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

Fourier Analysis of BIS (ProShares UltraShort Nasdaq Bio)


BIS (ProShares UltraShort Nasdaq Bio) appears to have interesting cyclic behaviour every 36 weeks (62.104*sine), 32 weeks (49.5039*sine), and 32 weeks (20.2815*cosine).

BIS (ProShares UltraShort Nasdaq Bio) has an average price of 374.08 (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 4/9/2010 to 1/17/2017 for BIS (ProShares UltraShort Nasdaq Bio), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0374.0774   0 
1262.0846 391.4615 (1*2π)/355355 weeks
254.63623 228.1703 (2*2π)/355178 weeks
329.3447 148.1938 (3*2π)/355118 weeks
427.23048 112.0081 (4*2π)/35589 weeks
528.06153 121.5882 (5*2π)/35571 weeks
6-11.47479 106.0053 (6*2π)/35559 weeks
7-17.42801 66.43945 (7*2π)/35551 weeks
8-1.57729 50.19547 (8*2π)/35544 weeks
97.17742 49.66779 (9*2π)/35539 weeks
102.75895 62.104 (10*2π)/35536 weeks
11-20.2815 49.50389 (11*2π)/35532 weeks
12-14.87951 29.1765 (12*2π)/35530 weeks
13-4.39336 25.46399 (13*2π)/35527 weeks
14-3.79852 25.56681 (14*2π)/35525 weeks
152.76234 22.51784 (15*2π)/35524 weeks
161.54226 25.74547 (16*2π)/35522 weeks
17-2.82272 27.75453 (17*2π)/35521 weeks
18-7.67813 18.49421 (18*2π)/35520 weeks
19-2.13689 15.84377 (19*2π)/35519 weeks
204.01637 13.12577 (20*2π)/35518 weeks
216.6881 19.0104 (21*2π)/35517 weeks
221.13514 19.52963 (22*2π)/35516 weeks
232.09009 13.74237 (23*2π)/35515 weeks
244.50001 18.25909 (24*2π)/35515 weeks
252.32651 17.73333 (25*2π)/35514 weeks
26-2.04667 21.36898 (26*2π)/35514 weeks
27-7.78096 13.37361 (27*2π)/35513 weeks
28-2.19808 4.64459 (28*2π)/35513 weeks
295.17927 7.75666 (29*2π)/35512 weeks
305.26982 11.48361 (30*2π)/35512 weeks
312.71069 12.64927 (31*2π)/35511 weeks
321.60565 12.70482 (32*2π)/35511 weeks
33-1.28898 8.6122 (33*2π)/35511 weeks
346.31089 5.68422 (34*2π)/35510 weeks
357.27326 13.65606 (35*2π)/35510 weeks
362.72639 15.10676 (36*2π)/35510 weeks
37-2.3739 13.54395 (37*2π)/35510 weeks
38-2.79519 9.04431 (38*2π)/3559 weeks
39-1.39873 5.23456 (39*2π)/3559 weeks
403.87822 6.15224 (40*2π)/3559 weeks
411.72797 11.30646 (41*2π)/3559 weeks
42-.94434 7.88816 (42*2π)/3558 weeks
43-2.28568 8.11162 (43*2π)/3558 weeks
44-1.72726 2.55671 (44*2π)/3558 weeks
452.34863 3.4211 (45*2π)/3558 weeks
463.7358 5.41047 (46*2π)/3558 weeks
472.28071 6.41744 (47*2π)/3558 weeks
48-.4282 5.05091 (48*2π)/3557 weeks
49-.55429 -1.51432 (49*2π)/3557 weeks
507.74056 -2.72419 (50*2π)/3557 weeks
5110.2938 4.55974 (51*2π)/3557 weeks
526.09165 7.22656 (52*2π)/3557 weeks
533.90787 5.93756 (53*2π)/3557 weeks
544.17127 2.06088 (54*2π)/3557 weeks
559.78682 3.95003 (55*2π)/3556 weeks
568.21092 7.80675 (56*2π)/3556 weeks
576.51233 8.20278 (57*2π)/3556 weeks
583.85329 7.88651 (58*2π)/3556 weeks
594.01762 6.16897 (59*2π)/3556 weeks
604.89435 6.77647 (60*2π)/3556 weeks
612.94611 8.47924 (61*2π)/3556 weeks
62.91001 6.38127 (62*2π)/3556 weeks
632.76148 3.84239 (63*2π)/3556 weeks
644.12959 5.70317 (64*2π)/3556 weeks
652.09379 6.24992 (65*2π)/3555 weeks
662.58288 3.80484 (66*2π)/3555 weeks
672.81549 3.59117 (67*2π)/3555 weeks
684.59163 3.54199 (68*2π)/3555 weeks
693.44884 4.84598 (69*2π)/3555 weeks
702.55091 3.77128 (70*2π)/3555 weeks
714.37342 2.49258 (71*2π)/3555 weeks
725.98729 3.6457 (72*2π)/3555 weeks
735.41687 5.70341 (73*2π)/3555 weeks
743.58295 6.26025 (74*2π)/3555 weeks
752.98757 4.86108 (75*2π)/3555 weeks
763.68775 5.1781 (76*2π)/3555 weeks
772.73355 5.60644 (77*2π)/3555 weeks
782.51742 4.82599 (78*2π)/3555 weeks
79.98372 3.60406 (79*2π)/3554 weeks
803.07757 1.78808 (80*2π)/3554 weeks
813.83722 3.28023 (81*2π)/3554 weeks
822.55725 3.95003 (82*2π)/3554 weeks
832.76724 2.26948 (83*2π)/3554 weeks
843.5686 1.4701 (84*2π)/3554 weeks
855.07727 2.81067 (85*2π)/3554 weeks
863.96484 2.87508 (86*2π)/3554 weeks
875.22357 1.99188 (87*2π)/3554 weeks
884.68405 3.76781 (88*2π)/3554 weeks
894.42664 3.67656 (89*2π)/3554 weeks
903.5532 2.53198 (90*2π)/3554 weeks
915.64419 1.62777 (91*2π)/3554 weeks
927.08026 2.94852 (92*2π)/3554 weeks
937.0181 5.72289 (93*2π)/3554 weeks
944.11437 6.89882 (94*2π)/3554 weeks
952.52238 6.29191 (95*2π)/3554 weeks
961.52103 4.39707 (96*2π)/3554 weeks
973.07263 3.51742 (97*2π)/3554 weeks
982.63092 4.93783 (98*2π)/3554 weeks
99.73711 3.98735 (99*2π)/3554 weeks
100.70655 2.24918 (100*2π)/3554 weeks
1012.55766 .67613 (101*2π)/3554 weeks
1025.00279 2.47412 (102*2π)/3553 weeks
1032.72746 4.69999 (103*2π)/3553 weeks
1041.26338 2.75674 (104*2π)/3553 weeks
1051.75966 1.58272 (105*2π)/3553 weeks
1061.87543 .79559 (106*2π)/3553 weeks
1073.53654 .27135 (107*2π)/3553 weeks
1084.42442 1.61524 (108*2π)/3553 weeks
1093.31024 1.84712 (109*2π)/3553 weeks
1103.94947 1.44414 (110*2π)/3553 weeks
1113.85056 1.75297 (111*2π)/3553 weeks
1124.18238 .93392 (112*2π)/3553 weeks
1135.70686 1.04677 (113*2π)/3553 weeks
1146.00955 2.86288 (114*2π)/3553 weeks
1154.67612 4.30389 (115*2π)/3553 weeks
1163.1507 3.61323 (116*2π)/3553 weeks
1173.39257 2.42018 (117*2π)/3553 weeks
1184.41237 2.72749 (118*2π)/3553 weeks
1193.5288 2.88879 (119*2π)/3553 weeks
1204.04451 2.92261 (120*2π)/3553 weeks
1213.29299 3.11198 (121*2π)/3553 weeks
1223.97948 2.6376 (122*2π)/3553 weeks
1233.69571 3.2959 (123*2π)/3553 weeks
1243.81069 3.26469 (124*2π)/3553 weeks
1253.93834 4.6651 (125*2π)/3553 weeks
1261.2609 5.7038 (126*2π)/3553 weeks
127-.20545 2.3397 (127*2π)/3553 weeks
1281.94477 1.28288 (128*2π)/3553 weeks
1293.3583 2.23268 (129*2π)/3553 weeks
1302.05528 4.93034 (130*2π)/3553 weeks
131-.93513 3.15604 (131*2π)/3553 weeks
132.17112 .70319 (132*2π)/3553 weeks
133.80439 .95791 (133*2π)/3553 weeks
1341.75163 .94133 (134*2π)/3553 weeks
135.92175 2.05806 (135*2π)/3553 weeks
136-.76528 .85663 (136*2π)/3553 weeks
137.22519 -1.97898 (137*2π)/3553 weeks
1383.18317 -2.49893 (138*2π)/3553 weeks
1393.96437 .03741 (139*2π)/3553 weeks
1403.10888 .75593 (140*2π)/3553 weeks
1412.59054 .74241 (141*2π)/3553 weeks
1422.35145 .41211 (142*2π)/3553 weeks
1432.08949 -.10031 (143*2π)/3552 weeks
1442.49321 -.76291 (144*2π)/3552 weeks
1453.66219 -.2087 (145*2π)/3552 weeks
1462.85643 .95514 (146*2π)/3552 weeks
1471.63301 .0549 (147*2π)/3552 weeks
1482.37131 -1.01549 (148*2π)/3552 weeks
1492.80021 -.93809 (149*2π)/3552 weeks
1502.58712 -1.09545 (150*2π)/3552 weeks
1513.51766 -1.67925 (151*2π)/3552 weeks
1524.00997 -1.0113 (152*2π)/3552 weeks
1533.65104 -.87453 (153*2π)/3552 weeks
1544.30595 -1.50589 (154*2π)/3552 weeks
1555.20614 .59533 (155*2π)/3552 weeks
1563.18722 1.36974 (156*2π)/3552 weeks
1572.09064 -.59933 (157*2π)/3552 weeks
1583.40732 -2.0323 (158*2π)/3552 weeks
1594.98736 -1.0533 (159*2π)/3552 weeks
1604.36032 .53641 (160*2π)/3552 weeks
1613.6374 .01863 (161*2π)/3552 weeks
1623.50022 -.1789 (162*2π)/3552 weeks
1633.87166 -.91585 (163*2π)/3552 weeks
1644.93039 -.80835 (164*2π)/3552 weeks
1654.61605 1.46135 (165*2π)/3552 weeks
1662.00034 .82619 (166*2π)/3552 weeks
1672.26944 -1.86261 (167*2π)/3552 weeks
1684.52727 -1.57678 (168*2π)/3552 weeks
1693.48356 -.97215 (169*2π)/3552 weeks
1704.97674 -1.75148 (170*2π)/3552 weeks
1715.10575 -.13076 (171*2π)/3552 weeks
1723.92962 -.77928 (172*2π)/3552 weeks
1734.76591 -1.41888 (173*2π)/3552 weeks
1745.29801 -1.00003 (174*2π)/3552 weeks
1755.33747 -.36501 (175*2π)/3552 weeks
1765.24288 -.79376 (176*2π)/3552 weeks
1775.87303 -.48089 (177*2π)/3552 weeks
1785.87303 .48089 (178*2π)/3552 weeks
1795.24288 .79376 (179*2π)/3552 weeks
1805.33747 .36501 (180*2π)/3552 weeks
1815.29801 1.00003 (181*2π)/3552 weeks
1824.76591 1.41888 (182*2π)/3552 weeks
1833.92962 .77928 (183*2π)/3552 weeks
1845.10575 .13076 (184*2π)/3552 weeks
1854.97674 1.75148 (185*2π)/3552 weeks
1863.48356 .97215 (186*2π)/3552 weeks
1874.52727 1.57678 (187*2π)/3552 weeks
1882.26944 1.86261 (188*2π)/3552 weeks
1892.00034 -.82619 (189*2π)/3552 weeks
1904.61605 -1.46135 (190*2π)/3552 weeks
1914.93039 .80835 (191*2π)/3552 weeks
1923.87166 .91585 (192*2π)/3552 weeks
1933.50022 .1789 (193*2π)/3552 weeks
1943.6374 -.01863 (194*2π)/3552 weeks
1954.36032 -.53641 (195*2π)/3552 weeks
1964.98736 1.0533 (196*2π)/3552 weeks
1973.40732 2.0323 (197*2π)/3552 weeks
1982.09064 .59933 (198*2π)/3552 weeks
1993.18722 -1.36974 (199*2π)/3552 weeks
2005.20614 -.59533 (200*2π)/3552 weeks
2014.30595 1.50589 (201*2π)/3552 weeks
2023.65104 .87453 (202*2π)/3552 weeks
2034.00997 1.0113 (203*2π)/3552 weeks
2043.51766 1.67925 (204*2π)/3552 weeks
2052.58712 1.09545 (205*2π)/3552 weeks
2062.80021 .93809 (206*2π)/3552 weeks
2072.37131 1.01549 (207*2π)/3552 weeks
2081.63301 -.0549 (208*2π)/3552 weeks
2092.85643 -.95514 (209*2π)/3552 weeks
2103.66219 .2087 (210*2π)/3552 weeks
2112.49321 .76291 (211*2π)/3552 weeks
2122.08949 .10031 (212*2π)/3552 weeks
2132.35145 -.41211 (213*2π)/3552 weeks
2142.59054 -.74241 (214*2π)/3552 weeks
2153.10888 -.75593 (215*2π)/3552 weeks
2163.96437 -.03741 (216*2π)/3552 weeks
2173.18317 2.49893 (217*2π)/3552 weeks
218.22519 1.97898 (218*2π)/3552 weeks
219-.76528 -.85663 (219*2π)/3552 weeks
220.92175 -2.05806 (220*2π)/3552 weeks
2211.75163 -.94133 (221*2π)/3552 weeks
222.80439 -.95791 (222*2π)/3552 weeks
223.17112 -.70319 (223*2π)/3552 weeks
224-.93513 -3.15604 (224*2π)/3552 weeks
2252.05528 -4.93034 (225*2π)/3552 weeks
2263.3583 -2.23268 (226*2π)/3552 weeks
2271.94477 -1.28288 (227*2π)/3552 weeks
228-.20545 -2.3397 (228*2π)/3552 weeks
2291.2609 -5.7038 (229*2π)/3552 weeks
2303.93834 -4.6651 (230*2π)/3552 weeks
2313.81069 -3.26469 (231*2π)/3552 weeks
2323.69571 -3.2959 (232*2π)/3552 weeks
2333.97948 -2.6376 (233*2π)/3552 weeks
2343.29299 -3.11198 (234*2π)/3552 weeks
2354.04451 -2.92261 (235*2π)/3552 weeks
2363.5288 -2.88879 (236*2π)/3552 weeks
2374.41237 -2.72749 (237*2π)/3551 weeks
2383.39257 -2.42018 (238*2π)/3551 weeks
2393.1507 -3.61323 (239*2π)/3551 weeks
2404.67612 -4.30389 (240*2π)/3551 weeks
2416.00955 -2.86288 (241*2π)/3551 weeks
2425.70686 -1.04677 (242*2π)/3551 weeks
2434.18238 -.93392 (243*2π)/3551 weeks
2443.85056 -1.75297 (244*2π)/3551 weeks
2453.94947 -1.44414 (245*2π)/3551 weeks
2463.31024 -1.84712 (246*2π)/3551 weeks
2474.42442 -1.61524 (247*2π)/3551 weeks
2483.53654 -.27135 (248*2π)/3551 weeks
2491.87543 -.79559 (249*2π)/3551 weeks
2501.75966 -1.58272 (250*2π)/3551 weeks
2511.26338 -2.75674 (251*2π)/3551 weeks
2522.72746 -4.69999 (252*2π)/3551 weeks
2535.00279 -2.47412 (253*2π)/3551 weeks
2542.55766 -.67613 (254*2π)/3551 weeks
255.70655 -2.24918 (255*2π)/3551 weeks
256.73711 -3.98735 (256*2π)/3551 weeks
2572.63092 -4.93783 (257*2π)/3551 weeks
2583.07263 -3.51742 (258*2π)/3551 weeks
2591.52103 -4.39707 (259*2π)/3551 weeks
2602.52238 -6.29191 (260*2π)/3551 weeks
2614.11437 -6.89882 (261*2π)/3551 weeks
2627.0181 -5.72289 (262*2π)/3551 weeks
2637.08026 -2.94852 (263*2π)/3551 weeks
2645.64419 -1.62777 (264*2π)/3551 weeks
2653.5532 -2.53198 (265*2π)/3551 weeks
2664.42664 -3.67656 (266*2π)/3551 weeks
2674.68405 -3.76781 (267*2π)/3551 weeks
2685.22357 -1.99188 (268*2π)/3551 weeks
2693.96484 -2.87508 (269*2π)/3551 weeks
2705.07727 -2.81067 (270*2π)/3551 weeks
2713.5686 -1.4701 (271*2π)/3551 weeks
2722.76724 -2.26948 (272*2π)/3551 weeks
2732.55725 -3.95003 (273*2π)/3551 weeks
2743.83722 -3.28023 (274*2π)/3551 weeks
2753.07757 -1.78808 (275*2π)/3551 weeks
276.98372 -3.60406 (276*2π)/3551 weeks
2772.51742 -4.82599 (277*2π)/3551 weeks
2782.73355 -5.60644 (278*2π)/3551 weeks
2793.68775 -5.1781 (279*2π)/3551 weeks
2802.98757 -4.86108 (280*2π)/3551 weeks
2813.58295 -6.26025 (281*2π)/3551 weeks
2825.41687 -5.70341 (282*2π)/3551 weeks
2835.98729 -3.6457 (283*2π)/3551 weeks
2844.37342 -2.49258 (284*2π)/3551 weeks
2852.55091 -3.77128 (285*2π)/3551 weeks
2863.44884 -4.84598 (286*2π)/3551 weeks
2874.59163 -3.54199 (287*2π)/3551 weeks
2882.81549 -3.59117 (288*2π)/3551 weeks
2892.58288 -3.80484 (289*2π)/3551 weeks
2902.09379 -6.24992 (290*2π)/3551 weeks
2914.12959 -5.70317 (291*2π)/3551 weeks
2922.76148 -3.84239 (292*2π)/3551 weeks
293.91001 -6.38127 (293*2π)/3551 weeks
2942.94611 -8.47924 (294*2π)/3551 weeks
2954.89435 -6.77647 (295*2π)/3551 weeks
2964.01762 -6.16897 (296*2π)/3551 weeks
2973.85329 -7.88651 (297*2π)/3551 weeks
2986.51233 -8.20278 (298*2π)/3551 weeks
2998.21092 -7.80675 (299*2π)/3551 weeks
3009.78682 -3.95003 (300*2π)/3551 weeks
3014.17127 -2.06088 (301*2π)/3551 weeks
3023.90787 -5.93756 (302*2π)/3551 weeks
3036.09165 -7.22656 (303*2π)/3551 weeks
30410.2938 -4.55974 (304*2π)/3551 weeks
3057.74056 2.72419 (305*2π)/3551 weeks
306-.55429 1.51432 (306*2π)/3551 weeks
307-.4282 -5.05091 (307*2π)/3551 weeks
3082.28071 -6.41744 (308*2π)/3551 weeks
3093.7358 -5.41047 (309*2π)/3551 weeks
3102.34863 -3.4211 (310*2π)/3551 weeks
311-1.72726 -2.55671 (311*2π)/3551 weeks
312-2.28568 -8.11162 (312*2π)/3551 weeks
313-.94434 -7.88816 (313*2π)/3551 weeks
3141.72797 -11.30646 (314*2π)/3551 weeks
3153.87822 -6.15224 (315*2π)/3551 weeks
316-1.39873 -5.23456 (316*2π)/3551 weeks
317-2.79519 -9.04431 (317*2π)/3551 weeks
318-2.3739 -13.54395 (318*2π)/3551 weeks
3192.72639 -15.10676 (319*2π)/3551 weeks
3207.27326 -13.65606 (320*2π)/3551 weeks
3216.31089 -5.68422 (321*2π)/3551 weeks
322-1.28898 -8.6122 (322*2π)/3551 weeks
3231.60565 -12.70482 (323*2π)/3551 weeks
3242.71069 -12.64927 (324*2π)/3551 weeks
3255.26982 -11.48361 (325*2π)/3551 weeks
3265.17927 -7.75666 (326*2π)/3551 weeks
327-2.19808 -4.64459 (327*2π)/3551 weeks
328-7.78096 -13.37361 (328*2π)/3551 weeks
329-2.04667 -21.36898 (329*2π)/3551 weeks
3302.32651 -17.73333 (330*2π)/3551 weeks
3314.50001 -18.25909 (331*2π)/3551 weeks
3322.09009 -13.74237 (332*2π)/3551 weeks
3331.13514 -19.52963 (333*2π)/3551 weeks
3346.6881 -19.0104 (334*2π)/3551 weeks
3354.01637 -13.12577 (335*2π)/3551 weeks
336-2.13689 -15.84377 (336*2π)/3551 weeks
337-7.67813 -18.49421 (337*2π)/3551 weeks
338-2.82272 -27.75453 (338*2π)/3551 weeks
3391.54226 -25.74547 (339*2π)/3551 weeks
3402.76234 -22.51784 (340*2π)/3551 weeks
341-3.79852 -25.56681 (341*2π)/3551 weeks
342-4.39336 -25.46399 (342*2π)/3551 weeks
343-14.87951 -29.1765 (343*2π)/3551 weeks
344-20.2815 -49.50389 (344*2π)/3551 weeks
3452.75895 -62.104 (345*2π)/3551 weeks
3467.17742 -49.66779 (346*2π)/3551 weeks
347-1.57729 -50.19547 (347*2π)/3551 weeks
348-17.42801 -66.43945 (348*2π)/3551 weeks
349-11.47479 -106.0053 (349*2π)/3551 weeks
35028.06153 -121.5882 (350*2π)/3551 weeks
35127.23048 -112.0081 (351*2π)/3551 weeks
35229.3447 -148.1938 (352*2π)/3551 weeks
35354.63623 -228.1703 (353*2π)/3551 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.