621.64373 -9.64798 (346*2π)/3681 weeks
34712.11277 2.9563 (347*2π)/3681 weeks
34823.68502 -5.49779 (348*2π)/3681 weeks
349.4515 17.34753 (349*2π)/3681 weeks
3501.02747 6.22211 (350*2π)/3681 weeks
351-11.13831 .97794 (351*2π)/3681 weeks
352-12.87293 -20.32109 (352*2π)/3681 weeks
3539.88393 -10.73767 (353*2π)/3681 weeks
35415.41447 -14.03886 (354*2π)/3681 weeks
355-1.30856 13.25223 (355*2π)/3681 weeks
356.34819 6.63703 (356*2π)/3681 weeks
357-41.43618 -5.59805 (357*2π)/3681 weeks
358-8.60296 -17.72065 (358*2π)/3681 weeks
359-58.08422 -18.76536 (359*2π)/3681 weeks
360-1.9031 -77.17797 (360*2π)/3681 weeks
361-14.40593 -50.37564 (361*2π)/3681 weeks
36222.23982 -51.92295 (362*2π)/3681 weeks
363-15.27552 -66.80653 (363*2π)/3681 weeks
36415.10291 -77.45001 (364*2π)/3681 weeks
36510.54441 -96.34327 (365*2π)/3681 weeks
36680.11854 -136.7043 (366*2π)/3681 weeks



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