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Fourier Analysis of UWTI (VelocityShares 3X Long Crude ET)


UWTI (VelocityShares 3X Long Crude ET) appears to have interesting cyclic behaviour every 25 weeks (374.1653*sine), 23 weeks (344.2539*sine), and 25 weeks (113.206*cosine).

UWTI (VelocityShares 3X Long Crude ET) has an average price of 1,996.4 (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 2/8/2012 to 12/5/2016 for UWTI (VelocityShares 3X Long Crude ET), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
01,996.395   0 
1-247.4573 1,873.659 (1*2π)/253253 weeks
2642.1106 219.9657 (2*2π)/253127 weeks
355.53765 563.6661 (3*2π)/25384 weeks
4440.4455 460.3341 (4*2π)/25363 weeks
5-111.4806 306.5182 (5*2π)/25351 weeks
6334.1343 285.9355 (6*2π)/25342 weeks
7106.8229 347.646 (7*2π)/25336 weeks
838.28973 282.1988 (8*2π)/25332 weeks
9198.9759 213.9952 (9*2π)/25328 weeks
10113.206 374.1653 (10*2π)/25325 weeks
11-57.21632 344.2539 (11*2π)/25323 weeks
12-50.53878 201.8273 (12*2π)/25321 weeks
13-66.59763 213.3847 (13*2π)/25319 weeks
14-61.2143 84.53564 (14*2π)/25318 weeks
15-26.52308 103.9904 (15*2π)/25317 weeks
1652.31092 75.89508 (16*2π)/25316 weeks
17-6.83926 127.8798 (17*2π)/25315 weeks
1822.96571 68.85627 (18*2π)/25314 weeks
1932.82419 106.054 (19*2π)/25313 weeks
2027.52101 73.73409 (20*2π)/25313 weeks
2152.55197 122.7381 (21*2π)/25312 weeks
22-5.02075 94.52456 (22*2π)/25312 weeks
2319.62536 82.07237 (23*2π)/25311 weeks
2450.88646 83.81285 (24*2π)/25311 weeks
25-2.00111 113.0165 (25*2π)/25310 weeks
2636.35582 71.93446 (26*2π)/25310 weeks
2712.57008 124.8631 (27*2π)/2539 weeks
28-26.19399 84.1867 (28*2π)/2539 weeks
29-5.461 68.60137 (29*2π)/2539 weeks
30-6.29758 55.65785 (30*2π)/2538 weeks
3128.10273 60.75955 (31*2π)/2538 weeks
32-29.36006 101.9965 (32*2π)/2538 weeks
33-17.25527 6.84366 (33*2π)/2538 weeks
3420.29226 50.56843 (34*2π)/2537 weeks
3512.21512 53.98079 (35*2π)/2537 weeks
36-12.32924 49.46066 (36*2π)/2537 weeks
378.4116 40.02319 (37*2π)/2537 weeks
38-3.75293 34.52026 (38*2π)/2537 weeks
393.45344 36.04744 (39*2π)/2536 weeks
4010.53373 21.99483 (40*2π)/2536 weeks
41.10238 35.4407 (41*2π)/2536 weeks
4214.47058 4.1678 (42*2π)/2536 weeks
4339.04747 16.67625 (43*2π)/2536 weeks
4440.87378 49.12864 (44*2π)/2536 weeks
459.75998 51.32236 (45*2π)/2536 weeks
463.2755 19.30055 (46*2π)/2536 weeks
4742.13451 22.13315 (47*2π)/2535 weeks
4812.30377 47.84518 (48*2π)/2535 weeks
4932.98465 24.43409 (49*2π)/2535 weeks
5014.65984 51.56272 (50*2π)/2535 weeks
5124.32028 20.31276 (51*2π)/2535 weeks
5220.7666 65.44456 (52*2π)/2535 weeks
53-6.30313 24.56676 (53*2π)/2535 weeks
5410.61012 21.25981 (54*2π)/2535 weeks
5541.39358 23.1932 (55*2π)/2535 weeks
565.2498 59.948 (56*2π)/2535 weeks
5715.82067 15.39301 (57*2π)/2534 weeks
5813.85513 48.51342 (58*2π)/2534 weeks
5910.02589 37.91692 (59*2π)/2534 weeks
60-15.09236 42.56202 (60*2π)/2534 weeks
61-1.75466 6.05132 (61*2π)/2534 weeks
627.99141 23.54645 (62*2π)/2534 weeks
63-8.0949 15.33074 (63*2π)/2534 weeks
6415.8397 -3.21678 (64*2π)/2534 weeks
6517.71007 20.74824 (65*2π)/2534 weeks
6620.08382 14.94698 (66*2π)/2534 weeks
672.56263 19.50959 (67*2π)/2534 weeks
6822.41995 11.46574 (68*2π)/2534 weeks
695.57013 19.40549 (69*2π)/2534 weeks
7015.20249 10.7076 (70*2π)/2534 weeks
7111.46769 4.5796 (71*2π)/2534 weeks
7229.55803 8.76903 (72*2π)/2534 weeks
7324.49535 25.32445 (73*2π)/2533 weeks
7410.14994 22.47181 (74*2π)/2533 weeks
7514.66824 12.33819 (75*2π)/2533 weeks
7614.14635 19.31434 (76*2π)/2533 weeks
7716.06594 15.44501 (77*2π)/2533 weeks
781.99336 26.43283 (78*2π)/2533 weeks
795.2761 -4.19314 (79*2π)/2533 weeks
8020.30059 13.66309 (80*2π)/2533 weeks
812.38589 18.21994 (81*2π)/2533 weeks
822.92102 -3.89051 (82*2π)/2533 weeks
8319.41385 .9506 (83*2π)/2533 weeks
848.16043 2.46197 (84*2π)/2533 weeks
8526.69414 -3.25421 (85*2π)/2533 weeks
8610.97224 9.01478 (86*2π)/2533 weeks
8730.6904 -4.92871 (87*2π)/2533 weeks
8812.95776 11.11737 (88*2π)/2533 weeks
8930.3978 1.8539 (89*2π)/2533 weeks
9014.54728 8.81714 (90*2π)/2533 weeks
9135.65386 7.8606 (91*2π)/2533 weeks
927.70424 21.88836 (92*2π)/2533 weeks
9314.70871 5.58233 (93*2π)/2533 weeks
946.61857 4.53661 (94*2π)/2533 weeks
9517.64191 -6.15381 (95*2π)/2533 weeks
9617.7571 5.69465 (96*2π)/2533 weeks
9712.39715 -14.02125 (97*2π)/2533 weeks
9838.65222 -5.25826 (98*2π)/2533 weeks
9936.18917 7.91199 (99*2π)/2533 weeks
10022.73499 15.42667 (100*2π)/2533 weeks
10127.43267 9.53493 (101*2π)/2533 weeks
10214.94838 15.3316 (102*2π)/2532 weeks
10322.74224 9.41211 (103*2π)/2532 weeks
10410.80123 10.702 (104*2π)/2532 weeks
10518.02775 9.67142 (105*2π)/2532 weeks
1068.7697 4.63478 (106*2π)/2532 weeks
10711.3032 3.97849 (107*2π)/2532 weeks
10817.68607 -6.77961 (108*2π)/2532 weeks
10915.75501 13.44898 (109*2π)/2532 weeks
110.31721 -4.514 (110*2π)/2532 weeks
11112.53015 -18.90862 (111*2π)/2532 weeks
11229.955 -6.06391 (112*2π)/2532 weeks
11313.89099 -7.99134 (113*2π)/2532 weeks
11431.65822 -17.72864 (114*2π)/2532 weeks
11541.10617 3.60311 (115*2π)/2532 weeks
11621.51264 7.00318 (116*2π)/2532 weeks
11725.97171 2.89349 (117*2π)/2532 weeks
11816.65444 -1.00072 (118*2π)/2532 weeks
11926.53674 -.89085 (119*2π)/2532 weeks
12026.31377 -4.09092 (120*2π)/2532 weeks
12123.99049 1.67575 (121*2π)/2532 weeks
12233.27324 5.60735 (122*2π)/2532 weeks
12313.68631 .29603 (123*2π)/2532 weeks
12436.05663 2.00115 (124*2π)/2532 weeks
12522.39946 12.99179 (125*2π)/2532 weeks
1267.57183 13.95041 (126*2π)/2532 weeks
1277.57183 -13.95041 (127*2π)/2532 weeks
12822.39946 -12.99179 (128*2π)/2532 weeks
12936.05663 -2.00115 (129*2π)/2532 weeks
13013.68631 -.29603 (130*2π)/2532 weeks
13133.27324 -5.60735 (131*2π)/2532 weeks
13223.99049 -1.67575 (132*2π)/2532 weeks
13326.31377 4.09092 (133*2π)/2532 weeks
13426.53674 .89085 (134*2π)/2532 weeks
13516.65444 1.00072 (135*2π)/2532 weeks
13625.97171 -2.89349 (136*2π)/2532 weeks
13721.51264 -7.00318 (137*2π)/2532 weeks
13841.10617 -3.60311 (138*2π)/2532 weeks
13931.65822 17.72864 (139*2π)/2532 weeks
14013.89099 7.99134 (140*2π)/2532 weeks
14129.955 6.06391 (141*2π)/2532 weeks
14212.53015 18.90862 (142*2π)/2532 weeks
143.31721 4.514 (143*2π)/2532 weeks
14415.75501 -13.44898 (144*2π)/2532 weeks
14517.68607 6.77961 (145*2π)/2532 weeks
14611.3032 -3.97849 (146*2π)/2532 weeks
1478.7697 -4.63478 (147*2π)/2532 weeks
14818.02775 -9.67142 (148*2π)/2532 weeks
14910.80123 -10.702 (149*2π)/2532 weeks
15022.74224 -9.41211 (150*2π)/2532 weeks
15114.94838 -15.3316 (151*2π)/2532 weeks
15227.43267 -9.53493 (152*2π)/2532 weeks
15322.73499 -15.42667 (153*2π)/2532 weeks
15436.18917 -7.91199 (154*2π)/2532 weeks
15538.65222 5.25826 (155*2π)/2532 weeks
15612.39715 14.02125 (156*2π)/2532 weeks
15717.7571 -5.69465 (157*2π)/2532 weeks
15817.64191 6.15381 (158*2π)/2532 weeks
1596.61857 -4.53661 (159*2π)/2532 weeks
16014.70871 -5.58233 (160*2π)/2532 weeks
1617.70424 -21.88836 (161*2π)/2532 weeks
16235.65386 -7.8606 (162*2π)/2532 weeks
16314.54728 -8.81714 (163*2π)/2532 weeks
16430.3978 -1.8539 (164*2π)/2532 weeks
16512.95776 -11.11737 (165*2π)/2532 weeks
16630.6904 4.92871 (166*2π)/2532 weeks
16710.97224 -9.01478 (167*2π)/2532 weeks
16826.69414 3.25421 (168*2π)/2532 weeks
1698.16043 -2.46197 (169*2π)/2531 weeks
17019.41385 -.9506 (170*2π)/2531 weeks
1712.92102 3.89051 (171*2π)/2531 weeks
1722.38589 -18.21994 (172*2π)/2531 weeks
17320.30059 -13.66309 (173*2π)/2531 weeks
1745.2761 4.19314 (174*2π)/2531 weeks
1751.99336 -26.43283 (175*2π)/2531 weeks
17616.06594 -15.44501 (176*2π)/2531 weeks
17714.14635 -19.31434 (177*2π)/2531 weeks
17814.66824 -12.33819 (178*2π)/2531 weeks
17910.14994 -22.47181 (179*2π)/2531 weeks
18024.49535 -25.32445 (180*2π)/2531 weeks
18129.55803 -8.76903 (181*2π)/2531 weeks
18211.46769 -4.5796 (182*2π)/2531 weeks
18315.20249 -10.7076 (183*2π)/2531 weeks
1845.57013 -19.40549 (184*2π)/2531 weeks
18522.41995 -11.46574 (185*2π)/2531 weeks
1862.56263 -19.50959 (186*2π)/2531 weeks
18720.08382 -14.94698 (187*2π)/2531 weeks
18817.71007 -20.74824 (188*2π)/2531 weeks
18915.8397 3.21678 (189*2π)/2531 weeks
190-8.0949 -15.33074 (190*2π)/2531 weeks
1917.99141 -23.54645 (191*2π)/2531 weeks
192-1.75466 -6.05132 (192*2π)/2531 weeks
193-15.09236 -42.56202 (193*2π)/2531 weeks
19410.02589 -37.91692 (194*2π)/2531 weeks
19513.85513 -48.51342 (195*2π)/2531 weeks
19615.82067 -15.39301 (196*2π)/2531 weeks
1975.2498 -59.948 (197*2π)/2531 weeks
19841.39358 -23.1932 (198*2π)/2531 weeks
19910.61012 -21.25981 (199*2π)/2531 weeks
200-6.30313 -24.56676 (200*2π)/2531 weeks
20120.7666 -65.44456 (201*2π)/2531 weeks
20224.32028 -20.31276 (202*2π)/2531 weeks
20314.65984 -51.56272 (203*2π)/2531 weeks
20432.98465 -24.43409 (204*2π)/2531 weeks
20512.30377 -47.84518 (205*2π)/2531 weeks
20642.13451 -22.13315 (206*2π)/2531 weeks
2073.2755 -19.30055 (207*2π)/2531 weeks
2089.75998 -51.32236 (208*2π)/2531 weeks
20940.87378 -49.12864 (209*2π)/2531 weeks
21039.04747 -16.67625 (210*2π)/2531 weeks
21114.47058 -4.1678 (211*2π)/2531 weeks
212.10238 -35.4407 (212*2π)/2531 weeks
21310.53373 -21.99483 (213*2π)/2531 weeks
2143.45344 -36.04744 (214*2π)/2531 weeks
215-3.75293 -34.52026 (215*2π)/2531 weeks
2168.4116 -40.02319 (216*2π)/2531 weeks
217-12.32924 -49.46066 (217*2π)/2531 weeks
21812.21512 -53.98079 (218*2π)/2531 weeks
21920.29226 -50.56843 (219*2π)/2531 weeks
220-17.25527 -6.84366 (220*2π)/2531 weeks
221-29.36006 -101.9965 (221*2π)/2531 weeks
22228.10273 -60.75955 (222*2π)/2531 weeks
223-6.29758 -55.65785 (223*2π)/2531 weeks
224-5.461 -68.60137 (224*2π)/2531 weeks
225-26.19399 -84.1867 (225*2π)/2531 weeks
22612.57008 -124.8631 (226*2π)/2531 weeks
22736.35582 -71.93446 (227*2π)/2531 weeks
228-2.00111 -113.0165 (228*2π)/2531 weeks
22950.88646 -83.81285 (229*2π)/2531 weeks
23019.62536 -82.07237 (230*2π)/2531 weeks
231-5.02075 -94.52456 (231*2π)/2531 weeks
23252.55197 -122.7381 (232*2π)/2531 weeks
23327.52101 -73.73409 (233*2π)/2531 weeks
23432.82419 -106.054 (234*2π)/2531 weeks
23522.96571 -68.85627 (235*2π)/2531 weeks
236-6.83926 -127.8798 (236*2π)/2531 weeks
23752.31092 -75.89508 (237*2π)/2531 weeks
238-26.52308 -103.9904 (238*2π)/2531 weeks
239-61.2143 -84.53564 (239*2π)/2531 weeks
240-66.59763 -213.3847 (240*2π)/2531 weeks
241-50.53878 -201.8273 (241*2π)/2531 weeks
242-57.21632 -344.2539 (242*2π)/2531 weeks
243113.206 -374.1653 (243*2π)/2531 weeks
244198.9759 -213.9952 (244*2π)/2531 weeks
24538.28973 -282.1988 (245*2π)/2531 weeks
246106.8229 -347.646 (246*2π)/2531 weeks
247334.1343 -285.9355 (247*2π)/2531 weeks
248-111.4806 -306.5182 (248*2π)/2531 weeks
249440.4455 -460.3341 (249*2π)/2531 weeks
25055.53765 -563.6661 (250*2π)/2531 weeks
251642.1106 -219.9657 (251*2π)/2531 weeks

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