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# Fourier Analysis of XCI (NYSE ARCA COMPUTER TECH INDEX)

XCI (NYSE ARCA COMPUTER TECH INDEX) appears to have interesting cyclic behaviour every 121 weeks (63.6835*sine), 111 weeks (60.1529*sine), and 83 weeks (26.5492*cosine).

XCI (NYSE ARCA COMPUTER TECH INDEX) has an average price of 774.83 (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 8/14/1991 to 1/16/2017 for XCI (NYSE ARCA COMPUTER TECH INDEX), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0774.8347   0
123.01582 -262.1113 (1*2π)/13281,328 weeks
219.12348 -401.8255 (2*2π)/1328664 weeks
3149.849 -221.2822 (3*2π)/1328443 weeks
4-53.43331 -50.53803 (4*2π)/1328332 weeks
5-12.92551 -191.8848 (5*2π)/1328266 weeks
650.88911 -90.52063 (6*2π)/1328221 weeks
7-70.70765 -24.00396 (7*2π)/1328190 weeks
818.22533 -90.18336 (8*2π)/1328166 weeks
920.29365 -50.32084 (9*2π)/1328148 weeks
10-24.79516 -17.29207 (10*2π)/1328133 weeks
1118.86514 -63.68351 (11*2π)/1328121 weeks
1226.25191 -60.15292 (12*2π)/1328111 weeks
13-23.0189 -24.35233 (13*2π)/1328102 weeks
1416.38548 -59.75608 (14*2π)/132895 weeks
151.85931 -20.10991 (15*2π)/132889 weeks
16-26.54917 -43.05511 (16*2π)/132883 weeks
1722.38436 -33.42389 (17*2π)/132878 weeks
182.81806 -26.65169 (18*2π)/132874 weeks
19-19.62134 -44.00811 (19*2π)/132870 weeks
202.25218 -21.77806 (20*2π)/132866 weeks
214.38547 -15.55146 (21*2π)/132863 weeks
22-7.62203 -32.74795 (22*2π)/132860 weeks
23-2.02261 -25.88453 (23*2π)/132858 weeks
24-1.32969 -22.2818 (24*2π)/132855 weeks
25-2.44225 -22.29284 (25*2π)/132853 weeks
26-5.20028 -26.7886 (26*2π)/132851 weeks
271.67446 -14.66519 (27*2π)/132849 weeks
28-10.98469 -26.3593 (28*2π)/132847 weeks
29-4.28867 -12.27533 (29*2π)/132846 weeks
304.91159 -21.23772 (30*2π)/132844 weeks
31-5.68002 -24.04248 (31*2π)/132843 weeks
32-12.34532 -7.80895 (32*2π)/132842 weeks
331.57718 -21.71918 (33*2π)/132840 weeks
341.39582 -11.91821 (34*2π)/132839 weeks
35-9.68553 -8.69507 (35*2π)/132838 weeks
36-1.90756 -22.37214 (36*2π)/132837 weeks
37-9.44846 -10.78268 (37*2π)/132836 weeks
38-3.89513 -14.10824 (38*2π)/132835 weeks
391.77992 -3.20299 (39*2π)/132834 weeks
40-7.26554 -6.69339 (40*2π)/132833 weeks
41.2922 -14.57957 (41*2π)/132832 weeks
429.74189 -10.36545 (42*2π)/132832 weeks
43-10.89068 -11.88899 (43*2π)/132831 weeks
44-1.58691 -10.41236 (44*2π)/132830 weeks
454.22802 -8.09621 (45*2π)/132830 weeks
46-6.31773 -8.45734 (46*2π)/132829 weeks
47.39422 -15.04996 (47*2π)/132828 weeks
48.94745 -8.80198 (48*2π)/132828 weeks
49-5.15127 -5.18128 (49*2π)/132827 weeks
50-3.4386 -10.38073 (50*2π)/132827 weeks
512.90014 -14.04814 (51*2π)/132826 weeks
52-2.50645 .86929 (52*2π)/132826 weeks
53-6.98135 -16.70481 (53*2π)/132825 weeks
54.00885 -7.30737 (54*2π)/132825 weeks
55-6.82456 -.12696 (55*2π)/132824 weeks
56-2.92294 -7.72894 (56*2π)/132824 weeks
572.47598 .06144 (57*2π)/132823 weeks
58-2.7367 -5.54396 (58*2π)/132823 weeks
594.31217 -6.73913 (59*2π)/132823 weeks
60-.48285 1.49861 (60*2π)/132822 weeks
612.21528 -8.21554 (61*2π)/132822 weeks
624.31868 -6.36318 (62*2π)/132821 weeks
631.87942 -.82754 (63*2π)/132821 weeks
643.76191 -10.58767 (64*2π)/132821 weeks
652.62751 -10.37827 (65*2π)/132820 weeks
66.14787 -3.64078 (66*2π)/132820 weeks
673.11077 -10.47372 (67*2π)/132820 weeks
68-.69572 -5.50377 (68*2π)/132820 weeks
691.36646 -9.47671 (69*2π)/132819 weeks
701.67202 -7.18505 (70*2π)/132819 weeks
71.42424 -7.91935 (71*2π)/132819 weeks
72-.96951 -6.89014 (72*2π)/132818 weeks
73.44279 -11.68501 (73*2π)/132818 weeks
74-3.36205 -6.49165 (74*2π)/132818 weeks
75-4.91489 -2.55484 (75*2π)/132818 weeks
761.5386 -7.64054 (76*2π)/132817 weeks
77-1.06388 -3.94448 (77*2π)/132817 weeks
78-3.26873 -4.53896 (78*2π)/132817 weeks
79.53158 -8.23758 (79*2π)/132817 weeks
80-3.06678 -2.04045 (80*2π)/132817 weeks
81-.789 1.83469 (81*2π)/132816 weeks
824.77903 -4.18455 (82*2π)/132816 weeks
833.22457 -9.26781 (83*2π)/132816 weeks
84-1.17699 -2.58154 (84*2π)/132816 weeks
85-.35692 -5.58311 (85*2π)/132816 weeks
864.31741 -2.34449 (86*2π)/132815 weeks
87.11641 -1.26213 (87*2π)/132815 weeks
883.38894 -9.81109 (88*2π)/132815 weeks
893.93483 -6.09214 (89*2π)/132815 weeks
90-2.85909 -4.61488 (90*2π)/132815 weeks
91.25996 -6.37351 (91*2π)/132815 weeks
924.54821 -1.22424 (92*2π)/132814 weeks
93-.32529 -4.003 (93*2π)/132814 weeks
944.6229 -11.70754 (94*2π)/132814 weeks
95-.98178 -3.27144 (95*2π)/132814 weeks
96-2.02632 -4.30257 (96*2π)/132814 weeks
976.53736 -4.24165 (97*2π)/132814 weeks
982.52194 -5.86671 (98*2π)/132814 weeks
99-.3533 -9.49281 (99*2π)/132813 weeks
100-2.21946 -4.1586 (100*2π)/132813 weeks
101.71227 -4.08761 (101*2π)/132813 weeks
1022.90824 -2.64471 (102*2π)/132813 weeks
1031.83342 -4.43282 (103*2π)/132813 weeks
1043.04063 -3.92054 (104*2π)/132813 weeks
105.64301 -4.39892 (105*2π)/132813 weeks
1061.88582 -9.53308 (106*2π)/132813 weeks
1075.62981 -4.24493 (107*2π)/132812 weeks
108-2.62171 -3.68595 (108*2π)/132812 weeks
1092.12715 -10.05742 (109*2π)/132812 weeks
1104.12975 -6.30394 (110*2π)/132812 weeks
111-3.53175 -1.25238 (111*2π)/132812 weeks
112-.17008 -10.1727 (112*2π)/132812 weeks
1133.85372 -1.4319 (113*2π)/132812 weeks
114-3.24031 -1.7289 (114*2π)/132812 weeks
1155.43939 -7.6547 (115*2π)/132812 weeks
1161.21238 -2.63769 (116*2π)/132811 weeks
117.27206 -3.69817 (117*2π)/132811 weeks
1186.74105 -5.78006 (118*2π)/132811 weeks
1192.5962 -4.32866 (119*2π)/132811 weeks
1203.94968 -9.33051 (120*2π)/132811 weeks
1211.51229 -8.11294 (121*2π)/132811 weeks
122-2.26282 -5.51931 (122*2π)/132811 weeks
1231.29548 -4.94332 (123*2π)/132811 weeks
1244.21195 -7.019 (124*2π)/132811 weeks
1251.63454 -7.04396 (125*2π)/132811 weeks
126-.23532 -10.87255 (126*2π)/132811 weeks
127-.69027 -3.6724 (127*2π)/132810 weeks
128-4.06419 -4.92189 (128*2π)/132810 weeks
1295.38167 -6.60694 (129*2π)/132810 weeks
1302.7692 -2.9224 (130*2π)/132810 weeks
131-3.50696 -9.00701 (131*2π)/132810 weeks
132.76345 -7.85663 (132*2π)/132810 weeks
133.59453 -2.17858 (133*2π)/132810 weeks
134.32286 -6.36779 (134*2π)/132810 weeks
1351.36157 -7.80921 (135*2π)/132810 weeks
136-1.39123 -6.21995 (136*2π)/132810 weeks
137.63968 -5.80239 (137*2π)/132810 weeks
138-1.18002 -4.8501 (138*2π)/132810 weeks
139.17547 -3.74691 (139*2π)/132810 weeks
1402.22107 -6.52343 (140*2π)/13289 weeks
1411.24164 -6.49774 (141*2π)/13289 weeks
142-2.01507 -7.5003 (142*2π)/13289 weeks
143-.97495 -4.67803 (143*2π)/13289 weeks
144-1.26665 -4.1595 (144*2π)/13289 weeks
1451.61247 -4.45113 (145*2π)/13289 weeks
1461.80833 -4.87843 (146*2π)/13289 weeks
147-.73398 -7.131 (147*2π)/13289 weeks
148-1.37278 -6.2865 (148*2π)/13289 weeks
149-.52252 -3.75465 (149*2π)/13289 weeks
1501.2478 -2.44843 (150*2π)/13289 weeks
1513.49672 -8.03309 (151*2π)/13289 weeks
152.84267 -6.38026 (152*2π)/13289 weeks
153-3.78911 -8.12615 (153*2π)/13289 weeks
154.74224 -6.66682 (154*2π)/13289 weeks
155-.541 -2.83885 (155*2π)/13289 weeks
156-.45915 -5.48158 (156*2π)/13289 weeks
1572.34647 -9.28034 (157*2π)/13288 weeks
158-.58006 -6.81904 (158*2π)/13288 weeks
159-2.19253 -3.41986 (159*2π)/13288 weeks
160.57338 -6.76672 (160*2π)/13288 weeks
1612.15453 -5.38073 (161*2π)/13288 weeks
162-1.02268 -8.93114 (162*2π)/13288 weeks
163-.83348 -9.78226 (163*2π)/13288 weeks
164-2.93707 -5.45985 (164*2π)/13288 weeks
165-1.92358 -3.80486 (165*2π)/13288 weeks
166.84539 -7.05552 (166*2π)/13288 weeks
167-1.26362 -7.97032 (167*2π)/13288 weeks
168-2.4206 -8.06356 (168*2π)/13288 weeks
169-4.12909 -5.85493 (169*2π)/13288 weeks
170-1.79234 -4.0628 (170*2π)/13288 weeks
171-.48593 -5.05252 (171*2π)/13288 weeks
172-1.26633 -5.55878 (172*2π)/13288 weeks
173-.03174 -8.34359 (173*2π)/13288 weeks
174-3.73281 -9.29401 (174*2π)/13288 weeks
175-3.67714 -4.36688 (175*2π)/13288 weeks
176-3.63268 -3.96343 (176*2π)/13288 weeks
177-.49609 -8.09435 (177*2π)/13288 weeks
178-2.39917 -5.13127 (178*2π)/13287 weeks
179-5.17563 -5.6326 (179*2π)/13287 weeks
180-2.52982 -6.38139 (180*2π)/13287 weeks
181-3.35629 -2.01249 (181*2π)/13287 weeks
182-3.10151 -4.64396 (182*2π)/13287 weeks
1831.45599 -4.70049 (183*2π)/13287 weeks
184-1.58083 -6.03612 (184*2π)/13287 weeks
185-4.41816 -7.48497 (185*2π)/13287 weeks
186-3.9665 -5.14846 (186*2π)/13287 weeks
187-1.69031 -2.37741 (187*2π)/13287 weeks
188-1.05228 -6.21346 (188*2π)/13287 weeks
189-1.21497 -7.42358 (189*2π)/13287 weeks
190-5.40211 -6.98572 (190*2π)/13287 weeks
191-6.05919 -3.9464 (191*2π)/13287 weeks
192-1.78057 -1.9603 (192*2π)/13287 weeks
193-1.81745 -5.6783 (193*2π)/13287 weeks
194-2.00087 -6.00602 (194*2π)/13287 weeks
195-4.69877 -5.20963 (195*2π)/13287 weeks
196-5.56665 -5.87246 (196*2π)/13287 weeks
197-4.47831 -1.13936 (197*2π)/13287 weeks
198-1.19395 -3.2264 (198*2π)/13287 weeks
199-1.27288 -6.17265 (199*2π)/13287 weeks
200-3.52812 -6.13638 (200*2π)/13287 weeks
201-6.0039 -4.47859 (201*2π)/13287 weeks
202-5.40023 -2.99271 (202*2π)/13287 weeks
203-1.66502 -1.78641 (203*2π)/13287 weeks
204-2.10532 -5.6322 (204*2π)/13287 weeks
205-2.41111 -6.84293 (205*2π)/13286 weeks
206-8.33253 -3.41088 (206*2π)/13286 weeks
207-4.02621 -4.10926 (207*2π)/13286 weeks
208-2.3925 -1.62465 (208*2π)/13286 weeks
209-4.92364 -4.41689 (209*2π)/13286 weeks
210-1.73472 -6.31505 (210*2π)/13286 weeks
211-5.6837 -3.69434 (211*2π)/13286 weeks
212-7.66111 -3.73042 (212*2π)/13286 weeks
213-3.11068 -1.45374 (213*2π)/13286 weeks
214-4.2462 -1.80222 (214*2π)/13286 weeks
215-3.63556 -5.64308 (215*2π)/13286 weeks
216-4.95317 -2.33156 (216*2π)/13286 weeks
217-6.53747 -1.49006 (217*2π)/13286 weeks
218-5.31998 -1.97583 (218*2π)/13286 weeks
219-1.21381 -.12531 (219*2π)/13286 weeks
220-3.31514 -1.32936 (220*2π)/13286 weeks
221-4.74532 -5.76257 (221*2π)/13286 weeks
222-4.66988 -2.02062 (222*2π)/13286 weeks
223-4.68817 .00534 (223*2π)/13286 weeks
224-3.58146 -1.78495 (224*2π)/13286 weeks
225-2.41456 -2.5479 (225*2π)/13286 weeks
226-3.68885 -2.2848 (226*2π)/13286 weeks
227-5.42939 -3.83887 (227*2π)/13286 weeks
228-4.47852 -1.28662 (228*2π)/13286 weeks
229-5.01396 .54476 (229*2π)/13286 weeks
230-2.54379 -1.49286 (230*2π)/13286 weeks
231-1.88718 -2.53651 (231*2π)/13286 weeks
232-4.79725 -1.90332 (232*2π)/13286 weeks
233-5.7764 -2.43981 (233*2π)/13286 weeks
234-3.39758 .82428 (234*2π)/13286 weeks
235-3.21718 -.18972 (235*2π)/13286 weeks
236-2.15357 -3.75105 (236*2π)/13286 weeks
237-3.36998 -.74996 (237*2π)/13286 weeks
238-6.6648 -2.20928 (238*2π)/13286 weeks
239-4.46688 -.68745 (239*2π)/13286 weeks
240-1.74817 1.93366 (240*2π)/13286 weeks
241-2.26828 -1.96571 (241*2π)/13286 weeks
242-4.22802 -3.91056 (242*2π)/13285 weeks
243-4.09626 -1.02591 (243*2π)/13285 weeks
244-6.36108 1.2183 (244*2π)/13285 weeks
245-3.10977 -1.00555 (245*2π)/13285 weeks
246-1.7856 1.51219 (246*2π)/13285 weeks
247-4.29214 -2.92052 (247*2π)/13285 weeks
248-3.54153 -1.36873 (248*2π)/13285 weeks
249-6.74668 1.74283 (249*2π)/13285 weeks
250-2.86082 1.90936 (250*2π)/13285 weeks
251-.66121 .51111 (251*2π)/13285 weeks
252-2.35995 -.43513 (252*2π)/13285 weeks
253-4.06083 -2.36179 (253*2π)/13285 weeks
254-4.37343 -1.59783 (254*2π)/13285 weeks
255-5.28944 4.25743 (255*2π)/13285 weeks
256-2.16528 2.26778 (256*2π)/13285 weeks
257.31013 -.44455 (257*2π)/13285 weeks
258-3.414 .68437 (258*2π)/13285 weeks
259-3.95224 -.95961 (259*2π)/13285 weeks
260-2.24573 1.68531 (260*2π)/13285 weeks
261-2.70077 2.82248 (261*2π)/13285 weeks
262.5997 -.25324 (262*2π)/13285 weeks
263-.83182 -1.00284 (263*2π)/13285 weeks
264-5.68073 -.38341 (264*2π)/13285 weeks
265-2.60153 -.12165 (265*2π)/13285 weeks
266-1.07054 3.09295 (266*2π)/13285 weeks
267-2.64334 1.1046 (267*2π)/13285 weeks
268-1.07081 -1.48894 (268*2π)/13285 weeks
269-2.26501 .67027 (269*2π)/13285 weeks
270-5.03807 .41748 (270*2π)/13285 weeks
271-2.22418 2.52166 (271*2π)/13285 weeks
272.17089 2.69863 (272*2π)/13285 weeks
273-1.48423 .58054 (273*2π)/13285 weeks
274-1.44535 -.31967 (274*2π)/13285 weeks
275-2.55955 .65165 (275*2π)/13285 weeks
276-3.49659 2.35004 (276*2π)/13285 weeks
277.25359 3.2265 (277*2π)/13285 weeks
278.7678 1.59279 (278*2π)/13285 weeks
279-1.15774 -1.18573 (279*2π)/13285 weeks
280-1.85178 .08054 (280*2π)/13285 weeks
281-1.09556 3.36602 (281*2π)/13285 weeks
282-1.41553 1.85438 (282*2π)/13285 weeks
2832.46959 .24793 (283*2π)/13285 weeks
284.97158 .26326 (284*2π)/13285 weeks
285-3.47843 -1.1669 (285*2π)/13285 weeks
286-.99588 .4614 (286*2π)/13285 weeks
287.3409 3.78591 (287*2π)/13285 weeks
288-.03216 .31051 (288*2π)/13285 weeks
2892.20715 -1.25652 (289*2π)/13285 weeks
290-2.50486 -1.08137 (290*2π)/13285 weeks
291-2.21944 .20386 (291*2π)/13285 weeks
292-1.54452 3.44959 (292*2π)/13285 weeks
293.98643 1.60027 (293*2π)/13285 weeks
2942.56197 -.11347 (294*2π)/13285 weeks
295-1.14058 -.88623 (295*2π)/13285 weeks
296-1.82692 -.26285 (296*2π)/13284 weeks
297-.53225 2.23839 (297*2π)/13284 weeks
298-.00065 1.50719 (298*2π)/13284 weeks
2991.01893 1.87275 (299*2π)/13284 weeks
3001.10987 -.60192 (300*2π)/13284 weeks
301-.44185 .73088 (301*2π)/13284 weeks
302-.95733 1.68501 (302*2π)/13284 weeks
3031.80067 1.93888 (303*2π)/13284 weeks
3043.58744 1.18224 (304*2π)/13284 weeks
3052.01295 -1.23139 (305*2π)/13284 weeks
306.32849 -1.86832 (306*2π)/13284 weeks
307-.16899 -.22889 (307*2π)/13284 weeks
3081.20904 1.3709 (308*2π)/13284 weeks
309.86974 -.76065 (309*2π)/13284 weeks
3102.3612 -.93293 (310*2π)/13284 weeks
311-.29275 -1.09111 (311*2π)/13284 weeks
312-.44916 -1.39643 (312*2π)/13284 weeks
313.21715 2.3 (313*2π)/13284 weeks
3141.20472 1.75366 (314*2π)/13284 weeks
3153.72384 -1.85963 (315*2π)/13284 weeks
3162.64861 -1.43635 (316*2π)/13284 weeks
317-2.19081 -1.86377 (317*2π)/13284 weeks
318-.09647 -1.28826 (318*2π)/13284 weeks
3191.97583 2.15435 (319*2π)/13284 weeks
3201.74889 -1.72931 (320*2π)/13284 weeks
3211.32718 -2.01131 (321*2π)/13284 weeks
322-.09845 -.94739 (322*2π)/13284 weeks
323-1.02176 -1.34318 (323*2π)/13284 weeks
324.69498 1.81508 (324*2π)/13284 weeks
3252.23439 .55666 (325*2π)/13284 weeks
3262.46732 -1.92779 (326*2π)/13284 weeks
3271.79454 -.78787 (327*2π)/13284 weeks
328.05261 -1.3175 (328*2π)/13284 weeks
3291.26733 .17955 (329*2π)/13284 weeks
3302.75741 -.59737 (330*2π)/13284 weeks
3313.82765 -1.59226 (331*2π)/13284 weeks
3321.89268 -3.64543 (332*2π)/13284 weeks
333-.09151 -3.52479 (333*2π)/13284 weeks
334-.42035 -1.11188 (334*2π)/13284 weeks
3351.58662 -.33712 (335*2π)/13284 weeks
3363.56727 -1.98647 (336*2π)/13284 weeks
3371.14102 -4.61411 (337*2π)/13284 weeks
338-.5269 -3.80404 (338*2π)/13284 weeks
339-1.06525 -1.03333 (339*2π)/13284 weeks
340.0129 -.36416 (340*2π)/13284 weeks
3412.23318 -.20835 (341*2π)/13284 weeks
3422.68455 -3.81753 (342*2π)/13284 weeks
343-.43151 -4.05139 (343*2π)/13284 weeks
344-1.13896 -2.0954 (344*2π)/13284 weeks
345.47158 .55001 (345*2π)/13284 weeks
3461.45775 .03429 (346*2π)/13284 weeks
3472.4867 -4.23042 (347*2π)/13284 weeks
3481.21212 -2.58645 (348*2π)/13284 weeks
349-1.41608 -2.03823 (349*2π)/13284 weeks
350.68811 -1.50995 (350*2π)/13284 weeks
3512.91813 -.05001 (351*2π)/13284 weeks
3522.3499 -2.35496 (352*2π)/13284 weeks
3531.75563 -5.14788 (353*2π)/13284 weeks
354.47719 -3.47053 (354*2π)/13284 weeks
355-.32624 -1.61905 (355*2π)/13284 weeks
3561.18357 -2.51164 (356*2π)/13284 weeks
3573.15688 -3.36454 (357*2π)/13284 weeks
358.69079 -4.04768 (358*2π)/13284 weeks
359-1.97723 -5.34327 (359*2π)/13284 weeks
360-.16249 -2.16406 (360*2π)/13284 weeks
361-.80944 .02652 (361*2π)/13284 weeks
3622.15564 -3.62806 (362*2π)/13284 weeks
3632.1855 -3.6527 (363*2π)/13284 weeks
364-1.37169 -4.4679 (364*2π)/13284 weeks
365-1.17878 -3.8975 (365*2π)/13284 weeks
3661.28617 -1.37108 (366*2π)/13284 weeks
367.44839 -2.40047 (367*2π)/13284 weeks
3681.00535 -5.36319 (368*2π)/13284 weeks
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