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Fourier Analysis of EZU (iShares MSCI Eurozone ETF)


EZU (iShares MSCI Eurozone ETF) appears to have interesting cyclic behaviour every 4 weeks (.5008*sine), 5 weeks (.4835*sine), and 2 weeks (.4234*cosine).

EZU (iShares MSCI Eurozone ETF) has an average price of 33.59 (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 EZU (iShares MSCI Eurozone ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
033.59361   0 
11.19723 -1.45583 (1*2π)/5959 weeks
2.59191 -1.33848 (2*2π)/5930 weeks
3.21694 -2.01486 (3*2π)/5920 weeks
4.22235 -.99598 (4*2π)/5915 weeks
5-.23373 -.97265 (5*2π)/5912 weeks
6.002 -.6729 (6*2π)/5910 weeks
7-.38727 -.26526 (7*2π)/598 weeks
8-.32055 -.16492 (8*2π)/597 weeks
9-.14776 .03625 (9*2π)/597 weeks
10-.31478 -.14722 (10*2π)/596 weeks
11-.04532 -.4835 (11*2π)/595 weeks
12.04937 -.30212 (12*2π)/595 weeks
13-.09876 -.26406 (13*2π)/595 weeks
14-.30344 -.50078 (14*2π)/594 weeks
15-.36831 -.26503 (15*2π)/594 weeks
16-.20839 -.09137 (16*2π)/594 weeks
17-.29763 -.15057 (17*2π)/593 weeks
18-.22182 -.01775 (18*2π)/593 weeks
19-.0487 -.06458 (19*2π)/593 weeks
20.01069 .10251 (20*2π)/593 weeks
21-.01043 -.13665 (21*2π)/593 weeks
22-.21415 -.06644 (22*2π)/593 weeks
23-.19945 -.1113 (23*2π)/593 weeks
24-.21318 -.14856 (24*2π)/592 weeks
25-.26635 .04418 (25*2π)/592 weeks
26-.42345 .02234 (26*2π)/592 weeks
27-.09327 .07152 (27*2π)/592 weeks
28-.09206 .11339 (28*2π)/592 weeks
29-.03569 -.15611 (29*2π)/592 weeks
30-.03569 .15611 (30*2π)/592 weeks
31-.09206 -.11339 (31*2π)/592 weeks
32-.09327 -.07152 (32*2π)/592 weeks
33-.42345 -.02234 (33*2π)/592 weeks
34-.26635 -.04418 (34*2π)/592 weeks
35-.21318 .14856 (35*2π)/592 weeks
36-.19945 .1113 (36*2π)/592 weeks
37-.21415 .06644 (37*2π)/592 weeks
38-.01043 .13665 (38*2π)/592 weeks
39.01069 -.10251 (39*2π)/592 weeks
40-.0487 .06458 (40*2π)/591 weeks
41-.22182 .01775 (41*2π)/591 weeks
42-.29763 .15057 (42*2π)/591 weeks
43-.20839 .09137 (43*2π)/591 weeks
44-.36831 .26503 (44*2π)/591 weeks
45-.30344 .50078 (45*2π)/591 weeks
46-.09876 .26406 (46*2π)/591 weeks
47.04937 .30212 (47*2π)/591 weeks
48-.04532 .4835 (48*2π)/591 weeks
49-.31478 .14722 (49*2π)/591 weeks
50-.14776 -.03625 (50*2π)/591 weeks
51-.32055 .16492 (51*2π)/591 weeks
52-.38727 .26526 (52*2π)/591 weeks
53.002 .6729 (53*2π)/591 weeks
54-.23373 .97265 (54*2π)/591 weeks
55.22235 .99598 (55*2π)/591 weeks
56.21694 2.01486 (56*2π)/591 weeks
57.59191 1.33848 (57*2π)/591 weeks



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