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Fourier Analysis of FUTY (Fidelity MSCI Utilities Index E)


FUTY (Fidelity MSCI Utilities Index E) appears to have interesting cyclic behaviour every 12 weeks (.3268*sine), 14 weeks (.3004*sine), and 13 weeks (.2889*sine).

FUTY (Fidelity MSCI Utilities Index E) has an average price of 27.39 (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 1/9/2017 for FUTY (Fidelity MSCI Utilities Index E), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
027.39055   0 
1.18695 -2.35702 (1*2π)/169169 weeks
2-.72196 -2.55376 (2*2π)/16985 weeks
3-.48275 -.50582 (3*2π)/16956 weeks
4-.33597 -.55326 (4*2π)/16942 weeks
5.29532 -.78861 (5*2π)/16934 weeks
6.18242 -.26028 (6*2π)/16928 weeks
7.08702 -.36058 (7*2π)/16924 weeks
8.19024 -.62425 (8*2π)/16921 weeks
9-.11217 -.31273 (9*2π)/16919 weeks
10-.07135 -.25751 (10*2π)/16917 weeks
11.16123 -.11738 (11*2π)/16915 weeks
12-.09492 -.3004 (12*2π)/16914 weeks
13.18018 -.28889 (13*2π)/16913 weeks
14-.21025 -.3268 (14*2π)/16912 weeks
15-.04733 -.15684 (15*2π)/16911 weeks
16-.02707 -.16781 (16*2π)/16911 weeks
17-.28837 -.09388 (17*2π)/16910 weeks
18.02404 -.27503 (18*2π)/1699 weeks
19-.03616 -.11954 (19*2π)/1699 weeks
20.03707 -.0579 (20*2π)/1698 weeks
21-.1166 -.2157 (21*2π)/1698 weeks
22-.12693 -.09579 (22*2π)/1698 weeks
23-.02646 -.06975 (23*2π)/1697 weeks
24-.14621 -.07726 (24*2π)/1697 weeks
25-.05561 -.11769 (25*2π)/1697 weeks
26-.127 -.05161 (26*2π)/1697 weeks
27.00662 .0111 (27*2π)/1696 weeks
28-.03533 -.13413 (28*2π)/1696 weeks
29-.05232 -.04523 (29*2π)/1696 weeks
30-.028 -.12552 (30*2π)/1696 weeks
31.04027 -.10517 (31*2π)/1695 weeks
32-.06324 -.12409 (32*2π)/1695 weeks
33-.09393 -.07124 (33*2π)/1695 weeks
34-.03193 -.14567 (34*2π)/1695 weeks
35-.20487 -.03867 (35*2π)/1695 weeks
36-.04142 .01939 (36*2π)/1695 weeks
37-.04725 -.08953 (37*2π)/1695 weeks
38-.09363 -.08742 (38*2π)/1694 weeks
39.05824 -.0199 (39*2π)/1694 weeks
40-.09118 .00625 (40*2π)/1694 weeks
41.05497 -.10622 (41*2π)/1694 weeks
42-.02158 -.05004 (42*2π)/1694 weeks
43-.09121 -.14431 (43*2π)/1694 weeks
44-.04554 -.06593 (44*2π)/1694 weeks
45-.07132 -.00609 (45*2π)/1694 weeks
46-.09773 -.04556 (46*2π)/1694 weeks
47-.02863 -.07489 (47*2π)/1694 weeks
48-.06065 -.05565 (48*2π)/1694 weeks
49-.04646 -.05699 (49*2π)/1693 weeks
50-.07107 .00053 (50*2π)/1693 weeks
51-.02875 -.04742 (51*2π)/1693 weeks
52-.09325 -.03029 (52*2π)/1693 weeks
53.00005 -.08456 (53*2π)/1693 weeks
54-.08665 -.00708 (54*2π)/1693 weeks
55-.10469 -.03986 (55*2π)/1693 weeks
56-.10055 -.00495 (56*2π)/1693 weeks
57-.0605 -.0105 (57*2π)/1693 weeks
58.00272 -.02857 (58*2π)/1693 weeks
59-.00139 .04592 (59*2π)/1693 weeks
60.02909 -.04246 (60*2π)/1693 weeks
61-.00093 -.02094 (61*2π)/1693 weeks
62-.0989 -.04808 (62*2π)/1693 weeks
63-.0311 -.00348 (63*2π)/1693 weeks
64-.0514 -.03226 (64*2π)/1693 weeks
65-.04758 .0045 (65*2π)/1693 weeks
66-.07929 .01813 (66*2π)/1693 weeks
67-.05672 -.02766 (67*2π)/1693 weeks
68-.06842 -.01889 (68*2π)/1692 weeks
69-.04934 -.02041 (69*2π)/1692 weeks
70-.09101 .02525 (70*2π)/1692 weeks
71-.06128 -.05006 (71*2π)/1692 weeks
72-.02432 -.02609 (72*2π)/1692 weeks
73-.09123 -.02047 (73*2π)/1692 weeks
74-.06274 .0096 (74*2π)/1692 weeks
75-.02505 -.01359 (75*2π)/1692 weeks
76-.04107 .0326 (76*2π)/1692 weeks
77-.03609 -.0248 (77*2π)/1692 weeks
78-.08012 -.03111 (78*2π)/1692 weeks
79-.05532 .04324 (79*2π)/1692 weeks
80-.07392 .00647 (80*2π)/1692 weeks
81-.02099 -.01781 (81*2π)/1692 weeks
82-.06472 -.03592 (82*2π)/1692 weeks
83-.03712 .02298 (83*2π)/1692 weeks
84-.02572 .00583 (84*2π)/1692 weeks
85-.02572 -.00583 (85*2π)/1692 weeks
86-.03712 -.02298 (86*2π)/1692 weeks
87-.06472 .03592 (87*2π)/1692 weeks
88-.02099 .01781 (88*2π)/1692 weeks
89-.07392 -.00647 (89*2π)/1692 weeks
90-.05532 -.04324 (90*2π)/1692 weeks
91-.08012 .03111 (91*2π)/1692 weeks
92-.03609 .0248 (92*2π)/1692 weeks
93-.04107 -.0326 (93*2π)/1692 weeks
94-.02505 .01359 (94*2π)/1692 weeks
95-.06274 -.0096 (95*2π)/1692 weeks
96-.09123 .02047 (96*2π)/1692 weeks
97-.02432 .02609 (97*2π)/1692 weeks
98-.06128 .05006 (98*2π)/1692 weeks
99-.09101 -.02525 (99*2π)/1692 weeks
100-.04934 .02041 (100*2π)/1692 weeks
101-.06842 .01889 (101*2π)/1692 weeks
102-.05672 .02766 (102*2π)/1692 weeks
103-.07929 -.01813 (103*2π)/1692 weeks
104-.04758 -.0045 (104*2π)/1692 weeks
105-.0514 .03226 (105*2π)/1692 weeks
106-.0311 .00348 (106*2π)/1692 weeks
107-.0989 .04808 (107*2π)/1692 weeks
108-.00093 .02094 (108*2π)/1692 weeks
109.02909 .04246 (109*2π)/1692 weeks
110-.00139 -.04592 (110*2π)/1692 weeks
111.00272 .02857 (111*2π)/1692 weeks
112-.0605 .0105 (112*2π)/1692 weeks
113-.10055 .00495 (113*2π)/1691 weeks
114-.10469 .03986 (114*2π)/1691 weeks
115-.08665 .00708 (115*2π)/1691 weeks
116.00005 .08456 (116*2π)/1691 weeks
117-.09325 .03029 (117*2π)/1691 weeks
118-.02875 .04742 (118*2π)/1691 weeks
119-.07107 -.00053 (119*2π)/1691 weeks
120-.04646 .05699 (120*2π)/1691 weeks
121-.06065 .05565 (121*2π)/1691 weeks
122-.02863 .07489 (122*2π)/1691 weeks
123-.09773 .04556 (123*2π)/1691 weeks
124-.07132 .00609 (124*2π)/1691 weeks
125-.04554 .06593 (125*2π)/1691 weeks
126-.09121 .14431 (126*2π)/1691 weeks
127-.02158 .05004 (127*2π)/1691 weeks
128.05497 .10622 (128*2π)/1691 weeks
129-.09118 -.00625 (129*2π)/1691 weeks
130.05824 .0199 (130*2π)/1691 weeks
131-.09363 .08742 (131*2π)/1691 weeks
132-.04725 .08953 (132*2π)/1691 weeks
133-.04142 -.01939 (133*2π)/1691 weeks
134-.20487 .03867 (134*2π)/1691 weeks
135-.03193 .14567 (135*2π)/1691 weeks
136-.09393 .07124 (136*2π)/1691 weeks
137-.06324 .12409 (137*2π)/1691 weeks
138.04027 .10517 (138*2π)/1691 weeks
139-.028 .12552 (139*2π)/1691 weeks
140-.05232 .04523 (140*2π)/1691 weeks
141-.03533 .13413 (141*2π)/1691 weeks
142.00662 -.0111 (142*2π)/1691 weeks
143-.127 .05161 (143*2π)/1691 weeks
144-.05561 .11769 (144*2π)/1691 weeks
145-.14621 .07726 (145*2π)/1691 weeks
146-.02646 .06975 (146*2π)/1691 weeks
147-.12693 .09579 (147*2π)/1691 weeks
148-.1166 .2157 (148*2π)/1691 weeks
149.03707 .0579 (149*2π)/1691 weeks
150-.03616 .11954 (150*2π)/1691 weeks
151.02404 .27503 (151*2π)/1691 weeks
152-.28837 .09388 (152*2π)/1691 weeks
153-.02707 .16781 (153*2π)/1691 weeks
154-.04733 .15684 (154*2π)/1691 weeks
155-.21025 .3268 (155*2π)/1691 weeks
156.18018 .28889 (156*2π)/1691 weeks
157-.09492 .3004 (157*2π)/1691 weeks
158.16123 .11738 (158*2π)/1691 weeks
159-.07135 .25751 (159*2π)/1691 weeks
160-.11217 .31273 (160*2π)/1691 weeks
161.19024 .62425 (161*2π)/1691 weeks
162.08702 .36058 (162*2π)/1691 weeks
163.18242 .26028 (163*2π)/1691 weeks
164.29532 .78861 (164*2π)/1691 weeks
165-.33597 .55326 (165*2π)/1691 weeks
166-.48275 .50582 (166*2π)/1691 weeks
167-.72196 2.55376 (167*2π)/1691 weeks

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