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# Fourier Analysis of FSENX (Fidelity Select Energy)

FSENX (Fidelity Select Energy) appears to have interesting cyclic behaviour every 143 weeks (2.0342*sine), 155 weeks (1.6781*cosine), and 169 weeks (1.451*cosine).

FSENX (Fidelity Select Energy) has an average price of 18.22 (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 7/14/1981 to 3/13/2017 for FSENX (Fidelity Select Energy), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
018.22215   0
16.5285 -17.6376 (1*2π)/18611,861 weeks
2-1.71005 -8.23066 (2*2π)/1861931 weeks
3-.08083 -3.43847 (3*2π)/1861620 weeks
41.14547 -5.00415 (4*2π)/1861465 weeks
5-2.59009 -3.73285 (5*2π)/1861372 weeks
6-1.34604 -.10563 (6*2π)/1861310 weeks
7.98913 -1.20495 (7*2π)/1861266 weeks
8-.17979 -1.84005 (8*2π)/1861233 weeks
9-.53201 -1.11735 (9*2π)/1861207 weeks
10-.66978 .20771 (10*2π)/1861186 weeks
111.45098 .08798 (11*2π)/1861169 weeks
121.67813 -1.26974 (12*2π)/1861155 weeks
13.46573 -2.03421 (13*2π)/1861143 weeks
14-.45124 -.9774 (14*2π)/1861133 weeks
15.51268 -.45043 (15*2π)/1861124 weeks
16.75439 -1.39371 (16*2π)/1861116 weeks
17-.23866 -1.6062 (17*2π)/1861109 weeks
18-.39583 -.36854 (18*2π)/1861103 weeks
19.59463 -.38507 (19*2π)/186198 weeks
20.52454 -1.30139 (20*2π)/186193 weeks
21-.51385 -1.30246 (21*2π)/186189 weeks
22-.62139 -.32606 (22*2π)/186185 weeks
23.05637 -.06801 (23*2π)/186181 weeks
24.7745 -.49874 (24*2π)/186178 weeks
25.21806 -1.23319 (25*2π)/186174 weeks
26-.3307 -.9247 (26*2π)/186172 weeks
27-.47559 -.38684 (27*2π)/186169 weeks
28.21928 -.12138 (28*2π)/186166 weeks
29.36588 -.84826 (29*2π)/186164 weeks
30-.16941 -1.02204 (30*2π)/186162 weeks
31-.50936 -.57498 (31*2π)/186160 weeks
32-.21882 -.24307 (32*2π)/186158 weeks
33-.13544 -.43341 (33*2π)/186156 weeks
34-.36906 -.3875 (34*2π)/186155 weeks
35-.27624 -.00643 (35*2π)/186153 weeks
36.39704 .00922 (36*2π)/186152 weeks
37.13438 -.58771 (37*2π)/186150 weeks
38-.16962 -.44849 (38*2π)/186149 weeks
39-.30112 -.119 (39*2π)/186148 weeks
40.26375 .18656 (40*2π)/186147 weeks
41.53226 -.51516 (41*2π)/186145 weeks
42.15464 -.68537 (42*2π)/186144 weeks
43-.18821 -.56307 (43*2π)/186143 weeks
44-.13268 -.31268 (44*2π)/186142 weeks
45-.02748 -.41117 (45*2π)/186141 weeks
46-.15027 -.53916 (46*2π)/186140 weeks
47-.31732 -.22114 (47*2π)/186140 weeks
48-.0984 -.03089 (48*2π)/186139 weeks
49.20299 -.13371 (49*2π)/186138 weeks
50.01385 -.46236 (50*2π)/186137 weeks
51-.17519 -.29313 (51*2π)/186136 weeks
52-.0411 -.00906 (52*2π)/186136 weeks
53.2216 -.21381 (53*2π)/186135 weeks
54.0989 -.32005 (54*2π)/186134 weeks
55.0531 -.38651 (55*2π)/186134 weeks
56.0032 -.24679 (56*2π)/186133 weeks
57.11635 -.41653 (57*2π)/186133 weeks
58-.02112 -.50562 (58*2π)/186132 weeks
59-.26155 -.41475 (59*2π)/186132 weeks
60-.253 -.11013 (60*2π)/186131 weeks
61-.04609 -.11616 (61*2π)/186131 weeks
62.12235 -.29892 (62*2π)/186130 weeks
63-.15936 -.43957 (63*2π)/186130 weeks
64-.16661 -.17315 (64*2π)/186129 weeks
65-.01573 -.23857 (65*2π)/186129 weeks
66-.13913 -.35456 (66*2π)/186128 weeks
67-.29789 -.16894 (67*2π)/186128 weeks
68-.16885 -.01213 (68*2π)/186127 weeks
69-.04683 -.04161 (69*2π)/186127 weeks
70.05885 -.14023 (70*2π)/186127 weeks
71-.09606 -.11709 (71*2π)/186126 weeks
72.00475 -.10768 (72*2π)/186126 weeks
73.00447 -.15683 (73*2π)/186125 weeks
74-.00394 -.24282 (74*2π)/186125 weeks
75-.14823 -.11422 (75*2π)/186125 weeks
76.05027 -.00645 (76*2π)/186124 weeks
77.15074 -.13323 (77*2π)/186124 weeks
78.02234 -.27279 (78*2π)/186124 weeks
79-.00665 -.16768 (79*2π)/186124 weeks
80.04359 -.24186 (80*2π)/186123 weeks
81-.0471 -.2595 (81*2π)/186123 weeks
82-.06332 -.1645 (82*2π)/186123 weeks
83.01228 -.18042 (83*2π)/186122 weeks
84-.07515 -.25303 (84*2π)/186122 weeks
85-.11559 -.15325 (85*2π)/186122 weeks
86.03214 -.10935 (86*2π)/186122 weeks
87.03158 -.28772 (87*2π)/186121 weeks
88-.08655 -.29091 (88*2π)/186121 weeks
89-.16717 -.21359 (89*2π)/186121 weeks
90-.19638 -.12043 (90*2π)/186121 weeks
91-.09596 -.04917 (91*2π)/186120 weeks
92-.05464 -.10284 (92*2π)/186120 weeks
93-.0701 -.12256 (93*2π)/186120 weeks
94-.07689 -.08035 (94*2π)/186120 weeks
95.01695 -.08102 (95*2π)/186120 weeks
96-.0547 -.22258 (96*2π)/186119 weeks
97-.10345 -.08475 (97*2π)/186119 weeks
98-.10393 -.12043 (98*2π)/186119 weeks
99-.05554 .00942 (99*2π)/186119 weeks
100.02603 -.03812 (100*2π)/186119 weeks
101.07267 -.15064 (101*2π)/186118 weeks
102-.1037 -.21354 (102*2π)/186118 weeks
103-.12245 -.00315 (103*2π)/186118 weeks
104.03414 -.02906 (104*2π)/186118 weeks
105.05062 -.11833 (105*2π)/186118 weeks
106-.00405 -.15305 (106*2π)/186118 weeks
107-.07449 -.11078 (107*2π)/186117 weeks
108.0375 -.11154 (108*2π)/186117 weeks
109-.03258 -.18995 (109*2π)/186117 weeks
110-.09585 -.1589 (110*2π)/186117 weeks
111-.12575 -.05122 (111*2π)/186117 weeks
112-.00599 .03243 (112*2π)/186117 weeks
113.08704 -.09167 (113*2π)/186116 weeks
114.03846 -.20464 (114*2π)/186116 weeks
115-.11424 -.19594 (115*2π)/186116 weeks
116-.16445 -.04369 (116*2π)/186116 weeks
117-.00372 .04608 (117*2π)/186116 weeks
118.07575 -.11047 (118*2π)/186116 weeks
119-.04716 -.14298 (119*2π)/186116 weeks
120-.04352 -.04973 (120*2π)/186116 weeks
121.06019 -.10842 (121*2π)/186115 weeks
122-.04889 -.20196 (122*2π)/186115 weeks
123-.14456 -.02728 (123*2π)/186115 weeks
124.03732 -.00626 (124*2π)/186115 weeks
125.00847 -.1302 (125*2π)/186115 weeks
126-.03564 -.089 (126*2π)/186115 weeks
127-.01506 -.05426 (127*2π)/186115 weeks
128.01351 -.12867 (128*2π)/186115 weeks
129-.06744 -.07043 (129*2π)/186114 weeks
130-.01435 -.0552 (130*2π)/186114 weeks
131.00622 -.07741 (131*2π)/186114 weeks
132.00705 -.07752 (132*2π)/186114 weeks
133.01866 -.06415 (133*2π)/186114 weeks
134.05205 -.11429 (134*2π)/186114 weeks
135-.03241 -.16497 (135*2π)/186114 weeks
136-.10185 -.09914 (136*2π)/186114 weeks
137-.00503 -.00101 (137*2π)/186114 weeks
138.07471 -.09972 (138*2π)/186113 weeks
139.02857 -.13057 (139*2π)/186113 weeks
140-.01776 -.18988 (140*2π)/186113 weeks
141-.1089 -.12588 (141*2π)/186113 weeks
142-.0528 -.05493 (142*2π)/186113 weeks
143-.03486 -.0883 (143*2π)/186113 weeks
144-.04568 -.05357 (144*2π)/186113 weeks
145.01188 -.05485 (145*2π)/186113 weeks
146-.00741 -.07319 (146*2π)/186113 weeks
147-.00781 -.131 (147*2π)/186113 weeks
148-.07017 -.09321 (148*2π)/186113 weeks
149-.03555 -.01817 (149*2π)/186112 weeks
150.02086 -.02196 (150*2π)/186112 weeks
151.05863 -.11041 (151*2π)/186112 weeks
152-.05263 -.13723 (152*2π)/186112 weeks
153-.0256 -.02801 (153*2π)/186112 weeks
154.06426 -.06401 (154*2π)/186112 weeks
155.03221 -.19116 (155*2π)/186112 weeks
156-.09998 -.14619 (156*2π)/186112 weeks
157-.03635 -.01677 (157*2π)/186112 weeks
158.02811 -.09927 (158*2π)/186112 weeks
159.00033 -.16057 (159*2π)/186112 weeks
160-.08496 -.1643 (160*2π)/186112 weeks
161-.13875 -.06079 (161*2π)/186112 weeks
162-.0407 .00393 (162*2π)/186111 weeks
163-.01561 -.05977 (163*2π)/186111 weeks
164-.04342 -.07036 (164*2π)/186111 weeks
165-.04985 -.03715 (165*2π)/186111 weeks
166.03435 -.00886 (166*2π)/186111 weeks
167.03369 -.09152 (167*2π)/186111 weeks
168.00944 -.07431 (168*2π)/186111 weeks
169.01758 -.10904 (169*2π)/186111 weeks
170-.01267 -.11762 (170*2π)/186111 weeks
171-.04036 -.12713 (171*2π)/186111 weeks
172-.06902 -.08109 (172*2π)/186111 weeks
173-.03043 -.08577 (173*2π)/186111 weeks
174-.04395 -.09064 (174*2π)/186111 weeks
175-.06981 -.04498 (175*2π)/186111 weeks
176.00234 -.05832 (176*2π)/186111 weeks
177-.03279 -.12113 (177*2π)/186111 weeks
178-.08404 -.05129 (178*2π)/186110 weeks
179-.02619 -.01014 (179*2π)/186110 weeks
180.02411 -.0553 (180*2π)/186110 weeks
181-.03068 -.10758 (181*2π)/186110 weeks
182-.05254 -.01254 (182*2π)/186110 weeks
183.0626 -.03854 (183*2π)/186110 weeks
184.00553 -.11835 (184*2π)/186110 weeks
185-.02462 -.11795 (185*2π)/186110 weeks
186-.07008 -.09603 (186*2π)/186110 weeks
187-.02549 -.0362 (187*2π)/186110 weeks
188.01885 -.10422 (188*2π)/186110 weeks
189-.02896 -.17484 (189*2π)/186110 weeks
190-.18284 -.10285 (190*2π)/186110 weeks
191-.08315 .05286 (191*2π)/186110 weeks
192.01935 -.00202 (192*2π)/186110 weeks
193.00205 -.11293 (193*2π)/186110 weeks
194-.09337 -.08068 (194*2π)/186110 weeks
195-.06689 .02109 (195*2π)/186110 weeks
196.03902 .00684 (196*2π)/18619 weeks
197.03711 -.10202 (197*2π)/18619 weeks
198-.03927 -.10837 (198*2π)/18619 weeks
199-.0681 -.05167 (199*2π)/18619 weeks
200-.0026 -.0438 (200*2π)/18619 weeks
201.01086 -.08357 (201*2π)/18619 weeks
202-.07606 -.12613 (202*2π)/18619 weeks
203-.1235 -.0086 (203*2π)/18619 weeks
204-.01112 .03323 (204*2π)/18619 weeks
205.04348 -.04768 (205*2π)/18619 weeks
206-.0136 -.1248 (206*2π)/18619 weeks
207-.07462 -.04206 (207*2π)/18619 weeks
208-.00381 -.03233 (208*2π)/18619 weeks
209-.02835 -.08504 (209*2π)/18619 weeks
210-.0623 -.04387 (210*2π)/18619 weeks
211-.03427 -.02436 (211*2π)/18619 weeks
212.03194 -.04364 (212*2π)/18619 weeks
213-.01025 -.11692 (213*2π)/18619 weeks
214-.07308 -.10472 (214*2π)/18619 weeks
215-.08838 -.01853 (215*2π)/18619 weeks
216-.03448 -.0491 (216*2π)/18619 weeks
217-.07722 -.01738 (217*2π)/18619 weeks
218-.02925 -.03532 (218*2π)/18619 weeks
219-.07533 .01593 (219*2π)/18618 weeks
220.01476 .00659 (220*2π)/18618 weeks
221-.0195 -.03033 (221*2π)/18618 weeks
222-.00592 -.01067 (222*2π)/18618 weeks
223.00266 -.01326 (223*2π)/18618 weeks
224.02626 -.02547 (224*2π)/18618 weeks
225.02764 -.06095 (225*2π)/18618 weeks
226.01147 -.07226 (226*2π)/18618 weeks
227-.02314 -.09674 (227*2π)/18618 weeks
228-.0501 -.0725 (228*2π)/18618 weeks
229-.0582 -.04845 (229*2π)/18618 weeks
230-.05105 -.0218 (230*2π)/18618 weeks
231-.02583 .01902 (231*2π)/18618 weeks
232.04751 -.00203 (232*2π)/18618 weeks
233.03865 -.10205 (233*2π)/18618 weeks
234-.07228 -.09683 (234*2π)/18618 weeks
235-.06131 -.01067 (235*2π)/18618 weeks
236-.03031 -.01995 (236*2π)/18618 weeks
237-.01511 .00117 (237*2π)/18618 weeks
238.00116 .02047 (238*2π)/18618 weeks
239.08348 -.01774 (239*2π)/18618 weeks
240.0059 -.11404 (240*2π)/18618 weeks
241-.06042 -.02892 (241*2π)/18618 weeks
242.03989 .03761 (242*2π)/18618 weeks
243.09715 -.08241 (243*2π)/18618 weeks
244-.01738 -.13385 (244*2π)/18618 weeks
245-.0315 -.05791 (245*2π)/18618 weeks
246.01295 -.03963 (246*2π)/18618 weeks
247.03177 -.1015 (247*2π)/18618 weeks
248-.06195 -.13847 (248*2π)/18618 weeks
249-.09423 -.0412 (249*2π)/18617 weeks
250-.0358 .01965 (250*2π)/18617 weeks
251.04593 -.0003 (251*2π)/18617 weeks
252.05268 -.1064 (252*2π)/18617 weeks
253-.03921 -.09299 (253*2π)/18617 weeks
254-.05131 -.04802 (254*2π)/18617 weeks
255-.03089 -.02758 (255*2π)/18617 weeks
256.00284 -.02467 (256*2π)/18617 weeks
257.03997 -.05816 (257*2π)/18617 weeks
258.01424 -.09808 (258*2π)/18617 weeks
259-.00499 -.11663 (259*2π)/18617 weeks
260-.05821 -.11682 (260*2π)/18617 weeks
261-.10669 -.06286 (261*2π)/18617 weeks
262-.05646 -.00699 (262*2π)/18617 weeks
263.00017 -.0105 (263*2π)/18617 weeks
264.00802 -.07822 (264*2π)/18617 weeks
265-.0592 -.08523 (265*2π)/18617 weeks
266-.08204 -.03328 (266*2π)/18617 weeks
267-.05599 .00221 (267*2π)/18617 weeks
268-.01175 .01528 (268*2π)/18617 weeks
269.03817 -.02696 (269*2π)/18617 weeks
270.0078 -.04823 (270*2π)/18617 weeks
271.01793 -.07224 (271*2π)/18617 weeks
272-.02742 -.06994 (272*2π)/18617 weeks
273-.02972 -.06503 (273*2π)/18617 weeks
274-.0346 -.05321 (274*2π)/18617 weeks
275-.01863 -.022 (275*2π)/18617 weeks
276.00952 -.05375 (276*2π)/18617 weeks
277-.00093 -.0674 (277*2π)/18617 weeks
278-.01511 -.10663 (278*2π)/18617 weeks
279-.07084 -.10172 (279*2π)/18617 weeks
280-.09593 -.04239 (280*2π)/18617 weeks
281-.05447 .00107 (281*2π)/18617 weeks
282-.02274 -.0154 (282*2π)/18617 weeks
283-.01959 -.02411 (283*2π)/18617 weeks
284-.00191 -.04176 (284*2π)/18617 weeks
285-.02313 -.05921 (285*2π)/18617 weeks
286-.03309 -.05975 (286*2π)/18617 weeks
287-.05558 -.035 (287*2π)/18616 weeks
288-.02659 -.01001 (288*2π)/18616 weeks
289-.00546 -.01341 (289*2π)/18616 weeks
290.01185 -.06387 (290*2π)/18616 weeks
291-.03552 -.08697 (291*2π)/18616 weeks
292-.07598 -.05765 (292*2π)/18616 weeks
293-.04274 -.00353 (293*2π)/18616 weeks
294-.00456 -.04265 (294*2π)/18616 weeks
295-.03952 -.07259 (295*2π)/18616 weeks
296-.0934 -.0178 (296*2π)/18616 weeks
297-.03862 .02064 (297*2π)/18616 weeks
298.00127 -.01824 (298*2π)/18616 weeks
299-.01841 -.04568 (299*2π)/18616 weeks
300-.04975 -.01849 (300*2π)/18616 weeks
301-.02832 .00976 (301*2π)/18616 weeks
302.00365 .00371 (302*2π)/18616 weeks
303.04522 -.04735 (303*2π)/18616 weeks
304-.03575 -.08184 (304*2π)/18616 weeks
305-.06173 -.00793 (305*2π)/18616 weeks
306-.00032 .01102 (306*2π)/18616 weeks
307.03339 -.04508 (307*2π)/18616 weeks
308-.0356 -.07014 (308*2π)/18616 weeks
309-.03528 -.01465 (309*2π)/18616 weeks
310-.00451 -.01854 (310*2π)/18616 weeks
311-.00498 -.03312 (311*2π)/18616 weeks
312-.00593 -.04404 (312*2π)/18616 weeks
313-.03073 -.04883 (313*2π)/18616 weeks
314-.03475 -.01555 (314*2π)/18616 weeks
315.00762 -.00499 (315*2π)/18616 weeks
316.02345 -.04178 (316*2π)/18616 weeks
317-.00961 -.06968 (317*2π)/18616 weeks
318-.03625 -.03842 (318*2π)/18616 weeks
319-.00453 -.01363 (319*2π)/18616 weeks
320.00282 -.04965 (320*2π)/18616 weeks
321.00521 -.03553 (321*2π)/18616 weeks
322.00266 -.04271 (322*2π)/18616 weeks
323.0179 -.08135 (323*2π)/18616 weeks
324-.04483 -.10199 (324*2π)/18616 weeks
325-.06252 -.05325 (325*2π)/18616 weeks
326-.04179 -.04142 (326*2π)/18616 weeks
327-.02615 -.04149 (327*2π)/18616 weeks
328-.03958 -.05833 (328*2π)/18616 weeks
329-.06808 -.03064 (329*2π)/18616 weeks
330-.03221 -.00573 (330*2π)/18616 weeks
331-.01751 -.02031 (331*2π)/18616 weeks
332-.00101 -.04548 (332*2π)/18616 weeks
333-.05683 -.05844 (333*2π)/18616 weeks
334-.0494 .00119 (334*2π)/18616 weeks
335-.00792 -.01881 (335*2π)/18616 weeks
336-.01749 -.03773 (336*2π)/18616 weeks
337-.0494 -.0522 (337*2π)/18616 weeks
338-.05305 -.00017 (338*2π)/18616 weeks
339-.00067 .00223 (339*2π)/18615 weeks
340-.01769 -.03319 (340*2π)/18615 weeks
341-.02293 -.02596 (341*2π)/18615 weeks
342-.03629 -.0131 (342*2π)/18615 weeks
343.00199 .00164 (343*2π)/18615 weeks
344.00896 -.0246 (344*2π)/18615 weeks
345-.0142 -.04513 (345*2π)/18615 weeks
346-.03385 -.00998 (346*2π)/18615 weeks
347.00729 -.00401 (347*2π)/18615 weeks
348.0096 -.02971 (348*2π)/18615 weeks
349.02474 -.04346 (349*2π)/18615 weeks
350-.0079 -.07423 (350*2π)/18615 weeks
351-.02604 -.03573 (351*2π)/18615 weeks
352-.01202 -.03797 (352*2π)/18615 weeks
353-.00638 -.04821 (353*2π)/18615 weeks
354-.02175 -.05678 (354*2π)/18615 weeks
355-.03623 -.04051 (355*2π)/18615 weeks
356-.00689 -.01328 (356*2π)/18615 weeks
357.00786 -.07012 (357*2π)/18615 weeks
358-.03111 -.07467 (358*2π)/18615 weeks
359-.07333 -.0616 (359*2π)/18615 weeks
360-.04312 -.0011 (360*2π)/18615 weeks
361-.01285 -.04812 (361*2π)/18615 weeks
362-.04709 -.03291 (362*2π)/18615 weeks
363-.03387 -.02312 (363*2π)/18615 weeks
364-.03293 -.01506 (364*2π)/18615 weeks
365-.00953 -.02861 (365*2π)/18615 weeks
366-.03222 -.04449 (366*2π)/18615 weeks
367-.05011 -.03955 (367*2π)/18615 weeks
368-.06127 .0071 (368*2π)/18615 weeks
369-.00724 .01722 (369*2π)/18615 weeks
370.00775 -.02044 (370*2π)/18615 weeks
371-.01563 -.04348 (371*2π)/18615 weeks
372-.03079 -.02074 (372*2π)/18615 weeks
373-.01295 -.01171 (373*2π)/18615 weeks
374.01345 -.01641 (374*2π)/18615 weeks
375.00108 -.05393 (375*2π)/18615 weeks
376-.02419 -.05831 (376*2π)/18615 weeks
377-.04352 -.03413 (377*2π)/18615 weeks
378-.01446 .00325 (378*2π)/18615 weeks
379.00725 -.05055 (379*2π)/18615 weeks
380-.03242 -.05155 (380*2π)/18615 weeks
381-.0384 -.02692 (381*2π)/18615 weeks
382-.02119 -.01077 (382*2π)/18615 weeks
383-.00121 -.04847 (383*2π)/18615 weeks
384-.06355 -.03899 (384*2π)/18615 weeks
385-.03048 .01871 (385*2π)/18615 weeks
386.0214 -.0059 (386*2π)/18615 weeks
387.02534 -.06329 (387*2π)/18615 weeks
388-.0471 -.09269 (388*2π)/18615 weeks
389-.06155 -.01506 (389*2π)/18615 weeks
390-.02943 -.01652 (390*2π)/18615 weeks
391-.01652 -.02524 (391*2π)/18615 weeks
392-.03644 -.03763 (392*2π)/18615 weeks
393-.0366 -.00678 (393*2π)/18615 weeks
394-.02028 -.00962 (394*2π)/18615 weeks
395.00406 -.02443 (395*2π)/18615 weeks
396-.02693 -.05414 (396*2π)/18615 weeks
397-.05049 -.0045 (397*2π)/18615 weeks
398.002 .01087 (398*2π)/18615 weeks
399.02574 -.04014 (399*2π)/18615 weeks
400-.02397