Back to list of Stocks    See Also: Seasonal Analysis of SQQQGenetic Algorithms Stock Portfolio Generator, and Fourier Calculator

Fourier Analysis of SQQQ (ProShares UltraPro Short QQQ)


SQQQ (ProShares UltraPro Short QQQ) appears to have interesting cyclic behaviour every 36 weeks (94.1522*sine), 23 weeks (88.8702*sine), and 24 weeks (80.8023*sine).

SQQQ (ProShares UltraPro Short QQQ) has an average price of 874.97 (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 2/11/2010 to 1/17/2017 for SQQQ (ProShares UltraPro Short QQQ), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0874.9669   0 
1698.322 824.4836 (1*2π)/363363 weeks
2296.3847 575.4678 (2*2π)/363182 weeks
3154.5261 448.3247 (3*2π)/363121 weeks
4128.237 360.7594 (4*2π)/36391 weeks
568.14023 376.8859 (5*2π)/36373 weeks
6-40.72211 300.1153 (6*2π)/36361 weeks
7-61.56464 195.9303 (7*2π)/36352 weeks
8-31.1368 128.6414 (8*2π)/36345 weeks
9-7.85258 107.5588 (9*2π)/36340 weeks
10-1.01282 94.15217 (10*2π)/36336 weeks
116.93463 60.37462 (11*2π)/36333 weeks
1241.0663 66.38797 (12*2π)/36330 weeks
1333.78656 71.59245 (13*2π)/36328 weeks
1447.16202 56.89178 (14*2π)/36326 weeks
1566.49547 80.80229 (15*2π)/36324 weeks
1630.83438 88.87022 (16*2π)/36323 weeks
1730.39169 61.15508 (17*2π)/36321 weeks
1851.06876 74.43951 (18*2π)/36320 weeks
1927.68056 85.13123 (19*2π)/36319 weeks
2021.08317 69.27721 (20*2π)/36318 weeks
2123.54654 53.32838 (21*2π)/36317 weeks
2236.74851 47.41083 (22*2π)/36317 weeks
2339.90026 60.67811 (23*2π)/36316 weeks
2428.91475 57.23814 (24*2π)/36315 weeks
2538.13231 51.03435 (25*2π)/36315 weeks
2643.67052 55.95242 (26*2π)/36314 weeks
2745.67775 74.80457 (27*2π)/36313 weeks
2821.63282 80.36181 (28*2π)/36313 weeks
292.91793 63.38144 (29*2π)/36313 weeks
3015.18834 43.4378 (30*2π)/36312 weeks
3129.89337 50.45152 (31*2π)/36312 weeks
3215.6082 60.36494 (32*2π)/36311 weeks
3311.13332 54.1131 (33*2π)/36311 weeks
343.92733 46.93726 (34*2π)/36311 weeks
3510.8616 31.08721 (35*2π)/36310 weeks
3623.67449 30.77215 (36*2π)/36310 weeks
3733.36369 42.59544 (37*2π)/36310 weeks
3820.01254 54.30035 (38*2π)/36310 weeks
3910.91684 49.78952 (39*2π)/3639 weeks
404.98376 42.01379 (40*2π)/3639 weeks
418.89431 33.8857 (41*2π)/3639 weeks
4213.75354 39.41638 (42*2π)/3639 weeks
436.67825 40.58632 (43*2π)/3638 weeks
44-5.2679 36.7828 (44*2π)/3638 weeks
45-2.62697 14.96167 (45*2π)/3638 weeks
4614.96767 15.04483 (46*2π)/3638 weeks
4713.95942 22.34413 (47*2π)/3638 weeks
4810.47444 20.83737 (48*2π)/3638 weeks
499.77751 9.139 (49*2π)/3637 weeks
5024.00274 -.83796 (50*2π)/3637 weeks
5144.22967 11.55308 (51*2π)/3637 weeks
5241.22916 32.40503 (52*2π)/3637 weeks
5327.06807 34.62145 (53*2π)/3637 weeks
5427.28817 28.15737 (54*2π)/3637 weeks
5532.87987 33.87944 (55*2π)/3637 weeks
5625.78941 44.60404 (56*2π)/3636 weeks
5714.70242 41.94896 (57*2π)/3636 weeks
5812.04431 36.81952 (58*2π)/3636 weeks
5910.10937 33.476 (59*2π)/3636 weeks
606.8466 31.06724 (60*2π)/3636 weeks
613.78657 27.32588 (61*2π)/3636 weeks
623.86077 17.40416 (62*2π)/3636 weeks
6315.20371 14.31921 (63*2π)/3636 weeks
6418.26299 22.06852 (64*2π)/3636 weeks
6514.6738 22.8238 (65*2π)/3636 weeks
6613.92245 22.05105 (66*2π)/3636 weeks
6715.99276 21.32151 (67*2π)/3635 weeks
6815.72458 22.71004 (68*2π)/3635 weeks
6910.61582 23.4402 (69*2π)/3635 weeks
7013.76053 15.27206 (70*2π)/3635 weeks
7117.63409 20.19959 (71*2π)/3635 weeks
7216.80746 21.96468 (72*2π)/3635 weeks
7317.69464 24.48633 (73*2π)/3635 weeks
7412.36405 27.54931 (74*2π)/3635 weeks
755.85286 23.82824 (75*2π)/3635 weeks
766.73001 18.07401 (76*2π)/3635 weeks
778.7726 16.22086 (77*2π)/3635 weeks
7812.46856 18.03425 (78*2π)/3635 weeks
797.88051 21.8303 (79*2π)/3635 weeks
805.1437 14.79908 (80*2π)/3635 weeks
816.3331 12.41481 (81*2π)/3634 weeks
8210.29369 8.71123 (82*2π)/3634 weeks
8311.05132 12.67413 (83*2π)/3634 weeks
847.38323 11.72262 (84*2π)/3634 weeks
8510.7271 6.47468 (85*2π)/3634 weeks
8612.86059 5.9945 (86*2π)/3634 weeks
8715.76601 5.89021 (87*2π)/3634 weeks
8819.15947 4.41357 (88*2π)/3634 weeks
8926.19707 7.79222 (89*2π)/3634 weeks
9023.24392 18.35883 (90*2π)/3634 weeks
9115.76491 19.81974 (91*2π)/3634 weeks
9212.28636 12.7437 (92*2π)/3634 weeks
9320.7257 9.09951 (93*2π)/3634 weeks
9422.91228 18.1144 (94*2π)/3634 weeks
9516.20953 21.06896 (95*2π)/3634 weeks
9611.2911 18.15065 (96*2π)/3634 weeks
9712.7474 16.17657 (97*2π)/3634 weeks
9814.21564 19.12697 (98*2π)/3634 weeks
996.56678 21.71954 (99*2π)/3634 weeks
100.10219 12.41013 (100*2π)/3634 weeks
1018.60203 4.97303 (101*2π)/3634 weeks
10212.57645 10.34329 (102*2π)/3634 weeks
1039.20395 12.75902 (103*2π)/3634 weeks
1043.57405 10.84515 (104*2π)/3633 weeks
1054.50748 1.08243 (105*2π)/3633 weeks
10613.61922 .08833 (106*2π)/3633 weeks
10715.92159 3.86963 (107*2π)/3633 weeks
10816.43788 2.86487 (108*2π)/3633 weeks
10921.39988 7.91018 (109*2π)/3633 weeks
11017.50196 12.34267 (110*2π)/3633 weeks
11114.29325 13.70896 (111*2π)/3633 weeks
11210.04198 12.52428 (112*2π)/3633 weeks
1139.77265 7.74635 (113*2π)/3633 weeks
11412.24781 8.53393 (114*2π)/3633 weeks
11510.56472 8.88238 (115*2π)/3633 weeks
1168.70698 7.45048 (116*2π)/3633 weeks
1178.0479 2.78725 (117*2π)/3633 weeks
11812.91359 2.27772 (118*2π)/3633 weeks
11913.95767 4.05205 (119*2π)/3633 weeks
12013.53207 4.86829 (120*2π)/3633 weeks
12113.8378 4.87426 (121*2π)/3633 weeks
12210.49238 3.94732 (122*2π)/3633 weeks
12313.10526 -1.49712 (123*2π)/3633 weeks
12417.9065 1.70293 (124*2π)/3633 weeks
12516.70391 3.95869 (125*2π)/3633 weeks
12615.17457 1.58019 (126*2π)/3633 weeks
12719.00187 -1.60018 (127*2π)/3633 weeks
12826.51879 2.49683 (128*2π)/3633 weeks
12925.74526 12.89398 (129*2π)/3633 weeks
13016.06515 13.81621 (130*2π)/3633 weeks
13114.92291 8.52623 (131*2π)/3633 weeks
13218.42033 7.15362 (132*2π)/3633 weeks
13321.28959 16.13832 (133*2π)/3633 weeks
1348.84993 20.34159 (134*2π)/3633 weeks
1352.41677 10.88608 (135*2π)/3633 weeks
1364.54505 5.50253 (136*2π)/3633 weeks
1378.89931 3.45767 (137*2π)/3633 weeks
1387.52466 6.20521 (138*2π)/3633 weeks
1393.79725 2.15817 (139*2π)/3633 weeks
1407.66586 -3.33971 (140*2π)/3633 weeks
14113.68735 -4.29885 (141*2π)/3633 weeks
14214.02517 1.38177 (142*2π)/3633 weeks
14311.02835 1.06983 (143*2π)/3633 weeks
14411.09274 -1.41135 (144*2π)/3633 weeks
14511.83933 -4.24735 (145*2π)/3633 weeks
14614.8241 -6.09397 (146*2π)/3632 weeks
14719.99791 -5.46807 (147*2π)/3632 weeks
14822.39973 .33987 (148*2π)/3632 weeks
14917.18028 3.13443 (149*2π)/3632 weeks
15016.83977 -2.66444 (150*2π)/3632 weeks
15122.57779 -1.74168 (151*2π)/3632 weeks
15223.67238 2.78234 (152*2π)/3632 weeks
15320.4971 6.70807 (153*2π)/3632 weeks
15417.37025 5.53446 (154*2π)/3632 weeks
15518.88761 3.71084 (155*2π)/3632 weeks
15620.73243 6.23094 (156*2π)/3632 weeks
15717.81662 10.81522 (157*2π)/3632 weeks
1589.4492 8.64817 (158*2π)/3632 weeks
15912.47019 1.08948 (159*2π)/3632 weeks
16017.17457 4.28768 (160*2π)/3632 weeks
16113.56506 7.07946 (161*2π)/3632 weeks
1629.80259 4.40722 (162*2π)/3632 weeks
1639.98101 -.81362 (163*2π)/3632 weeks
16416.40001 -1.58544 (164*2π)/3632 weeks
16517.73331 .80681 (165*2π)/3632 weeks
16618.1848 3.88137 (166*2π)/3632 weeks
16715.58082 6.36311 (167*2π)/3632 weeks
16812.69127 4.00224 (168*2π)/3632 weeks
16915.43859 4.55476 (169*2π)/3632 weeks
17012.09477 8.25652 (170*2π)/3632 weeks
1716.47349 5.98106 (171*2π)/3632 weeks
1726.01979 .64604 (172*2π)/3632 weeks
1735.8561 -1.40561 (173*2π)/3632 weeks
1748.67373 -5.83647 (174*2π)/3632 weeks
17510.57309 -5.19755 (175*2π)/3632 weeks
1768.96051 -8.43868 (176*2π)/3632 weeks
17713.77793 -12.22521 (177*2π)/3632 weeks
17821.36536 -11.70723 (178*2π)/3632 weeks
17924.88675 -5.32554 (179*2π)/3632 weeks
18022.4377 -4.70233 (180*2π)/3632 weeks
18126.10775 -3.00346 (181*2π)/3632 weeks
18226.10775 3.00346 (182*2π)/3632 weeks
18322.4377 4.70233 (183*2π)/3632 weeks
18424.88675 5.32554 (184*2π)/3632 weeks
18521.36536 11.70723 (185*2π)/3632 weeks
18613.77793 12.22521 (186*2π)/3632 weeks
1878.96051 8.43868 (187*2π)/3632 weeks
18810.57309 5.19755 (188*2π)/3632 weeks
1898.67373 5.83647 (189*2π)/3632 weeks
1905.8561 1.40561 (190*2π)/3632 weeks
1916.01979 -.64604 (191*2π)/3632 weeks
1926.47349 -5.98106 (192*2π)/3632 weeks
19312.09477 -8.25652 (193*2π)/3632 weeks
19415.43859 -4.55476 (194*2π)/3632 weeks
19512.69127 -4.00224 (195*2π)/3632 weeks
19615.58082 -6.36311 (196*2π)/3632 weeks
19718.1848 -3.88137 (197*2π)/3632 weeks
19817.73331 -.80681 (198*2π)/3632 weeks
19916.40001 1.58544 (199*2π)/3632 weeks
2009.98101 .81362 (200*2π)/3632 weeks
2019.80259 -4.40722 (201*2π)/3632 weeks
20213.56506 -7.07946 (202*2π)/3632 weeks
20317.17457 -4.28768 (203*2π)/3632 weeks
20412.47019 -1.08948 (204*2π)/3632 weeks
2059.4492 -8.64817 (205*2π)/3632 weeks
20617.81662 -10.81522 (206*2π)/3632 weeks
20720.73243 -6.23094 (207*2π)/3632 weeks
20818.88761 -3.71084 (208*2π)/3632 weeks
20917.37025 -5.53446 (209*2π)/3632 weeks
21020.4971 -6.70807 (210*2π)/3632 weeks
21123.67238 -2.78234 (211*2π)/3632 weeks
21222.57779 1.74168 (212*2π)/3632 weeks
21316.83977 2.66444 (213*2π)/3632 weeks
21417.18028 -3.13443 (214*2π)/3632 weeks
21522.39973 -.33987 (215*2π)/3632 weeks
21619.99791 5.46807 (216*2π)/3632 weeks
21714.8241 6.09397 (217*2π)/3632 weeks
21811.83933 4.24735 (218*2π)/3632 weeks
21911.09274 1.41135 (219*2π)/3632 weeks
22011.02835 -1.06983 (220*2π)/3632 weeks
22114.02517 -1.38177 (221*2π)/3632 weeks
22213.68735 4.29885 (222*2π)/3632 weeks
2237.66586 3.33971 (223*2π)/3632 weeks
2243.79725 -2.15817 (224*2π)/3632 weeks
2257.52466 -6.20521 (225*2π)/3632 weeks
2268.89931 -3.45767 (226*2π)/3632 weeks
2274.54505 -5.50253 (227*2π)/3632 weeks
2282.41677 -10.88608 (228*2π)/3632 weeks
2298.84993 -20.34159 (229*2π)/3632 weeks
23021.28959 -16.13832 (230*2π)/3632 weeks
23118.42033 -7.15362 (231*2π)/3632 weeks
23214.92291 -8.52623 (232*2π)/3632 weeks
23316.06515 -13.81621 (233*2π)/3632 weeks
23425.74526 -12.89398 (234*2π)/3632 weeks
23526.51879 -2.49683 (235*2π)/3632 weeks
23619.00187 1.60018 (236*2π)/3632 weeks
23715.17457 -1.58019 (237*2π)/3632 weeks
23816.70391 -3.95869 (238*2π)/3632 weeks
23917.9065 -1.70293 (239*2π)/3632 weeks
24013.10526 1.49712 (240*2π)/3632 weeks
24110.49238 -3.94732 (241*2π)/3632 weeks
24213.8378 -4.87426 (242*2π)/3632 weeks
24313.53207 -4.86829 (243*2π)/3631 weeks
24413.95767 -4.05205 (244*2π)/3631 weeks
24512.91359 -2.27772 (245*2π)/3631 weeks
2468.0479 -2.78725 (246*2π)/3631 weeks
2478.70698 -7.45048 (247*2π)/3631 weeks
24810.56472 -8.88238 (248*2π)/3631 weeks
24912.24781 -8.53393 (249*2π)/3631 weeks
2509.77265 -7.74635 (250*2π)/3631 weeks
25110.04198 -12.52428 (251*2π)/3631 weeks
25214.29325 -13.70896 (252*2π)/3631 weeks
25317.50196 -12.34267 (253*2π)/3631 weeks
25421.39988 -7.91018 (254*2π)/3631 weeks
25516.43788 -2.86487 (255*2π)/3631 weeks
25615.92159 -3.86963 (256*2π)/3631 weeks
25713.61922 -.08833 (257*2π)/3631 weeks
2584.50748 -1.08243 (258*2π)/3631 weeks
2593.57405 -10.84515 (259*2π)/3631 weeks
2609.20395 -12.75902 (260*2π)/3631 weeks
26112.57645 -10.34329 (261*2π)/3631 weeks
2628.60203 -4.97303 (262*2π)/3631 weeks
263.10219 -12.41013 (263*2π)/3631 weeks
2646.56678 -21.71954 (264*2π)/3631 weeks
26514.21564 -19.12697 (265*2π)/3631 weeks
26612.7474 -16.17657 (266*2π)/3631 weeks
26711.2911 -18.15065 (267*2π)/3631 weeks
26816.20953 -21.06896 (268*2π)/3631 weeks
26922.91228 -18.1144 (269*2π)/3631 weeks
27020.7257 -9.09951 (270*2π)/3631 weeks
27112.28636 -12.7437 (271*2π)/3631 weeks
27215.76491 -19.81974 (272*2π)/3631 weeks
27323.24392 -18.35883 (273*2π)/3631 weeks
27426.19707 -7.79222 (274*2π)/3631 weeks
27519.15947 -4.41357 (275*2π)/3631 weeks
27615.76601 -5.89021 (276*2π)/3631 weeks
27712.86059 -5.9945 (277*2π)/3631 weeks
27810.7271 -6.47468 (278*2π)/3631 weeks
2797.38323 -11.72262 (279*2π)/3631 weeks
28011.05132 -12.67413 (280*2π)/3631 weeks
28110.29369 -8.71123 (281*2π)/3631 weeks
2826.3331 -12.41481 (282*2π)/3631 weeks
2835.1437 -14.79908 (283*2π)/3631 weeks
2847.88051 -21.8303 (284*2π)/3631 weeks
28512.46856 -18.03425 (285*2π)/3631 weeks
2868.7726 -16.22086 (286*2π)/3631 weeks
2876.73001 -18.07401 (287*2π)/3631 weeks
2885.85286 -23.82824 (288*2π)/3631 weeks
28912.36405 -27.54931 (289*2π)/3631 weeks
29017.69464 -24.48633 (290*2π)/3631 weeks
29116.80746 -21.96468 (291*2π)/3631 weeks
29217.63409 -20.19959 (292*2π)/3631 weeks
29313.76053 -15.27206 (293*2π)/3631 weeks
29410.61582 -23.4402 (294*2π)/3631 weeks
29515.72458 -22.71004 (295*2π)/3631 weeks
29615.99276 -21.32151 (296*2π)/3631 weeks
29713.92245 -22.05105 (297*2π)/3631 weeks
29814.6738 -22.8238 (298*2π)/3631 weeks
29918.26299 -22.06852 (299*2π)/3631 weeks
30015.20371 -14.31921 (300*2π)/3631 weeks
3013.86077 -17.40416 (301*2π)/3631 weeks
3023.78657 -27.32588 (302*2π)/3631 weeks
3036.8466 -31.06724 (303*2π)/3631 weeks
30410.10937 -33.476 (304*2π)/3631 weeks
30512.04431 -36.81952 (305*2π)/3631 weeks
30614.70242 -41.94896 (306*2π)/3631 weeks
30725.78941 -44.60404 (307*2π)/3631 weeks
30832.87987 -33.87944 (308*2π)/3631 weeks
30927.28817 -28.15737 (309*2π)/3631 weeks
31027.06807 -34.62145 (310*2π)/3631 weeks
31141.22916 -32.40503 (311*2π)/3631 weeks
31244.22967 -11.55308 (312*2π)/3631 weeks
31324.00274 .83796 (313*2π)/3631 weeks
3149.77751 -9.139 (314*2π)/3631 weeks
31510.47444 -20.83737 (315*2π)/3631 weeks
31613.95942 -22.34413 (316*2π)/3631 weeks
31714.96767 -15.04483 (317*2π)/3631 weeks
318-2.62697 -14.96167 (318*2π)/3631 weeks
319-5.2679 -36.7828 (319*2π)/3631 weeks
3206.67825 -40.58632 (320*2π)/3631 weeks
32113.75354 -39.41638 (321*2π)/3631 weeks
3228.89431 -33.8857 (322*2π)/3631 weeks
3234.98376 -42.01379 (323*2π)/3631 weeks
32410.91684 -49.78952 (324*2π)/3631 weeks
32520.01254 -54.30035 (325*2π)/3631 weeks
32633.36369 -42.59544 (326*2π)/3631 weeks
32723.67449 -30.77215 (327*2π)/3631 weeks
32810.8616 -31.08721 (328*2π)/3631 weeks
3293.92733 -46.93726 (329*2π)/3631 weeks
33011.13332 -54.1131 (330*2π)/3631 weeks
33115.6082 -60.36494 (331*2π)/3631 weeks
33229.89337 -50.45152 (332*2π)/3631 weeks
33315.18834 -43.4378 (333*2π)/3631 weeks
3342.91793 -63.38144 (334*2π)/3631 weeks
33521.63282 -80.36181 (335*2π)/3631 weeks
33645.67775 -74.80457 (336*2π)/3631 weeks
33743.67052 -55.95242 (337*2π)/3631 weeks
33838.13231 -51.03435 (338*2π)/3631 weeks
33928.91475 -57.23814 (339*2π)/3631 weeks
34039.90026 -60.67811 (340*2π)/3631 weeks
34136.74851 -47.41083 (341*2π)/3631 weeks
34223.54654 -53.32838 (342*2π)/3631 weeks
34321.08317 -69.27721 (343*2π)/3631 weeks
34427.68056 -85.13123 (344*2π)/3631 weeks
34551.06876 -74.43951 (345*2π)/3631 weeks
34630.39169 -61.15508 (346*2π)/3631 weeks
34730.83438 -88.87022 (347*2π)/3631 weeks
34866.49547 -80.80229 (348*2π)/3631 weeks
34947.16202 -56.89178 (349*2π)/3631 weeks
35033.78656 -71.59245 (350*2π)/3631 weeks
35141.0663 -66.38797 (351*2π)/3631 weeks
3526.93463 -60.37462 (352*2π)/3631 weeks
353-1.01282 -94.15217 (353*2π)/3631 weeks
354-7.85258 -107.5588 (354*2π)/3631 weeks
355-31.1368 -128.6414 (355*2π)/3631 weeks
356-61.56464 -195.9303 (356*2π)/3631 weeks
357-40.72211 -300.1153 (357*2π)/3631 weeks
35868.14023 -376.8859 (358*2π)/3631 weeks
359128.237 -360.7594 (359*2π)/3631 weeks
360154.5261 -448.3247 (360*2π)/3631 weeks
361296.3847 -575.4678 (361*2π)/3631 weeks

Problems, Comments, Suggestions? Click here to contact Greg Thatcher

Please read my Disclaimer





Copyright (c) 2013 Thatcher Development Software, LLC. All rights reserved. No claim to original U.S. Gov't works.