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Fourier Analysis of FHLC (Fidelity MSCI Health Care Index)


FHLC (Fidelity MSCI Health Care Index) appears to have interesting cyclic behaviour every 16 weeks (.5412*sine), 12 weeks (.4066*sine), and 13 weeks (.3387*sine).

FHLC (Fidelity MSCI Health Care Index) has an average price of 31.56 (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 10/24/2013 to 3/20/2017 for FHLC (Fidelity MSCI Health Care Index), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
031.55901   0 
1-2.32582 -2.20904 (1*2π)/179179 weeks
2.70044 -2.42145 (2*2π)/17990 weeks
3-.564 -.56489 (3*2π)/17960 weeks
4.2085 -.44972 (4*2π)/17945 weeks
5.22726 -.57791 (5*2π)/17936 weeks
6.12611 -.90631 (6*2π)/17930 weeks
7-.3124 -.52454 (7*2π)/17926 weeks
8.10717 -.76969 (8*2π)/17922 weeks
9-.3044 -.59677 (9*2π)/17920 weeks
10.23288 -.08676 (10*2π)/17918 weeks
11.00675 -.54122 (11*2π)/17916 weeks
12-.04098 -.27318 (12*2π)/17915 weeks
13-.12848 -.1644 (13*2π)/17914 weeks
14-.16382 -.33873 (14*2π)/17913 weeks
15-.08738 -.40663 (15*2π)/17912 weeks
16-.03859 -.25418 (16*2π)/17911 weeks
17-.15041 -.29011 (17*2π)/17911 weeks
18-.23081 -.1995 (18*2π)/17910 weeks
19-.00219 -.17947 (19*2π)/1799 weeks
20.01409 -.11353 (20*2π)/1799 weeks
21-.1138 -.13443 (21*2π)/1799 weeks
22-.09346 -.2267 (22*2π)/1798 weeks
23-.23151 -.27108 (23*2π)/1798 weeks
24-.21674 -.01433 (24*2π)/1797 weeks
25-.07245 -.12183 (25*2π)/1797 weeks
26-.12958 -.14419 (26*2π)/1797 weeks
27-.10212 -.12918 (27*2π)/1797 weeks
28-.05478 -.05187 (28*2π)/1796 weeks
29.04552 -.17306 (29*2π)/1796 weeks
30-.06309 -.25034 (30*2π)/1796 weeks
31-.08541 -.06181 (31*2π)/1796 weeks
32-.1194 -.08085 (32*2π)/1796 weeks
33.03447 -.12584 (33*2π)/1795 weeks
34-.05481 -.10541 (34*2π)/1795 weeks
35-.10199 .0249 (35*2π)/1795 weeks
36-.08001 -.1566 (36*2π)/1795 weeks
37-.04644 -.02707 (37*2π)/1795 weeks
38-.03266 -.07344 (38*2π)/1795 weeks
39-.10266 -.21564 (39*2π)/1795 weeks
40-.09621 -.0523 (40*2π)/1794 weeks
41.00511 -.12237 (41*2π)/1794 weeks
42-.08843 -.00142 (42*2π)/1794 weeks
43-.18321 -.05914 (43*2π)/1794 weeks
44.03865 -.0476 (44*2π)/1794 weeks
45-.11611 -.00846 (45*2π)/1794 weeks
46.01317 .01245 (46*2π)/1794 weeks
47.04778 -.12528 (47*2π)/1794 weeks
48-.08537 -.01989 (48*2π)/1794 weeks
49-.03226 -.08193 (49*2π)/1794 weeks
50-.11587 -.08697 (50*2π)/1794 weeks
51-.05615 .00166 (51*2π)/1794 weeks
52-.07986 -.05829 (52*2π)/1793 weeks
53-.15043 -.07699 (53*2π)/1793 weeks
54-.02535 -.03726 (54*2π)/1793 weeks
55-.08318 -.02275 (55*2π)/1793 weeks
56-.02527 -.09282 (56*2π)/1793 weeks
57-.14511 -.02885 (57*2π)/1793 weeks
58-.03562 -.0214 (58*2π)/1793 weeks
59-.07956 -.0604 (59*2π)/1793 weeks
60-.06965 .0097 (60*2π)/1793 weeks
61-.0519 -.05871 (61*2π)/1793 weeks
62-.00771 .00809 (62*2π)/1793 weeks
63-.05374 -.05872 (63*2π)/1793 weeks
64-.02187 -.02256 (64*2π)/1793 weeks
65-.02709 -.03032 (65*2π)/1793 weeks
66-.04749 -.02272 (66*2π)/1793 weeks
67-.14565 -.05415 (67*2π)/1793 weeks
68-.08039 -.03215 (68*2π)/1793 weeks
69-.01189 .04389 (69*2π)/1793 weeks
70-.13295 -.00591 (70*2π)/1793 weeks
71-.01724 -.00773 (71*2π)/1793 weeks
72-.06731 -.01862 (72*2π)/1792 weeks
73-.06555 -.0313 (73*2π)/1792 weeks
74-.06813 -.06179 (74*2π)/1792 weeks
75-.12977 -.01303 (75*2π)/1792 weeks
76-.06326 -.03307 (76*2π)/1792 weeks
77-.11381 .00905 (77*2π)/1792 weeks
78.02362 .01005 (78*2π)/1792 weeks
79-.10637 -.01554 (79*2π)/1792 weeks
80.00996 .01412 (80*2π)/1792 weeks
81-.11346 -.01059 (81*2π)/1792 weeks
82-.10673 -.01635 (82*2π)/1792 weeks
83-.0673 -.04658 (83*2π)/1792 weeks
84-.07489 .02223 (84*2π)/1792 weeks
85-.05071 -.04257 (85*2π)/1792 weeks
86-.06231 .04516 (86*2π)/1792 weeks
87-.05197 .00249 (87*2π)/1792 weeks
88-.03926 .03625 (88*2π)/1792 weeks
89-.04847 -.04576 (89*2π)/1792 weeks
90-.04847 .04576 (90*2π)/1792 weeks
91-.03926 -.03625 (91*2π)/1792 weeks
92-.05197 -.00249 (92*2π)/1792 weeks
93-.06231 -.04516 (93*2π)/1792 weeks
94-.05071 .04257 (94*2π)/1792 weeks
95-.07489 -.02223 (95*2π)/1792 weeks
96-.0673 .04658 (96*2π)/1792 weeks
97-.10673 .01635 (97*2π)/1792 weeks
98-.11346 .01059 (98*2π)/1792 weeks
99.00996 -.01412 (99*2π)/1792 weeks
100-.10637 .01554 (100*2π)/1792 weeks
101.02362 -.01005 (101*2π)/1792 weeks
102-.11381 -.00905 (102*2π)/1792 weeks
103-.06326 .03307 (103*2π)/1792 weeks
104-.12977 .01303 (104*2π)/1792 weeks
105-.06813 .06179 (105*2π)/1792 weeks
106-.06555 .0313 (106*2π)/1792 weeks
107-.06731 .01862 (107*2π)/1792 weeks
108-.01724 .00773 (108*2π)/1792 weeks
109-.13295 .00591 (109*2π)/1792 weeks
110-.01189 -.04389 (110*2π)/1792 weeks
111-.08039 .03215 (111*2π)/1792 weeks
112-.14565 .05415 (112*2π)/1792 weeks
113-.04749 .02272 (113*2π)/1792 weeks
114-.02709 .03032 (114*2π)/1792 weeks
115-.02187 .02256 (115*2π)/1792 weeks
116-.05374 .05872 (116*2π)/1792 weeks
117-.00771 -.00809 (117*2π)/1792 weeks
118-.0519 .05871 (118*2π)/1792 weeks
119-.06965 -.0097 (119*2π)/1792 weeks
120-.07956 .0604 (120*2π)/1791 weeks
121-.03562 .0214 (121*2π)/1791 weeks
122-.14511 .02885 (122*2π)/1791 weeks
123-.02527 .09282 (123*2π)/1791 weeks
124-.08318 .02275 (124*2π)/1791 weeks
125-.02535 .03726 (125*2π)/1791 weeks
126-.15043 .07699 (126*2π)/1791 weeks
127-.07986 .05829 (127*2π)/1791 weeks
128-.05615 -.00166 (128*2π)/1791 weeks
129-.11587 .08697 (129*2π)/1791 weeks
130-.03226 .08193 (130*2π)/1791 weeks
131-.08537 .01989 (131*2π)/1791 weeks
132.04778 .12528 (132*2π)/1791 weeks
133.01317 -.01245 (133*2π)/1791 weeks
134-.11611 .00846 (134*2π)/1791 weeks
135.03865 .0476 (135*2π)/1791 weeks
136-.18321 .05914 (136*2π)/1791 weeks
137-.08843 .00142 (137*2π)/1791 weeks
138.00511 .12237 (138*2π)/1791 weeks
139-.09621 .0523 (139*2π)/1791 weeks
140-.10266 .21564 (140*2π)/1791 weeks
141-.03266 .07344 (141*2π)/1791 weeks
142-.04644 .02707 (142*2π)/1791 weeks
143-.08001 .1566 (143*2π)/1791 weeks
144-.10199 -.0249 (144*2π)/1791 weeks
145-.05481 .10541 (145*2π)/1791 weeks
146.03447 .12584 (146*2π)/1791 weeks
147-.1194 .08085 (147*2π)/1791 weeks
148-.08541 .06181 (148*2π)/1791 weeks
149-.06309 .25034 (149*2π)/1791 weeks
150.04552 .17306 (150*2π)/1791 weeks
151-.05478 .05187 (151*2π)/1791 weeks
152-.10212 .12918 (152*2π)/1791 weeks
153-.12958 .14419 (153*2π)/1791 weeks
154-.07245 .12183 (154*2π)/1791 weeks
155-.21674 .01433 (155*2π)/1791 weeks
156-.23151 .27108 (156*2π)/1791 weeks
157-.09346 .2267 (157*2π)/1791 weeks
158-.1138 .13443 (158*2π)/1791 weeks
159.01409 .11353 (159*2π)/1791 weeks
160-.00219 .17947 (160*2π)/1791 weeks
161-.23081 .1995 (161*2π)/1791 weeks
162-.15041 .29011 (162*2π)/1791 weeks
163-.03859 .25418 (163*2π)/1791 weeks
164-.08738 .40663 (164*2π)/1791 weeks
165-.16382 .33873 (165*2π)/1791 weeks
166-.12848 .1644 (166*2π)/1791 weeks
167-.04098 .27318 (167*2π)/1791 weeks
168.00675 .54122 (168*2π)/1791 weeks
169.23288 .08676 (169*2π)/1791 weeks
170-.3044 .59677 (170*2π)/1791 weeks
171.10717 .76969 (171*2π)/1791 weeks
172-.3124 .52454 (172*2π)/1791 weeks
173.12611 .90631 (173*2π)/1791 weeks
174.22726 .57791 (174*2π)/1791 weeks
175.2085 .44972 (175*2π)/1791 weeks
176-.564 .56489 (176*2π)/1791 weeks
177.70044 2.42145 (177*2π)/1791 weeks

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