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# Fourier Analysis of BTK (NYSE ARCA BIOTECH INDEX)

BTK (NYSE ARCA BIOTECH INDEX) appears to have interesting cyclic behaviour every 85 weeks (117.8395*sine), 73 weeks (107.381*sine), and 79 weeks (107.315*sine).

BTK (NYSE ARCA BIOTECH INDEX) has an average price of 1,101.64 (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.

## Fourier Analysis

Using data from 2/28/1996 to 3/20/2017 for BTK (NYSE ARCA BIOTECH INDEX), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
01,101.643   0
1605.1478 -806.4077 (1*2π)/11001,100 weeks
2169.8522 -697.6625 (2*2π)/1100550 weeks
3-38.05225 -553.3541 (3*2π)/1100367 weeks
4-31.80505 -391.3743 (4*2π)/1100275 weeks
5-115.5036 -183.4571 (5*2π)/1100220 weeks
6-77.64161 -60.83191 (6*2π)/1100183 weeks
7-45.30394 -117.9284 (7*2π)/1100157 weeks
8-22.21345 -77.39826 (8*2π)/1100138 weeks
934.21931 -44.3133 (9*2π)/1100122 weeks
1052.37989 -74.74812 (10*2π)/1100110 weeks
1162.504 -68.76043 (11*2π)/1100100 weeks
1229.39663 -100.9548 (12*2π)/110092 weeks
1320.3851 -117.8395 (13*2π)/110085 weeks
1423.18429 -107.315 (14*2π)/110079 weeks
15-2.26968 -107.381 (15*2π)/110073 weeks
16-48.17319 -66.1088 (16*2π)/110069 weeks
17-10.46696 -56.49964 (17*2π)/110065 weeks
18-7.75545 -68.08736 (18*2π)/110061 weeks
19-19.23604 -54.97142 (19*2π)/110058 weeks
20-16.98503 -31.53239 (20*2π)/110055 weeks
216.35757 -35.35293 (21*2π)/110052 weeks
2212.36994 -46.31767 (22*2π)/110050 weeks
23-12.83315 -49.53444 (23*2π)/110048 weeks
24-8.32799 -21.39818 (24*2π)/110046 weeks
254.43244 -34.40771 (25*2π)/110044 weeks
262.5425 -31.20728 (26*2π)/110042 weeks
278.46579 -36.66385 (27*2π)/110041 weeks
283.33701 -34.16497 (28*2π)/110039 weeks
296.34128 -25.28492 (29*2π)/110038 weeks
30-6.5157 -33.17619 (30*2π)/110037 weeks
312.39355 -36.77485 (31*2π)/110035 weeks
3213.76519 -15.83453 (32*2π)/110034 weeks
3315.49927 -23.15222 (33*2π)/110033 weeks
349.11667 -42.92778 (34*2π)/110032 weeks
35-9.74032 -43.10787 (35*2π)/110031 weeks
3611.80217 -37.44624 (36*2π)/110031 weeks
371.54437 -47.19945 (37*2π)/110030 weeks
38-10.37979 -22.95672 (38*2π)/110029 weeks
39-1.45312 -26.21841 (39*2π)/110028 weeks
40-4.98584 -32.1677 (40*2π)/110028 weeks
41-3.38344 -26.38504 (41*2π)/110027 weeks
42-.53933 -33.17532 (42*2π)/110026 weeks
43-8.20792 -29.5061 (43*2π)/110026 weeks
44-9.57308 -11.39138 (44*2π)/110025 weeks
45-6.88462 -13.61096 (45*2π)/110024 weeks
46-4.48318 -16.31773 (46*2π)/110024 weeks
4715.66844 -22.10541 (47*2π)/110023 weeks
4811.82934 -23.57409 (48*2π)/110023 weeks
496.83123 -22.6022 (49*2π)/110022 weeks
50-3.35367 -27.51245 (50*2π)/110022 weeks
512.45512 -32.33783 (51*2π)/110022 weeks
52.13499 -34.87647 (52*2π)/110021 weeks
53-4.68104 -21.75985 (53*2π)/110021 weeks
54-2.59831 -28.60826 (54*2π)/110020 weeks
55-10.74257 -33.42141 (55*2π)/110020 weeks
56-19.77386 -21.87624 (56*2π)/110020 weeks
57-18.85837 -17.06174 (57*2π)/110019 weeks
58-13.34314 -14.87787 (58*2π)/110019 weeks
59-8.35074 -5.46669 (59*2π)/110019 weeks
60-6.82504 .27934 (60*2π)/110018 weeks
615.79576 -5.6629 (61*2π)/110018 weeks
626.04027 -18.4453 (62*2π)/110018 weeks
633.45193 -15.02409 (63*2π)/110017 weeks
649.40366 -14.72569 (64*2π)/110017 weeks
652.90999 -15.17601 (65*2π)/110017 weeks
665.58221 -17.32672 (66*2π)/110017 weeks
671.9024 -26.00591 (67*2π)/110016 weeks
68.17708 -19.24966 (68*2π)/110016 weeks
699.24069 -18.89832 (69*2π)/110016 weeks
70-1.93196 -20.92879 (70*2π)/110016 weeks
71-9.68116 -25.06822 (71*2π)/110015 weeks
72-7.73122 -19.18204 (72*2π)/110015 weeks
73-1.43704 -14.53768 (73*2π)/110015 weeks
74-.98858 -11.53106 (74*2π)/110015 weeks
75-1.37456 -18.50037 (75*2π)/110015 weeks
76-7.39283 -21.25061 (76*2π)/110014 weeks
77-8.44391 -16.31269 (77*2π)/110014 weeks
78-2.82896 -15.5046 (78*2π)/110014 weeks
79-8.2387 -12.243 (79*2π)/110014 weeks
80-3.78886 -3.6747 (80*2π)/110014 weeks
817.25484 -8.41593 (81*2π)/110014 weeks
821.92748 -16.56328 (82*2π)/110013 weeks
83-1.24989 -19.43818 (83*2π)/110013 weeks
843.13839 -16.58042 (84*2π)/110013 weeks
851.81073 -18.46916 (85*2π)/110013 weeks
86-9.94429 -20.10311 (86*2π)/110013 weeks
87-9.75448 -15.97178 (87*2π)/110013 weeks
88-6.30598 -14.6866 (88*2π)/110013 weeks
89-1.52153 -10.2276 (89*2π)/110012 weeks
90-4.23075 -12.49234 (90*2π)/110012 weeks
91-5.36653 -14.30651 (91*2π)/110012 weeks
92-8.37705 -13.94313 (92*2π)/110012 weeks
93-4.77679 -12.35377 (93*2π)/110012 weeks
94-6.06996 -13.06298 (94*2π)/110012 weeks
95-6.91346 -6.4422 (95*2π)/110012 weeks
96-3.64388 -8.74992 (96*2π)/110011 weeks
97-1.73289 -9.0591 (97*2π)/110011 weeks
98-1.37518 -12.02743 (98*2π)/110011 weeks
99-3.1091 -11.84176 (99*2π)/110011 weeks
100-6.56128 -14.88242 (100*2π)/110011 weeks
101-5.94229 -8.78838 (101*2π)/110011 weeks
102-2.46709 -5.89411 (102*2π)/110011 weeks
103-1.92963 -12.9682 (103*2π)/110011 weeks
104-3.30592 -14.32032 (104*2π)/110011 weeks
105-7.83197 -9.56181 (105*2π)/110010 weeks
106-5.02858 -7.71669 (106*2π)/110010 weeks
107-2.77416 -6.72918 (107*2π)/110010 weeks
108-.60532 -10.12304 (108*2π)/110010 weeks
109-7.70812 -10.93609 (109*2π)/110010 weeks
110-5.80738 -9.53198 (110*2π)/110010 weeks
111-1.59985 -7.8702 (111*2π)/110010 weeks
112-5.44905 -5.22519 (112*2π)/110010 weeks
113-5.27408 -4.51645 (113*2π)/110010 weeks
114-.06361 -8.41821 (114*2π)/110010 weeks
115-.18556 -10.97507 (115*2π)/110010 weeks
116-2.97779 -9.81157 (116*2π)/11009 weeks
117-3.51324 -6.86988 (117*2π)/11009 weeks
118-4.73252 -8.09833 (118*2π)/11009 weeks
119-4.78107 -7.54668 (119*2π)/11009 weeks
120-4.21624 -4.61011 (120*2π)/11009 weeks
1211.65332 -5.44489 (121*2π)/11009 weeks
1222.46666 -7.10157 (122*2π)/11009 weeks
123-1.71864 -6.2425 (123*2π)/11009 weeks
1241.61865 -5.83924 (124*2π)/11009 weeks
1253.62444 -14.06943 (125*2π)/11009 weeks
1263.4743 -15.7139 (126*2π)/11009 weeks
127-3.13265 -14.15286 (127*2π)/11009 weeks
128-10.0122 -9.13555 (128*2π)/11009 weeks
129-7.21732 -6.2223 (129*2π)/11009 weeks
130-2.49318 -10.87346 (130*2π)/11008 weeks
1312.6593 -8.07322 (131*2π)/11008 weeks
1322.10592 -9.36195 (132*2π)/11008 weeks
133-4.69221 -10.71357 (133*2π)/11008 weeks
134-6.60714 -11.22682 (134*2π)/11008 weeks
135-2.68863 -7.42096 (135*2π)/11008 weeks
136.6514 -9.14574 (136*2π)/11008 weeks
1373.77014 -10.64154 (137*2π)/11008 weeks
138-2.59315 -15.43533 (138*2π)/11008 weeks
139-6.2884 -15.86455 (139*2π)/11008 weeks
140-6.7907 -15.05409 (140*2π)/11008 weeks
141-8.64481 -15.01168 (141*2π)/11008 weeks
142-13.76925 -9.66417 (142*2π)/11008 weeks
143-9.62154 -6.82856 (143*2π)/11008 weeks
144-11.74418 -7.17145 (144*2π)/11008 weeks
145-10.66653 -4.72415 (145*2π)/11008 weeks
146-8.37469 -3.79577 (146*2π)/11008 weeks
147-10.32558 -1.87654 (147*2π)/11007 weeks
148-4.47695 -.56201 (148*2π)/11007 weeks
149-5.98405 -2.09792 (149*2π)/11007 weeks
150-4.80454 1.33085 (150*2π)/11007 weeks
151-.03367 -.50487 (151*2π)/11007 weeks
152.68042 -6.52645 (152*2π)/11007 weeks
153-.9676 -6.55741 (153*2π)/11007 weeks
154-2.26771 -2.74464 (154*2π)/11007 weeks
155.17899 -4.72109 (155*2π)/11007 weeks
156-1.42511 -11.29244 (156*2π)/11007 weeks
157-5.88606 -7.68716 (157*2π)/11007 weeks
158-1.93029 -3.46368 (158*2π)/11007 weeks
159-2.81721 -7.07622 (159*2π)/11007 weeks
160-4.88306 -6.36967 (160*2π)/11007 weeks
161-6.22422 -6.21083 (161*2π)/11007 weeks
162-4.90922 -5.04753 (162*2π)/11007 weeks
163-1.52249 -3.44257 (163*2π)/11007 weeks
164-2.66448 -3.82879 (164*2π)/11007 weeks
165-1.06639 -4.31299 (165*2π)/11007 weeks
166-3.26325 -7.44187 (166*2π)/11007 weeks
167-4.22013 -6.92464 (167*2π)/11007 weeks
168-4.40736 -6.31137 (168*2π)/11007 weeks
169-6.28095 -1.63924 (169*2π)/11007 weeks
170-4.3627 .10048 (170*2π)/11006 weeks
171.63275 -4.03588 (171*2π)/11006 weeks
172-.91116 -3.89396 (172*2π)/11006 weeks
173.9272 -2.07884 (173*2π)/11006 weeks
174.39837 -6.00152 (174*2π)/11006 weeks
175-.81057 -4.54629 (175*2π)/11006 weeks
1762.98636 -6.95004 (176*2π)/11006 weeks
177-.05375 -6.68648 (177*2π)/11006 weeks
178-2.10613 -7.81042 (178*2π)/11006 weeks
179-1.82244 -11.51896 (179*2π)/11006 weeks
180-3.43468 -7.38663 (180*2π)/11006 weeks
181-1.68848 -5.44292 (181*2π)/11006 weeks
182-3.46908 -6.56781 (182*2π)/11006 weeks
183-3.59464 -6.28175 (183*2π)/11006 weeks
184-1.71367 -8.45703 (184*2π)/11006 weeks
185-2.01004 -7.18327 (185*2π)/11006 weeks
186-4.27405 -7.94297 (186*2π)/11006 weeks
187-6.51608 -7.89711 (187*2π)/11006 weeks
188-7.44245 -6.5336 (188*2π)/11006 weeks
189-4.64756 -4.05412 (189*2π)/11006 weeks
190-3.46021 -4.36629 (190*2π)/11006 weeks
191-4.91705 -4.31835 (191*2π)/11006 weeks
192-3.23479 -3.91224 (192*2π)/11006 weeks
193-2.58086 -5.61807 (193*2π)/11006 weeks
194-3.30999 -5.74879 (194*2π)/11006 weeks
195-3.95375 -5.1477 (195*2π)/11006 weeks
196-5.97914 -5.61271 (196*2π)/11006 weeks
197-3.39904 -2.84949 (197*2π)/11006 weeks
198-2.38496 -4.52615 (198*2π)/11006 weeks
199-4.91876 -3.64574 (199*2π)/11006 weeks
200-3.77348 -2.17793 (200*2π)/11006 weeks
201-2.96743 -3.86953 (201*2π)/11005 weeks
202.38599 -4.08248 (202*2π)/11005 weeks
2031.27952 -4.49705 (203*2π)/11005 weeks
204-3.87417 -6.90744 (204*2π)/11005 weeks
205-4.59232 -8.31616 (205*2π)/11005 weeks
206-1.05067 -8.33002 (206*2π)/11005 weeks
207-4.91978 -5.13688 (207*2π)/11005 weeks
208-5.40583 -4.05105 (208*2π)/11005 weeks
209-5.20447 -6.72433 (209*2π)/11005 weeks
210-5.57307 -5.45498 (210*2π)/11005 weeks
211-5.43039 -6.15348 (211*2π)/11005 weeks
212-6.21811 -3.15214 (212*2π)/11005 weeks
213-5.63097 -1.93081 (213*2π)/11005 weeks
214-6.38102 -.48298 (214*2π)/11005 weeks
215-2.57945 -2.10045 (215*2π)/11005 weeks
216-2.0727 -3.55935 (216*2π)/11005 weeks
217-1.63075 -.37779 (217*2π)/11005 weeks
218-.86836 -2.17156 (218*2π)/11005 weeks
219-3.25872 -5.48515 (219*2π)/11005 weeks
220-2.6019 -5.45011 (220*2π)/11005 weeks
221-2.20261 -6.00857 (221*2π)/11005 weeks
222-4.35676 -3.8283 (222*2π)/11005 weeks
223-3.90913 -3.24984 (223*2π)/11005 weeks
224-5.65452 -2.26416 (224*2π)/11005 weeks
225-3.36438 -2.19223 (225*2π)/11005 weeks
226-.83447 -5.1913 (226*2π)/11005 weeks
227-2.67465 -1.70841 (227*2π)/11005 weeks
228-1.31389 -3.19868 (228*2π)/11005 weeks
229-3.87701 -4.7248 (229*2π)/11005 weeks
230-2.85016 -4.31997 (230*2π)/11005 weeks
231-1.81205 -3.52641 (231*2π)/11005 weeks
232-2.95416 -3.42785 (232*2π)/11005 weeks
233-1.2007 -1.99716 (233*2π)/11005 weeks
234-2.15098 -5.09206 (234*2π)/11005 weeks
235-3.18014 -4.74318 (235*2π)/11005 weeks
236-1.74408 -5.51184 (236*2π)/11005 weeks
237-1.40914 -5.40871 (237*2π)/11005 weeks
238-1.4056 -5.54941 (238*2π)/11005 weeks
239-4.03174 -5.78082 (239*2π)/11005 weeks
240-5.89549 -8.05842 (240*2π)/11005 weeks
241-5.3011 -5.28709 (241*2π)/11005 weeks
242-5.98984 -4.44628 (242*2π)/11005 weeks
243-6.52335 -2.43291 (243*2π)/11005 weeks
244-5.45141 -1.84337 (244*2π)/11005 weeks
245-3.74799 -2.10638 (245*2π)/11004 weeks
246-4.20545 -2.56466 (246*2π)/11004 weeks
247-3.59051 -2.09896 (247*2π)/11004 weeks
248-2.52217 -.84361 (248*2π)/11004 weeks
249-1.99399 -1.93288 (249*2π)/11004 weeks
250-2.21547 -2.80205 (250*2π)/11004 weeks
251-1.44314 -3.27298 (251*2π)/11004 weeks
252-1.61376 -5.41588 (252*2π)/11004 weeks
253-1.53451 -5.62162 (253*2π)/11004 weeks
254-4.2568 -4.40093 (254*2π)/11004 weeks
255-6.35075 -4.43392 (255*2π)/11004 weeks
256-6.29596 -4.24248 (256*2π)/11004 weeks
257-3.80559 -2.74171 (257*2π)/11004 weeks
258-3.04688 -.57896 (258*2π)/11004 weeks
259-4.19026 -1.06239 (259*2π)/11004 weeks
260-2.36301 -3.28993 (260*2π)/11004 weeks
261-.88397 -5.58899 (261*2π)/11004 weeks
262-4.48608 -4.46151 (262*2π)/11004 weeks
263-4.98743 -4.34222 (263*2π)/11004 weeks
264-6.65282 -2.81336 (264*2π)/11004 weeks
265-5.82982 -2.85063 (265*2π)/11004 weeks
266-5.43659 -1.41657 (266*2π)/11004 weeks
267-5.51297 -.7567 (267*2π)/11004 weeks
268-4.41042 1.76964 (268*2π)/11004 weeks
269-1.79364 1.59168 (269*2π)/11004 weeks
270-.14572 -1.4307 (270*2π)/11004 weeks
271.54802 -3.90482 (271*2π)/11004 weeks
272-1.49093 -4.99069 (272*2π)/11004 weeks
273-5.67984 -4.29769 (273*2π)/11004 weeks
274-5.05434 -2.22217 (274*2π)/11004 weeks
275-5.01125 -2.92667 (275*2π)/11004 weeks
276-5.54375 -.84079 (276*2π)/11004 weeks
277-2.63767 1.17911 (277*2π)/11004 weeks
278-2.35816 -.94252 (278*2π)/11004 weeks
279-2.94754 -1.50367 (279*2π)/11004 weeks
280-3.67327 -1.14341 (280*2π)/11004 weeks
281-3.03946 -.42198 (281*2π)/11004 weeks
282-.74054 1.60903 (282*2π)/11004 weeks
283.26894 -1.51916 (283*2π)/11004 weeks
284-1.96319 -1.06389 (284*2π)/11004 weeks
285-.69622 -1.02158 (285*2π)/11004 weeks
2861.67612 -2.75191 (286*2π)/11004 weeks
287-1.15298 -3.45903 (287*2π)/11004 weeks
288.15657 -2.71363 (288*2π)/11004 weeks
289.4426 -5.00716 (289*2π)/11004 weeks
290-2.68688 -5.50409 (290*2π)/11004 weeks
291-2.67836 -5.18835 (291*2π)/11004 weeks
292-4.18249 -4.4564 (292*2π)/11004 weeks
293-3.92192 -3.13859 (293*2π)/11004 weeks
294-3.69494 -1.87801 (294*2π)/11004 weeks
295-3.78512 -1.58409 (295*2π)/11004 weeks
296-1.6781 -1.92973 (296*2π)/11004 weeks
297-2.52431 -2.7248 (297*2π)/11004 weeks
298-2.31599 -2.04981 (298*2π)/11004 weeks
299-.29343 -2.47498 (299*2π)/11004 weeks
300-.63306 -3.17015 (300*2π)/11004 weeks
301-1.87728 -2.8971 (301*2π)/11004 weeks
302-1.77779 -4.73338 (302*2π)/11004 weeks
303-3.3114 -5.92967 (303*2π)/11004 weeks
304-2.26189 -3.92931 (304*2π)/11004 weeks
305-2.74274 -4.58517 (305*2π)/11004 weeks
306-5.80735 -3.92792 (306*2π)/11004 weeks
307-5.65082 -2.86117 (307*2π)/11004 weeks
308-3.60591 -3.72648 (308*2π)/11004 weeks
309-4.77561 -3.1631 (309*2π)/11004 weeks
310-3.83413 -.78506 (310*2π)/11004 weeks
311-3.40383 -.30942 (311*2π)/11004 weeks
312-4.1541 -2.6244 (312*2π)/11004 weeks
313-2.94335 -1.47232 (313*2π)/11004 weeks
314-2.56519 -1.58826 (314*2π)/11004 weeks
315-2.07671 -.70166 (315*2π)/11003 weeks
316-.89445 -1.88618 (316*2π)/11003 weeks
317-3.61941 -3.52934 (317*2π)/11003 weeks
318-3.59328 -2.85791 (318*2π)/11003 weeks
319-.96511 -1.42532 (319*2π)/11003 weeks
320-1.29967 -3.13705 (320*2π)/11003 weeks
321-3.02242 -3.07654 (321*2π)/11003 weeks
322-2.97928 -3.44603 (322*2π)/11003 weeks
323-2.55356 -5.3739 (323*2π)/11003 weeks
324-4.08975 -3.77196 (324*2π)/11003 weeks
325-5.02748 -1.99278 (325*2π)/11003 weeks
326-4.62489 -3.10406 (326*2π)/11003 weeks
327-5.55371 -2.72308 (327*2π)/11003 weeks
328-5.01777 -.37529 (328*2π)/11003 weeks
329-3.58163 1.17713 (329*2π)/11003 weeks
330-3.09301 -.9622 (330*2π)/11003 weeks
331-2.76009 -.91606 (331*2π)/11003 weeks
332-1.45308 -1.48095 (332*2π)/11003 weeks
333-2.27809 -.75045 (333*2π)/11003 weeks
334-1.95747 -2.24584 (334*2π)/11003 weeks
335-3.30221 -4.1515 (335*2π)/11003 weeks
336-2.7876 -1.64337 (336*2π)/11003 weeks
337-2.88406 -1.79341 (337*2π)/11003 weeks
338-3.36608 -1.26553 (338*2π)/11003 weeks
339-3.22665 -1.03693 (339*2π)/11003 weeks
340-2.08186 -1.81232 (340*2π)/11003 weeks
341-1.98381 -1.1027 (341*2π)/11003 weeks
342-.67572 -1.57521 (342*2π)/11003 weeks
343-2.33025 -2.52232 (343*2π)/11003 weeks
344-2.52103 -2.84757 (344*2π)/11003 weeks
345-2.06867 -3.12573 (345*2π)/11003 weeks
346-2.36962 -3.87627 (346*2π)/11003 weeks
347-2.74467 -2.54183 (347*2π)/11003 weeks
348-4.31645 -2.51713 (348*2π)/11003 weeks
349-4.37214 -3.11104 (349*2π)/11003 weeks
350-3.71252 -2.78764 (350*2π)/11003 weeks
351-4.32603 -1.0489 (351*2π)/11003 weeks
352-3.38927 -1.38629 (352*2π)/11003 weeks
353-3.81585 -1.72311 (353*2π)/11003 weeks
354-3.07616 -1.01338 (354*2π)/11003 weeks
355-2.38227 -.58821 (355*2π)/11003 weeks
356-1.48567 -1.60712 (356*2π)/11003 weeks
357-2.00592 -2.42327 (357*2π)/11003 weeks
358-2.63718 -2.72749 (358*2π)/11003 weeks
359-2.04585 -1.84986 (359*2π)/11003 weeks
360-2.80309 -4.37958 (360*2π)/11003 weeks
361-3.67987 -2.14485 (361*2π)/11003 weeks
362-3.06174 -2.86652 (362*2π)/11003 weeks
363-4.13414 -3.07764 (363*2π)/11003 weeks
364-4.56259 -2.78024 (364*2π)/11003 weeks
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