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# Fourier Analysis of CTBK (City Bank)

CTBK (City Bank) appears to have interesting cyclic behaviour every 19 weeks (.016*sine), 11 weeks (.0155*sine), and 15 weeks (.0123*sine).

CTBK (City Bank) has an average price of .1 (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 5/28/2010 to 6/4/2018 for CTBK (City Bank), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0.09795   0
1.01099 .11159 (1*2π)/189189 weeks
2-.01496 -.00622 (2*2π)/18995 weeks
3.03985 .02922 (3*2π)/18963 weeks
4.00025 .02008 (4*2π)/18947 weeks
5.01362 .01703 (5*2π)/18938 weeks
6-.00402 .02302 (6*2π)/18932 weeks
7.00769 .00365 (7*2π)/18927 weeks
8.00674 .01913 (8*2π)/18924 weeks
9-.00004 .01275 (9*2π)/18921 weeks
10.00038 .01599 (10*2π)/18919 weeks
11-.00473 .0017 (11*2π)/18917 weeks
12.01086 .00504 (12*2π)/18916 weeks
13-.00379 .01235 (13*2π)/18915 weeks
14.0022 .00687 (14*2π)/18914 weeks
15-.00535 .00259 (15*2π)/18913 weeks
16.00734 -.00138 (16*2π)/18912 weeks
17.00703 .01552 (17*2π)/18911 weeks
18-.00489 .00443 (18*2π)/18911 weeks
19.00011 .00008 (19*2π)/18910 weeks
20.00634 .00425 (20*2π)/1899 weeks
21.00445 .00912 (21*2π)/1899 weeks
22-.00489 .0069 (22*2π)/1899 weeks
23.00037 .00061 (23*2π)/1898 weeks
24.00344 .00272 (24*2π)/1898 weeks
25.00283 .00527 (25*2π)/1898 weeks
26-.00243 .00691 (26*2π)/1897 weeks
27-.00291 -.00172 (27*2π)/1897 weeks
28.00543 .00155 (28*2π)/1897 weeks
29.0015 .00284 (29*2π)/1897 weeks
30-.00117 .00472 (30*2π)/1896 weeks
31-.00165 .00105 (31*2π)/1896 weeks
32.00479 -.00038 (32*2π)/1896 weeks
33.00244 .00463 (33*2π)/1896 weeks
34.00101 .00423 (34*2π)/1896 weeks
35-.00004 .00049 (35*2π)/1895 weeks
36.00161 .00027 (36*2π)/1895 weeks
37.0037 .00267 (37*2π)/1895 weeks
38-.00246 .00507 (38*2π)/1895 weeks
39-.0004 -.00033 (39*2π)/1895 weeks
40.00275 .00321 (40*2π)/1895 weeks
41-.00044 .00119 (41*2π)/1895 weeks
42.00063 .0031 (42*2π)/1895 weeks
43.00037 .00151 (43*2π)/1894 weeks
44.00137 .00159 (44*2π)/1894 weeks
45.00083 -.00032 (45*2π)/1894 weeks
46.00087 .00149 (46*2π)/1894 weeks
47-.00125 .00079 (47*2π)/1894 weeks
48.00237 .00197 (48*2π)/1894 weeks
49-.00152 .00157 (49*2π)/1894 weeks
50.00216 -.00074 (50*2π)/1894 weeks
51.00339 .00255 (51*2π)/1894 weeks
52-.00139 .00065 (52*2π)/1894 weeks
53.00115 -.00062 (53*2π)/1894 weeks
54.0018 -.00041 (54*2π)/1894 weeks
55.003 .00097 (55*2π)/1893 weeks
56-.00171 .00256 (56*2π)/1893 weeks
57.00167 -.0029 (57*2π)/1893 weeks
58.00324 .00205 (58*2π)/1893 weeks
59.00041 .00115 (59*2π)/1893 weeks
60.0016 .00117 (60*2π)/1893 weeks
61.00296 .0007 (61*2π)/1893 weeks
62.00252 .00045 (62*2π)/1893 weeks
63-.00024 -.00211 (63*2π)/1893 weeks
64.00402 .00225 (64*2π)/1893 weeks
65-.00167 .0039 (65*2π)/1893 weeks
66.00106 -.00475 (66*2π)/1893 weeks
67.00448 .00374 (67*2π)/1893 weeks
68-.00038 .00219 (68*2π)/1893 weeks
69.00131 -.00099 (69*2π)/1893 weeks
70.0007 .00026 (70*2π)/1893 weeks
71.00392 .00158 (71*2π)/1893 weeks
72.00018 .00109 (72*2π)/1893 weeks
73.00221 -.00105 (73*2π)/1893 weeks
74.00106 .00114 (74*2π)/1893 weeks
75.00185 .00063 (75*2π)/1893 weeks
76.00124 -.00103 (76*2π)/1892 weeks
77.00315 .00138 (77*2π)/1892 weeks
78-.00046 .00298 (78*2π)/1892 weeks
79.00224 -.00382 (79*2π)/1892 weeks
80.00373 .00061 (80*2π)/1892 weeks
81-.00122 .00385 (81*2π)/1892 weeks
82.00203 .00022 (82*2π)/1892 weeks
83.00316 -.0011 (83*2π)/1892 weeks
84.00187 .00171 (84*2π)/1892 weeks
85.0023 .00195 (85*2π)/1892 weeks
86.0018 -.00093 (86*2π)/1892 weeks
87.00082 .00014 (87*2π)/1892 weeks
88.00038 -.00018 (88*2π)/1892 weeks
89.00281 .00225 (89*2π)/1892 weeks
90-.00102 .00009 (90*2π)/1892 weeks
91-.00039 .00058 (91*2π)/1892 weeks
92-.00067 .00152 (92*2π)/1892 weeks
93.00505 .00007 (93*2π)/1892 weeks
94-.00132 .00334 (94*2π)/1892 weeks
95-.00132 -.00334 (95*2π)/1892 weeks
96.00505 -.00007 (96*2π)/1892 weeks
97-.00067 -.00152 (97*2π)/1892 weeks
98-.00039 -.00058 (98*2π)/1892 weeks
99-.00102 -.00009 (99*2π)/1892 weeks
100.00281 -.00225 (100*2π)/1892 weeks
101.00038 .00018 (101*2π)/1892 weeks
102.00082 -.00014 (102*2π)/1892 weeks
103.0018 .00093 (103*2π)/1892 weeks
104.0023 -.00195 (104*2π)/1892 weeks
105.00187 -.00171 (105*2π)/1892 weeks
106.00316 .0011 (106*2π)/1892 weeks
107.00203 -.00022 (107*2π)/1892 weeks
108-.00122 -.00385 (108*2π)/1892 weeks
109.00373 -.00061 (109*2π)/1892 weeks
110.00224 .00382 (110*2π)/1892 weeks
111-.00046 -.00298 (111*2π)/1892 weeks
112.00315 -.00138 (112*2π)/1892 weeks
113.00124 .00103 (113*2π)/1892 weeks
114.00185 -.00063 (114*2π)/1892 weeks
115.00106 -.00114 (115*2π)/1892 weeks
116.00221 .00105 (116*2π)/1892 weeks
117.00018 -.00109 (117*2π)/1892 weeks
118.00392 -.00158 (118*2π)/1892 weeks
119.0007 -.00026 (119*2π)/1892 weeks
120.00131 .00099 (120*2π)/1892 weeks
121-.00038 -.00219 (121*2π)/1892 weeks
122.00448 -.00374 (122*2π)/1892 weeks
123.00106 .00475 (123*2π)/1892 weeks
124-.00167 -.0039 (124*2π)/1892 weeks
125.00402 -.00225 (125*2π)/1892 weeks
126-.00024 .00211 (126*2π)/1892 weeks
127.00252 -.00045 (127*2π)/1891 weeks
128.00296 -.0007 (128*2π)/1891 weeks
129.0016 -.00117 (129*2π)/1891 weeks
130.00041 -.00115 (130*2π)/1891 weeks
131.00324 -.00205 (131*2π)/1891 weeks
132.00167 .0029 (132*2π)/1891 weeks
133-.00171 -.00256 (133*2π)/1891 weeks
134.003 -.00097 (134*2π)/1891 weeks
135.0018 .00041 (135*2π)/1891 weeks
136.00115 .00062 (136*2π)/1891 weeks
137-.00139 -.00065 (137*2π)/1891 weeks
138.00339 -.00255 (138*2π)/1891 weeks
139.00216 .00074 (139*2π)/1891 weeks
140-.00152 -.00157 (140*2π)/1891 weeks
141.00237 -.00197 (141*2π)/1891 weeks
142-.00125 -.00079 (142*2π)/1891 weeks
143.00087 -.00149 (143*2π)/1891 weeks
144.00083 .00032 (144*2π)/1891 weeks
145.00137 -.00159 (145*2π)/1891 weeks
146.00037 -.00151 (146*2π)/1891 weeks
147.00063 -.0031 (147*2π)/1891 weeks
148-.00044 -.00119 (148*2π)/1891 weeks
149.00275 -.00321 (149*2π)/1891 weeks
150-.0004 .00033 (150*2π)/1891 weeks
151-.00246 -.00507 (151*2π)/1891 weeks
152.0037 -.00267 (152*2π)/1891 weeks
153.00161 -.00027 (153*2π)/1891 weeks
154-.00004 -.00049 (154*2π)/1891 weeks
155.00101 -.00423 (155*2π)/1891 weeks
156.00244 -.00463 (156*2π)/1891 weeks
157.00479 .00038 (157*2π)/1891 weeks
158-.00165 -.00105 (158*2π)/1891 weeks
159-.00117 -.00472 (159*2π)/1891 weeks
160.0015 -.00284 (160*2π)/1891 weeks
161.00543 -.00155 (161*2π)/1891 weeks
162-.00291 .00172 (162*2π)/1891 weeks
163-.00243 -.00691 (163*2π)/1891 weeks
164.00283 -.00527 (164*2π)/1891 weeks
165.00344 -.00272 (165*2π)/1891 weeks
166.00037 -.00061 (166*2π)/1891 weeks
167-.00489 -.0069 (167*2π)/1891 weeks
168.00445 -.00912 (168*2π)/1891 weeks
169.00634 -.00425 (169*2π)/1891 weeks
170.00011 -.00008 (170*2π)/1891 weeks
171-.00489 -.00443 (171*2π)/1891 weeks
172.00703 -.01552 (172*2π)/1891 weeks
173.00734 .00138 (173*2π)/1891 weeks
174-.00535 -.00259 (174*2π)/1891 weeks
175.0022 -.00687 (175*2π)/1891 weeks
176-.00379 -.01235 (176*2π)/1891 weeks
177.01086 -.00504 (177*2π)/1891 weeks
178-.00473 -.0017 (178*2π)/1891 weeks
179.00038 -.01599 (179*2π)/1891 weeks
180-.00004 -.01275 (180*2π)/1891 weeks
181.00674 -.01913 (181*2π)/1891 weeks
182.00769 -.00365 (182*2π)/1891 weeks
183-.00402 -.02302 (183*2π)/1891 weeks
184.01362 -.01703 (184*2π)/1891 weeks
185.00025 -.02008 (185*2π)/1891 weeks
186.03985 -.02922 (186*2π)/1891 weeks
187-.01496 .00622 (187*2π)/1891 weeks