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# Fourier Analysis of AZSEY (Allianz SE)

AZSEY (Allianz SE) appears to have interesting cyclic behaviour every 12 weeks (.3279*sine), 12 weeks (.2529*cosine), and 8 weeks (.1556*cosine).

AZSEY (Allianz SE) has an average price of 17.79 (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 1/4/2016 to 5/21/2018 for AZSEY (Allianz SE), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
017.79398   0
1.63324 -4.9717 (1*2π)/121121 weeks
2-.24339 -1.19431 (2*2π)/12161 weeks
3-.17504 -.6586 (3*2π)/12140 weeks
4-.33041 -.61703 (4*2π)/12130 weeks
5-.04225 -.64692 (5*2π)/12124 weeks
6.05549 -.5766 (6*2π)/12120 weeks
7.21522 -.51109 (7*2π)/12117 weeks
8.11086 -.3777 (8*2π)/12115 weeks
9-.13169 -.40087 (9*2π)/12113 weeks
10-.25285 -.32792 (10*2π)/12112 weeks
11-.02089 -.14501 (11*2π)/12111 weeks
12-.03798 -.21739 (12*2π)/12110 weeks
13.01853 -.04185 (13*2π)/1219 weeks
14-.04895 -.22193 (14*2π)/1219 weeks
15-.12747 -.11524 (15*2π)/1218 weeks
16-.15562 -.14453 (16*2π)/1218 weeks
17-.07317 .02748 (17*2π)/1217 weeks
18-.05465 -.00343 (18*2π)/1217 weeks
19-.00418 .00504 (19*2π)/1216 weeks
20-.07372 -.1103 (20*2π)/1216 weeks
21-.14728 -.15206 (21*2π)/1216 weeks
22-.11531 -.18699 (22*2π)/1216 weeks
23-.11898 -.10667 (23*2π)/1215 weeks
24-.00707 -.12714 (24*2π)/1215 weeks
25-.04513 -.01509 (25*2π)/1215 weeks
26-.01969 -.02894 (26*2π)/1215 weeks
27-.12736 -.05778 (27*2π)/1214 weeks
28-.06812 -.05626 (28*2π)/1214 weeks
29-.12993 -.10117 (29*2π)/1214 weeks
30-.0668 -.05915 (30*2π)/1214 weeks
31-.05305 -.07274 (31*2π)/1214 weeks
32-.02567 -.03364 (32*2π)/1214 weeks
33.00606 -.01467 (33*2π)/1214 weeks
34-.05628 -.0401 (34*2π)/1214 weeks
35-.0892 -.11409 (35*2π)/1213 weeks
36-.02098 -.03696 (36*2π)/1213 weeks
37-.07532 -.10647 (37*2π)/1213 weeks
38-.1352 -.01434 (38*2π)/1213 weeks
39-.05265 .00947 (39*2π)/1213 weeks
40-.00455 -.01227 (40*2π)/1213 weeks
41.00082 .04571 (41*2π)/1213 weeks
42-.01886 -.05324 (42*2π)/1213 weeks
43-.03816 -.05929 (43*2π)/1213 weeks
44-.0452 -.02373 (44*2π)/1213 weeks
45-.10225 .0009 (45*2π)/1213 weeks
46-.1448 -.0654 (46*2π)/1213 weeks
47-.06406 .01186 (47*2π)/1213 weeks
48-.07688 .01414 (48*2π)/1213 weeks
49-.08185 -.01426 (49*2π)/1212 weeks
50-.03148 -.01461 (50*2π)/1212 weeks
51-.05968 .01158 (51*2π)/1212 weeks
52-.06162 .01211 (52*2π)/1212 weeks
53-.08903 .00666 (53*2π)/1212 weeks
54-.07756 -.03105 (54*2π)/1212 weeks
55-.08838 -.0107 (55*2π)/1212 weeks
56-.009 .00073 (56*2π)/1212 weeks
57-.04873 .00892 (57*2π)/1212 weeks
58-.04418 .00492 (58*2π)/1212 weeks
59-.10824 -.05473 (59*2π)/1212 weeks
60-.04963 -.04042 (60*2π)/1212 weeks
61-.04963 .04042 (61*2π)/1212 weeks
62-.10824 .05473 (62*2π)/1212 weeks
63-.04418 -.00492 (63*2π)/1212 weeks
64-.04873 -.00892 (64*2π)/1212 weeks
65-.009 -.00073 (65*2π)/1212 weeks
66-.08838 .0107 (66*2π)/1212 weeks
67-.07756 .03105 (67*2π)/1212 weeks
68-.08903 -.00666 (68*2π)/1212 weeks
69-.06162 -.01211 (69*2π)/1212 weeks
70-.05968 -.01158 (70*2π)/1212 weeks
71-.03148 .01461 (71*2π)/1212 weeks
72-.08185 .01426 (72*2π)/1212 weeks
73-.07688 -.01414 (73*2π)/1212 weeks
74-.06406 -.01186 (74*2π)/1212 weeks
75-.1448 .0654 (75*2π)/1212 weeks
76-.10225 -.0009 (76*2π)/1212 weeks
77-.0452 .02373 (77*2π)/1212 weeks
78-.03816 .05929 (78*2π)/1212 weeks
79-.01886 .05324 (79*2π)/1212 weeks
80.00082 -.04571 (80*2π)/1212 weeks
81-.00455 .01227 (81*2π)/1211 weeks
82-.05265 -.00947 (82*2π)/1211 weeks
83-.1352 .01434 (83*2π)/1211 weeks
84-.07532 .10647 (84*2π)/1211 weeks
85-.02098 .03696 (85*2π)/1211 weeks
86-.0892 .11409 (86*2π)/1211 weeks
87-.05628 .0401 (87*2π)/1211 weeks
88.00606 .01467 (88*2π)/1211 weeks
89-.02567 .03364 (89*2π)/1211 weeks
90-.05305 .07274 (90*2π)/1211 weeks
91-.0668 .05915 (91*2π)/1211 weeks
92-.12993 .10117 (92*2π)/1211 weeks
93-.06812 .05626 (93*2π)/1211 weeks
94-.12736 .05778 (94*2π)/1211 weeks
95-.01969 .02894 (95*2π)/1211 weeks
96-.04513 .01509 (96*2π)/1211 weeks
97-.00707 .12714 (97*2π)/1211 weeks
98-.11898 .10667 (98*2π)/1211 weeks
99-.11531 .18699 (99*2π)/1211 weeks
100-.14728 .15206 (100*2π)/1211 weeks
101-.07372 .1103 (101*2π)/1211 weeks
102-.00418 -.00504 (102*2π)/1211 weeks
103-.05465 .00343 (103*2π)/1211 weeks
104-.07317 -.02748 (104*2π)/1211 weeks
105-.15562 .14453 (105*2π)/1211 weeks
106-.12747 .11524 (106*2π)/1211 weeks
107-.04895 .22193 (107*2π)/1211 weeks
108.01853 .04185 (108*2π)/1211 weeks
109-.03798 .21739 (109*2π)/1211 weeks
110-.02089 .14501 (110*2π)/1211 weeks
111-.25285 .32792 (111*2π)/1211 weeks
112-.13169 .40087 (112*2π)/1211 weeks
113.11086 .3777 (113*2π)/1211 weeks
114.21522 .51109 (114*2π)/1211 weeks
115.05549 .5766 (115*2π)/1211 weeks
116-.04225 .64692 (116*2π)/1211 weeks
117-.33041 .61703 (117*2π)/1211 weeks
118-.17504 .6586 (118*2π)/1211 weeks
119-.24339 1.19431 (119*2π)/1211 weeks