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Fourier Analysis of NOBL (ProShares S&P 500 Dividend Aristocrats ETF)


NOBL (ProShares S&P 500 Dividend Aristocrats ETF) appears to have interesting cyclic behaviour every 6 weeks (.5303*cosine), 4 weeks (.4692*sine), and 5 weeks (.4379*sine).

NOBL (ProShares S&P 500 Dividend Aristocrats ETF) has an average price of 52.58 (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 1/4/2016 to 7/17/2017 for NOBL (ProShares S&P 500 Dividend Aristocrats ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
052.58197   0 
1-1.16202 -1.85482 (1*2π)/5858 weeks
2.30518 -2.1201 (2*2π)/5829 weeks
3-.80005 -1.76449 (3*2π)/5819 weeks
4.13678 -1.3802 (4*2π)/5815 weeks
5-.21805 -1.04365 (5*2π)/5812 weeks
6-.43345 -.89562 (6*2π)/5810 weeks
7-.47661 -.30308 (7*2π)/588 weeks
8-.19797 -.27233 (8*2π)/587 weeks
9-.09471 -.40199 (9*2π)/586 weeks
10-.5303 -.24543 (10*2π)/586 weeks
11.07825 -.39222 (11*2π)/585 weeks
12-.1098 -.43794 (12*2π)/585 weeks
13-.33215 -.46919 (13*2π)/584 weeks
14-.21559 -.40943 (14*2π)/584 weeks
15-.32415 -.26112 (15*2π)/584 weeks
16-.18243 -.24829 (16*2π)/584 weeks
17-.31471 -.20224 (17*2π)/583 weeks
18-.19005 -.01265 (18*2π)/583 weeks
19.01797 -.10648 (19*2π)/583 weeks
20-.17428 -.07096 (20*2π)/583 weeks
21-.08652 -.13418 (21*2π)/583 weeks
22-.19981 -.11508 (22*2π)/583 weeks
23-.23945 -.21575 (23*2π)/583 weeks
24-.26902 -.1049 (24*2π)/582 weeks
25-.32408 .1532 (25*2π)/582 weeks
26-.28975 -.00563 (26*2π)/582 weeks
27-.23509 .04181 (27*2π)/582 weeks
28-.14453 -.03019 (28*2π)/582 weeks
29-.12299   (29*2π)/582 weeks
30-.14453 .03019 (30*2π)/582 weeks
31-.23509 -.04181 (31*2π)/582 weeks
32-.28975 .00563 (32*2π)/582 weeks
33-.32408 -.1532 (33*2π)/582 weeks
34-.26902 .1049 (34*2π)/582 weeks
35-.23945 .21575 (35*2π)/582 weeks
36-.19981 .11508 (36*2π)/582 weeks
37-.08652 .13418 (37*2π)/582 weeks
38-.17428 .07096 (38*2π)/582 weeks
39.01797 .10648 (39*2π)/581 weeks
40-.19005 .01265 (40*2π)/581 weeks
41-.31471 .20224 (41*2π)/581 weeks
42-.18243 .24829 (42*2π)/581 weeks
43-.32415 .26112 (43*2π)/581 weeks
44-.21559 .40943 (44*2π)/581 weeks
45-.33215 .46919 (45*2π)/581 weeks
46-.1098 .43794 (46*2π)/581 weeks
47.07825 .39222 (47*2π)/581 weeks
48-.5303 .24543 (48*2π)/581 weeks
49-.09471 .40199 (49*2π)/581 weeks
50-.19797 .27233 (50*2π)/581 weeks
51-.47661 .30308 (51*2π)/581 weeks
52-.43345 .89562 (52*2π)/581 weeks
53-.21805 1.04365 (53*2π)/581 weeks
54.13678 1.3802 (54*2π)/581 weeks
55-.80005 1.76449 (55*2π)/581 weeks
56.30518 2.1201 (56*2π)/581 weeks



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