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# Fourier Analysis of JPST (JPMorgan Ultra-Short Income ETF)

JPST (JPMorgan Ultra-Short Income ETF) appears to have interesting cyclic behaviour every 5 weeks (.0239*sine), 6 weeks (.0234*sine), and 5 weeks (.0219*cosine).

JPST (JPMorgan Ultra-Short Income ETF) has an average price of 49.64 (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 5/19/2017 to 6/4/2018 for JPST (JPMorgan Ultra-Short Income ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
049.64166   0
1-.01892 -.27034 (1*2π)/5656 weeks
2.00096 -.15492 (2*2π)/5628 weeks
3-.00707 -.10751 (3*2π)/5619 weeks
4-.01247 -.08191 (4*2π)/5614 weeks
5-.01794 -.04996 (5*2π)/5611 weeks
6-.02131 -.04754 (6*2π)/569 weeks
7-.01669 -.04729 (7*2π)/568 weeks
8-.01745 -.0326 (8*2π)/567 weeks
9-.01957 -.03757 (9*2π)/566 weeks
10-.01603 -.02341 (10*2π)/566 weeks
11-.0158 -.01778 (11*2π)/565 weeks
12-.02187 -.02391 (12*2π)/565 weeks
13-.01305 -.02283 (13*2π)/564 weeks
14-.01458 -.00941 (14*2π)/564 weeks
15-.02074 -.01538 (15*2π)/564 weeks
16-.01244 -.01116 (16*2π)/564 weeks
17-.02038 -.0082 (17*2π)/563 weeks
18-.01907 -.01873 (18*2π)/563 weeks
19-.01206 -.00832 (19*2π)/563 weeks
20-.01711 -.00582 (20*2π)/563 weeks
21-.01641 -.00756 (21*2π)/563 weeks
22-.01718 -.00595 (22*2π)/563 weeks
23-.01547 -.00035 (23*2π)/562 weeks
24-.01372 -.00705 (24*2π)/562 weeks
25-.01476 -.00447 (25*2π)/562 weeks
26-.01685 .00297 (26*2π)/562 weeks
27-.01818 -.00468 (27*2π)/562 weeks
28-.0188   (28*2π)/562 weeks
29-.01818 .00468 (29*2π)/562 weeks
30-.01685 -.00297 (30*2π)/562 weeks
31-.01476 .00447 (31*2π)/562 weeks
32-.01372 .00705 (32*2π)/562 weeks
33-.01547 .00035 (33*2π)/562 weeks
34-.01718 .00595 (34*2π)/562 weeks
35-.01641 .00756 (35*2π)/562 weeks
36-.01711 .00582 (36*2π)/562 weeks
37-.01206 .00832 (37*2π)/562 weeks
38-.01907 .01873 (38*2π)/561 weeks
39-.02038 .0082 (39*2π)/561 weeks
40-.01244 .01116 (40*2π)/561 weeks
41-.02074 .01538 (41*2π)/561 weeks
42-.01458 .00941 (42*2π)/561 weeks
43-.01305 .02283 (43*2π)/561 weeks
44-.02187 .02391 (44*2π)/561 weeks
45-.0158 .01778 (45*2π)/561 weeks
46-.01603 .02341 (46*2π)/561 weeks
47-.01957 .03757 (47*2π)/561 weeks
48-.01745 .0326 (48*2π)/561 weeks
49-.01669 .04729 (49*2π)/561 weeks
50-.02131 .04754 (50*2π)/561 weeks
51-.01794 .04996 (51*2π)/561 weeks
52-.01247 .08191 (52*2π)/561 weeks
53-.00707 .10751 (53*2π)/561 weeks
54.00096 .15492 (54*2π)/561 weeks