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Fourier Analysis of DAX (Recon Capital DAX Germany ETF)


DAX (Recon Capital DAX Germany ETF) appears to have interesting cyclic behaviour every 11 weeks (.296*sine), 6 weeks (.1932*sine), and 8 weeks (.1685*sine).

DAX (Recon Capital DAX Germany ETF) has an average price of 24.9 (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 10/23/2014 to 3/20/2017 for DAX (Recon Capital DAX Germany ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
024.89635   0 
11.23108 1.29839 (1*2π)/127127 weeks
2-.49391 .0189 (2*2π)/12764 weeks
3-.04419 -.27678 (3*2π)/12742 weeks
4.23755 -.42574 (4*2π)/12732 weeks
5.26049 .03276 (5*2π)/12725 weeks
6-.22705 -.56524 (6*2π)/12721 weeks
7.02523 .41671 (7*2π)/12718 weeks
8-.16999 -.02135 (8*2π)/12716 weeks
9-.00458 -.09702 (9*2π)/12714 weeks
10-.05586 .04726 (10*2π)/12713 weeks
11-.10347 .00659 (11*2π)/12712 weeks
12.03762 -.29596 (12*2π)/12711 weeks
13-.11057 -.10107 (13*2π)/12710 weeks
14-.05334 -.11021 (14*2π)/1279 weeks
15.00634 -.05428 (15*2π)/1278 weeks
16-.00443 -.16852 (16*2π)/1278 weeks
17.04077 -.08159 (17*2π)/1277 weeks
18.02512 -.0198 (18*2π)/1277 weeks
19-.01409 -.10501 (19*2π)/1277 weeks
20-.13363 -.01717 (20*2π)/1276 weeks
21.00666 -.19319 (21*2π)/1276 weeks
22-.0022 -.09101 (22*2π)/1276 weeks
23.03085 .16092 (23*2π)/1276 weeks
24-.01889 -.10897 (24*2π)/1275 weeks
25.04884 .05209 (25*2π)/1275 weeks
26-.05872 -.0665 (26*2π)/1275 weeks
27.08634 -.05305 (27*2π)/1275 weeks
28-.06436 .03123 (28*2π)/1275 weeks
29.04863 .00289 (29*2π)/1274 weeks
30-.04244 -.03772 (30*2π)/1274 weeks
31.0752 .09368 (31*2π)/1274 weeks
32-.12492 .04246 (32*2π)/1274 weeks
33.02467 -.03133 (33*2π)/1274 weeks
34-.06203 .04382 (34*2π)/1274 weeks
35-.04364 -.06218 (35*2π)/1274 weeks
36-.11061 -.04488 (36*2π)/1274 weeks
37-.04116 .00442 (37*2π)/1273 weeks
38-.03821 .05817 (38*2π)/1273 weeks
39-.01797 -.00374 (39*2π)/1273 weeks
40-.03463 -.07936 (40*2π)/1273 weeks
41-.01364 .01741 (41*2π)/1273 weeks
42-.04937 -.04634 (42*2π)/1273 weeks
43.04324 -.01539 (43*2π)/1273 weeks
44-.00637 .02873 (44*2π)/1273 weeks
45-.13256 -.00295 (45*2π)/1273 weeks
46-.02461 -.01259 (46*2π)/1273 weeks
47.00147 -.02957 (47*2π)/1273 weeks
48-.0428 -.02228 (48*2π)/1273 weeks
49-.0196 -.0046 (49*2π)/1273 weeks
50-.07031 .01371 (50*2π)/1273 weeks
51-.02431 -.00044 (51*2π)/1272 weeks
52-.01466 -.0005 (52*2π)/1272 weeks
53-.07665 -.05725 (53*2π)/1272 weeks
54-.02065 .00757 (54*2π)/1272 weeks
55.02837 .05951 (55*2π)/1272 weeks
56-.04519 .02846 (56*2π)/1272 weeks
57-.04126 -.04862 (57*2π)/1272 weeks
58.02175 -.0123 (58*2π)/1272 weeks
59-.00451 -.01361 (59*2π)/1272 weeks
60-.12999 -.02648 (60*2π)/1272 weeks
61.03356 .04092 (61*2π)/1272 weeks
62-.00809 .00236 (62*2π)/1272 weeks
63.00926 -.0385 (63*2π)/1272 weeks
64.00926 .0385 (64*2π)/1272 weeks
65-.00809 -.00236 (65*2π)/1272 weeks
66.03356 -.04092 (66*2π)/1272 weeks
67-.12999 .02648 (67*2π)/1272 weeks
68-.00451 .01361 (68*2π)/1272 weeks
69.02175 .0123 (69*2π)/1272 weeks
70-.04126 .04862 (70*2π)/1272 weeks
71-.04519 -.02846 (71*2π)/1272 weeks
72.02837 -.05951 (72*2π)/1272 weeks
73-.02065 -.00757 (73*2π)/1272 weeks
74-.07665 .05725 (74*2π)/1272 weeks
75-.01466 .0005 (75*2π)/1272 weeks
76-.02431 .00044 (76*2π)/1272 weeks
77-.07031 -.01371 (77*2π)/1272 weeks
78-.0196 .0046 (78*2π)/1272 weeks
79-.0428 .02228 (79*2π)/1272 weeks
80.00147 .02957 (80*2π)/1272 weeks
81-.02461 .01259 (81*2π)/1272 weeks
82-.13256 .00295 (82*2π)/1272 weeks
83-.00637 -.02873 (83*2π)/1272 weeks
84.04324 .01539 (84*2π)/1272 weeks
85-.04937 .04634 (85*2π)/1271 weeks
86-.01364 -.01741 (86*2π)/1271 weeks
87-.03463 .07936 (87*2π)/1271 weeks
88-.01797 .00374 (88*2π)/1271 weeks
89-.03821 -.05817 (89*2π)/1271 weeks
90-.04116 -.00442 (90*2π)/1271 weeks
91-.11061 .04488 (91*2π)/1271 weeks
92-.04364 .06218 (92*2π)/1271 weeks
93-.06203 -.04382 (93*2π)/1271 weeks
94.02467 .03133 (94*2π)/1271 weeks
95-.12492 -.04246 (95*2π)/1271 weeks
96.0752 -.09368 (96*2π)/1271 weeks
97-.04244 .03772 (97*2π)/1271 weeks
98.04863 -.00289 (98*2π)/1271 weeks
99-.06436 -.03123 (99*2π)/1271 weeks
100.08634 .05305 (100*2π)/1271 weeks
101-.05872 .0665 (101*2π)/1271 weeks
102.04884 -.05209 (102*2π)/1271 weeks
103-.01889 .10897 (103*2π)/1271 weeks
104.03085 -.16092 (104*2π)/1271 weeks
105-.0022 .09101 (105*2π)/1271 weeks
106.00666 .19319 (106*2π)/1271 weeks
107-.13363 .01717 (107*2π)/1271 weeks
108-.01409 .10501 (108*2π)/1271 weeks
109.02512 .0198 (109*2π)/1271 weeks
110.04077 .08159 (110*2π)/1271 weeks
111-.00443 .16852 (111*2π)/1271 weeks
112.00634 .05428 (112*2π)/1271 weeks
113-.05334 .11021 (113*2π)/1271 weeks
114-.11057 .10107 (114*2π)/1271 weeks
115.03762 .29596 (115*2π)/1271 weeks
116-.10347 -.00659 (116*2π)/1271 weeks
117-.05586 -.04726 (117*2π)/1271 weeks
118-.00458 .09702 (118*2π)/1271 weeks
119-.16999 .02135 (119*2π)/1271 weeks
120.02523 -.41671 (120*2π)/1271 weeks
121-.22705 .56524 (121*2π)/1271 weeks
122.26049 -.03276 (122*2π)/1271 weeks
123.23755 .42574 (123*2π)/1271 weeks
124-.04419 .27678 (124*2π)/1271 weeks
125-.49391 -.0189 (125*2π)/1271 weeks

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