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# Fourier Analysis of FINUX (Fidelity International Bond Fu)

FINUX (Fidelity International Bond Fu) appears to have interesting cyclic behaviour every 22 weeks (.0406*cosine), 24 weeks (.0382*sine), and 22 weeks (.0284*sine).

FINUX (Fidelity International Bond Fu) has an average price of 8.74 (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 5/23/2012 to 6/26/2017 for FINUX (Fidelity International Bond Fu), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
08.74239   0
1.04413 .42906 (1*2π)/267267 weeks
2.05361 -.11858 (2*2π)/267134 weeks
3-.07844 .26388 (3*2π)/26789 weeks
4-.04376 .11111 (4*2π)/26767 weeks
5.10982 .05758 (5*2π)/26753 weeks
6.01124 -.05611 (6*2π)/26745 weeks
7.02399 -.05208 (7*2π)/26738 weeks
8-.00867 -.00136 (8*2π)/26733 weeks
9-.02099 -.03429 (9*2π)/26730 weeks
10-.03013 -.02365 (10*2π)/26727 weeks
11.00095 .03817 (11*2π)/26724 weeks
12.04064 .02836 (12*2π)/26722 weeks
13-.00855 -.02302 (13*2π)/26721 weeks
14.0169 -.02553 (14*2π)/26719 weeks
15-.00004 -.01682 (15*2π)/26718 weeks
16.01157 -.00137 (16*2π)/26717 weeks
17.01391 -.01 (17*2π)/26716 weeks
18-.0125 .00784 (18*2π)/26715 weeks
19-.00883 .02239 (19*2π)/26714 weeks
20-.01995 .00454 (20*2π)/26713 weeks
21.01243 -.00501 (21*2π)/26713 weeks
22-.00735 -.00355 (22*2π)/26712 weeks
23.00645 .015 (23*2π)/26712 weeks
24-.0075 -.01022 (24*2π)/26711 weeks
25-.00769 -.012 (25*2π)/26711 weeks
26.00089 -.00264 (26*2π)/26710 weeks
27-.00884 .00438 (27*2π)/26710 weeks
28-.00741 -.00188 (28*2π)/26710 weeks
29.01102 -.00441 (29*2π)/2679 weeks
30.01913 .00799 (30*2π)/2679 weeks
31-.01851 .00044 (31*2π)/2679 weeks
32-.00801 .01397 (32*2π)/2678 weeks
33-.00306 -.00708 (33*2π)/2678 weeks
34.0086 -.00013 (34*2π)/2678 weeks
35.00042 .01353 (35*2π)/2678 weeks
36.00246 -.00208 (36*2π)/2677 weeks
37-.01188 .00039 (37*2π)/2677 weeks
38.00724 .00246 (38*2π)/2677 weeks
39.00956 .00474 (39*2π)/2677 weeks
40.00136 .00422 (40*2π)/2677 weeks
41-.01153 -.00003 (41*2π)/2677 weeks
42-.02016 -.00316 (42*2π)/2676 weeks
43.00709 -.00342 (43*2π)/2676 weeks
44-.0029 .00588 (44*2π)/2676 weeks
45.00541 .00493 (45*2π)/2676 weeks
46-.01002 -.0041 (46*2π)/2676 weeks
47.00892 .00445 (47*2π)/2676 weeks
48-.00029 -.02101 (48*2π)/2676 weeks
49-.00681 -.00013 (49*2π)/2675 weeks
50-.00099 .00978 (50*2π)/2675 weeks
51.0013 .01318 (51*2π)/2675 weeks
52.00466 -.00277 (52*2π)/2675 weeks
53.00734 -.00863 (53*2π)/2675 weeks
54.01609 -.00433 (54*2π)/2675 weeks
55-.00062 -.00052 (55*2π)/2675 weeks
56-.00857 .00375 (56*2π)/2675 weeks
57-.00295 -.00904 (57*2π)/2675 weeks
58.00263 .00052 (58*2π)/2675 weeks
59-.00357 .00225 (59*2π)/2675 weeks
60.00172 .0074 (60*2π)/2674 weeks
61-.00207 -.00521 (61*2π)/2674 weeks
62.01121 -.00405 (62*2π)/2674 weeks
63-.00555 -.01308 (63*2π)/2674 weeks
64-.01496 .00814 (64*2π)/2674 weeks
65.002 .00559 (65*2π)/2674 weeks
66-.00167 .00498 (66*2π)/2674 weeks
67-.00403 .00301 (67*2π)/2674 weeks
68.00252 -.00384 (68*2π)/2674 weeks
69.00293 .00897 (69*2π)/2674 weeks
70.00326 -.00139 (70*2π)/2674 weeks
71.00119 -.00214 (71*2π)/2674 weeks
72.00109 -.00457 (72*2π)/2674 weeks
73-.00413 .0071 (73*2π)/2674 weeks
74.003 .00053 (74*2π)/2674 weeks
75-.00681 -.0038 (75*2π)/2674 weeks
76.00885 .00007 (76*2π)/2674 weeks
77.00185 -.00144 (77*2π)/2673 weeks
78-.00228 -.00061 (78*2π)/2673 weeks
79.00024 -.00394 (79*2π)/2673 weeks
80-.00487 -.00056 (80*2π)/2673 weeks
81.00163 .00328 (81*2π)/2673 weeks
82.00491 .00235 (82*2π)/2673 weeks
83.00124 -.00271 (83*2π)/2673 weeks
84-.00488 .01364 (84*2π)/2673 weeks
85.00193 .00195 (85*2π)/2673 weeks
86.00235 -.00018 (86*2π)/2673 weeks
87.00582 -.00484 (87*2π)/2673 weeks
88.00279 -.00683 (88*2π)/2673 weeks
89-.00405 .0014 (89*2π)/2673 weeks
90-.00072 .00164 (90*2π)/2673 weeks
91-.00673 -.00009 (91*2π)/2673 weeks
92-.00134 -.00363 (92*2π)/2673 weeks
93.00424 -.00059 (93*2π)/2673 weeks
94.0009 -.00324 (94*2π)/2673 weeks
95-.00477 -.00227 (95*2π)/2673 weeks
96-.00752 -.00271 (96*2π)/2673 weeks
97.00364 .00214 (97*2π)/2673 weeks
98.00815 -.0008 (98*2π)/2673 weeks
99-.0001 .00562 (99*2π)/2673 weeks
100.00321 -.00372 (100*2π)/2673 weeks
101-.0004 -.00689 (101*2π)/2673 weeks
102-.00012 .00473 (102*2π)/2673 weeks
103.00199 .00096 (103*2π)/2673 weeks
104.00182 .00396 (104*2π)/2673 weeks
105-.00255 .00307 (105*2π)/2673 weeks
106.00098 .00549 (106*2π)/2673 weeks
107.00239 .00208 (107*2π)/2672 weeks
108.00197 .00051 (108*2π)/2672 weeks
109.00029 .00512 (109*2π)/2672 weeks
110.00016 -.00446 (110*2π)/2672 weeks
111-.00021 .00091 (111*2π)/2672 weeks
112.00379 -.00081 (112*2π)/2672 weeks
113.00365 .00205 (113*2π)/2672 weeks
114.00046 .00524 (114*2π)/2672 weeks
115-.0022 .00458 (115*2π)/2672 weeks
116.00149 -.00424 (116*2π)/2672 weeks
117.00168 .00027 (117*2π)/2672 weeks
118.00091 -.00381 (118*2π)/2672 weeks
119-.00127 .00107 (119*2π)/2672 weeks
120.00207 .00103 (120*2π)/2672 weeks
121-.00122 .00292 (121*2π)/2672 weeks
122.01058 -.00639 (122*2π)/2672 weeks
123-.00523 .00421 (123*2π)/2672 weeks
124-.00414 .0015 (124*2π)/2672 weeks
125-.00166 -.00125 (125*2π)/2672 weeks
126.0016 -.0018 (126*2π)/2672 weeks
127-.00193 -.0031 (127*2π)/2672 weeks
128-.00507 .00519 (128*2π)/2672 weeks
129-.00216 .00652 (129*2π)/2672 weeks
130.00048 -.00147 (130*2π)/2672 weeks
131.00771 -.00439 (131*2π)/2672 weeks
132-.00639 -.00268 (132*2π)/2672 weeks
133-.00536 .00789 (133*2π)/2672 weeks
134-.00536 -.00789 (134*2π)/2672 weeks
135-.00639 .00268 (135*2π)/2672 weeks
136.00771 .00439 (136*2π)/2672 weeks
137.00048 .00147 (137*2π)/2672 weeks
138-.00216 -.00652 (138*2π)/2672 weeks
139-.00507 -.00519 (139*2π)/2672 weeks
140-.00193 .0031 (140*2π)/2672 weeks
141.0016 .0018 (141*2π)/2672 weeks
142-.00166 .00125 (142*2π)/2672 weeks
143-.00414 -.0015 (143*2π)/2672 weeks
144-.00523 -.00421 (144*2π)/2672 weeks
145.01058 .00639 (145*2π)/2672 weeks
146-.00122 -.00292 (146*2π)/2672 weeks
147.00207 -.00103 (147*2π)/2672 weeks
148-.00127 -.00107 (148*2π)/2672 weeks
149.00091 .00381 (149*2π)/2672 weeks
150.00168 -.00027 (150*2π)/2672 weeks
151.00149 .00424 (151*2π)/2672 weeks
152-.0022 -.00458 (152*2π)/2672 weeks
153.00046 -.00524 (153*2π)/2672 weeks
154.00365 -.00205 (154*2π)/2672 weeks
155.00379 .00081 (155*2π)/2672 weeks
156-.00021 -.00091 (156*2π)/2672 weeks
157.00016 .00446 (157*2π)/2672 weeks
158.00029 -.00512 (158*2π)/2672 weeks
159.00197 -.00051 (159*2π)/2672 weeks
160.00239 -.00208 (160*2π)/2672 weeks
161.00098 -.00549 (161*2π)/2672 weeks
162-.00255 -.00307 (162*2π)/2672 weeks
163.00182 -.00396 (163*2π)/2672 weeks
164.00199 -.00096 (164*2π)/2672 weeks
165-.00012 -.00473 (165*2π)/2672 weeks
166-.0004 .00689 (166*2π)/2672 weeks
167.00321 .00372 (167*2π)/2672 weeks
168-.0001 -.00562 (168*2π)/2672 weeks
169.00815 .0008 (169*2π)/2672 weeks
170.00364 -.00214 (170*2π)/2672 weeks
171-.00752 .00271 (171*2π)/2672 weeks
172-.00477 .00227 (172*2π)/2672 weeks
173.0009 .00324 (173*2π)/2672 weeks
174.00424 .00059 (174*2π)/2672 weeks
175-.00134 .00363 (175*2π)/2672 weeks
176-.00673 .00009 (176*2π)/2672 weeks
177-.00072 -.00164 (177*2π)/2672 weeks
178-.00405 -.0014 (178*2π)/2672 weeks
179.00279 .00683 (179*2π)/2671 weeks
180.00582 .00484 (180*2π)/2671 weeks
181.00235 .00018 (181*2π)/2671 weeks
182.00193 -.00195 (182*2π)/2671 weeks
183-.00488 -.01364 (183*2π)/2671 weeks
184.00124 .00271 (184*2π)/2671 weeks
185.00491 -.00235 (185*2π)/2671 weeks
186.00163 -.00328 (186*2π)/2671 weeks
187-.00487 .00056 (187*2π)/2671 weeks
188.00024 .00394 (188*2π)/2671 weeks
189-.00228 .00061 (189*2π)/2671 weeks
190.00185 .00144 (190*2π)/2671 weeks
191.00885 -.00007 (191*2π)/2671 weeks
192-.00681 .0038 (192*2π)/2671 weeks
193.003 -.00053 (193*2π)/2671 weeks
194-.00413 -.0071 (194*2π)/2671 weeks
195.00109 .00457 (195*2π)/2671 weeks
196.00119 .00214 (196*2π)/2671 weeks
197.00326 .00139 (197*2π)/2671 weeks
198.00293 -.00897 (198*2π)/2671 weeks
199.00252 .00384 (199*2π)/2671 weeks
200-.00403 -.00301 (200*2π)/2671 weeks
201-.00167 -.00498 (201*2π)/2671 weeks
202.002 -.00559 (202*2π)/2671 weeks
203-.01496 -.00814 (203*2π)/2671 weeks
204-.00555 .01308 (204*2π)/2671 weeks
205.01121 .00405 (205*2π)/2671 weeks
206-.00207 .00521 (206*2π)/2671 weeks
207.00172 -.0074 (207*2π)/2671 weeks
208-.00357 -.00225 (208*2π)/2671 weeks
209.00263 -.00052 (209*2π)/2671 weeks
210-.00295 .00904 (210*2π)/2671 weeks
211-.00857 -.00375 (211*2π)/2671 weeks
212-.00062 .00052 (212*2π)/2671 weeks
213.01609 .00433 (213*2π)/2671 weeks
214.00734 .00863 (214*2π)/2671 weeks
215.00466 .00277 (215*2π)/2671 weeks
216.0013 -.01318 (216*2π)/2671 weeks
217-.00099 -.00978 (217*2π)/2671 weeks
218-.00681 .00013 (218*2π)/2671 weeks
219-.00029 .02101 (219*2π)/2671 weeks
220.00892 -.00445 (220*2π)/2671 weeks
221-.01002 .0041 (221*2π)/2671 weeks
222.00541 -.00493 (222*2π)/2671 weeks
223-.0029 -.00588 (223*2π)/2671 weeks
224.00709 .00342 (224*2π)/2671 weeks
225-.02016 .00316 (225*2π)/2671 weeks
226-.01153 .00003 (226*2π)/2671 weeks
227.00136 -.00422 (227*2π)/2671 weeks
228.00956 -.00474 (228*2π)/2671 weeks
229.00724 -.00246 (229*2π)/2671 weeks
230-.01188 -.00039 (230*2π)/2671 weeks
231.00246 .00208 (231*2π)/2671 weeks
232.00042 -.01353 (232*2π)/2671 weeks
233.0086 .00013 (233*2π)/2671 weeks
234-.00306 .00708 (234*2π)/2671 weeks
235-.00801 -.01397 (235*2π)/2671 weeks
236-.01851 -.00044 (236*2π)/2671 weeks
237.01913 -.00799 (237*2π)/2671 weeks
238.01102 .00441 (238*2π)/2671 weeks
239-.00741 .00188 (239*2π)/2671 weeks
240-.00884 -.00438 (240*2π)/2671 weeks
241.00089 .00264 (241*2π)/2671 weeks
242-.00769 .012 (242*2π)/2671 weeks
243-.0075 .01022 (243*2π)/2671 weeks
244.00645 -.015 (244*2π)/2671 weeks
245-.00735 .00355 (245*2π)/2671 weeks
246.01243 .00501 (246*2π)/2671 weeks
247-.01995 -.00454 (247*2π)/2671 weeks
248-.00883 -.02239 (248*2π)/2671 weeks
249-.0125 -.00784 (249*2π)/2671 weeks
250.01391 .01 (250*2π)/2671 weeks
251.01157 .00137 (251*2π)/2671 weeks
252-.00004 .01682 (252*2π)/2671 weeks
253.0169 .02553 (253*2π)/2671 weeks
254-.00855 .02302 (254*2π)/2671 weeks
255.04064 -.02836 (255*2π)/2671 weeks
256.00095 -.03817 (256*2π)/2671 weeks
257-.03013 .02365 (257*2π)/2671 weeks
258-.02099 .03429 (258*2π)/2671 weeks
259-.00867 .00136 (259*2π)/2671 weeks
260.02399 .05208 (260*2π)/2671 weeks
261.01124 .05611 (261*2π)/2671 weeks
262.10982 -.05758 (262*2π)/2671 weeks
263-.04376 -.11111 (263*2π)/2671 weeks
264-.07844 -.26388 (264*2π)/2671 weeks
265.05361 .11858 (265*2π)/2671 weeks