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# Fourier Analysis of JESVX (John Hancock Variable Insurace Tr Small)

JESVX (John Hancock Variable Insurace Tr Small) appears to have interesting cyclic behaviour every 6 weeks (.1347*sine), 7 weeks (.094*cosine), and 5 weeks (.0884*cosine).

JESVX (John Hancock Variable Insurace Tr Small) has an average price of 20.3 (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 2/1/2017 to 6/4/2018 for JESVX (John Hancock Variable Insurace Tr Small), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
020.30216   0
1.53162 .28972 (1*2π)/7171 weeks
2-.11067 .45984 (2*2π)/7136 weeks
3.40667 -.18687 (3*2π)/7124 weeks
4.18565 .10586 (4*2π)/7118 weeks
5-.10577 -.10145 (5*2π)/7114 weeks
6.2295 .10675 (6*2π)/7112 weeks
7-.11671 .00845 (7*2π)/7110 weeks
8.06584 -.05463 (8*2π)/719 weeks
9-.0986 .16803 (9*2π)/718 weeks
10.09401 -.07536 (10*2π)/717 weeks
11.03509 -.13468 (11*2π)/716 weeks
12-.07949 .02956 (12*2π)/716 weeks
13-.01837 .08831 (13*2π)/715 weeks
14-.08837 .04442 (14*2π)/715 weeks
15-.02782 -.05495 (15*2π)/715 weeks
16.02553 -.02601 (16*2π)/714 weeks
17.05948 .02331 (17*2π)/714 weeks
18-.00302 -.06359 (18*2π)/714 weeks
19-.06942 -.00276 (19*2π)/714 weeks
20.00983 .01773 (20*2π)/714 weeks
21.01809 .01474 (21*2π)/713 weeks
22.00061 -.07493 (22*2π)/713 weeks
23-.01503 -.07836 (23*2π)/713 weeks
24-.03374 .04068 (24*2π)/713 weeks
25.04122 .06735 (25*2π)/713 weeks
26.07168 .01617 (26*2π)/713 weeks
27-.00605 .01118 (27*2π)/713 weeks
28.00067 .02222 (28*2π)/713 weeks
29-.06572 .03264 (29*2π)/712 weeks
30-.02327 -.0284 (30*2π)/712 weeks
31.0046 .0189 (31*2π)/712 weeks
32-.03886 -.03534 (32*2π)/712 weeks
33.07289 -.03965 (33*2π)/712 weeks
34-.01991 -.01354 (34*2π)/712 weeks
35.00319 -.04342 (35*2π)/712 weeks
36.00319 .04342 (36*2π)/712 weeks
37-.01991 .01354 (37*2π)/712 weeks
38.07289 .03965 (38*2π)/712 weeks
39-.03886 .03534 (39*2π)/712 weeks
40.0046 -.0189 (40*2π)/712 weeks
41-.02327 .0284 (41*2π)/712 weeks
42-.06572 -.03264 (42*2π)/712 weeks
43.00067 -.02222 (43*2π)/712 weeks
44-.00605 -.01118 (44*2π)/712 weeks
45.07168 -.01617 (45*2π)/712 weeks
46.04122 -.06735 (46*2π)/712 weeks
47-.03374 -.04068 (47*2π)/712 weeks
48-.01503 .07836 (48*2π)/711 weeks
49.00061 .07493 (49*2π)/711 weeks
50.01809 -.01474 (50*2π)/711 weeks
51.00983 -.01773 (51*2π)/711 weeks
52-.06942 .00276 (52*2π)/711 weeks
53-.00302 .06359 (53*2π)/711 weeks
54.05948 -.02331 (54*2π)/711 weeks
55.02553 .02601 (55*2π)/711 weeks
56-.02782 .05495 (56*2π)/711 weeks
57-.08837 -.04442 (57*2π)/711 weeks
58-.01837 -.08831 (58*2π)/711 weeks
59-.07949 -.02956 (59*2π)/711 weeks
60.03509 .13468 (60*2π)/711 weeks
61.09401 .07536 (61*2π)/711 weeks
62-.0986 -.16803 (62*2π)/711 weeks
63.06584 .05463 (63*2π)/711 weeks
64-.11671 -.00845 (64*2π)/711 weeks
65.2295 -.10675 (65*2π)/711 weeks
66-.10577 .10145 (66*2π)/711 weeks
67.18565 -.10586 (67*2π)/711 weeks
68.40667 .18687 (68*2π)/711 weeks
69-.11067 -.45984 (69*2π)/711 weeks