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# Fourier Analysis of CST (CST Brands, Inc. Common Stock)

CST (CST Brands, Inc. Common Stock) appears to have interesting cyclic behaviour every 21 weeks (.8044*sine), 12 weeks (.7009*sine), and 13 weeks (.629*sine).

CST (CST Brands, Inc. Common Stock) has an average price of 37.94 (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 4/17/2013 to 3/20/2017 for CST (CST Brands, Inc. Common Stock), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
037.93591   0
1.10691 -4.42629 (1*2π)/206206 weeks
22.8742 -5.14612 (2*2π)/206103 weeks
3-1.82662 -1.38625 (3*2π)/20669 weeks
4-.25371 -2.25333 (4*2π)/20652 weeks
5-.43332 -.55275 (5*2π)/20641 weeks
6.53854 -.72068 (6*2π)/20634 weeks
7.3043 -.87363 (7*2π)/20629 weeks
8-.83962 -.02093 (8*2π)/20626 weeks
9-.20804 -.92349 (9*2π)/20623 weeks
10-.32359 -.80437 (10*2π)/20621 weeks
11-.32286 -.51349 (11*2π)/20619 weeks
12.30392 -.59667 (12*2π)/20617 weeks
13-.34419 -.52462 (13*2π)/20616 weeks
14-.15475 -.35296 (14*2π)/20615 weeks
15-.13039 .01089 (15*2π)/20614 weeks
16.22434 -.629 (16*2π)/20613 weeks
17-.30987 -.70093 (17*2π)/20612 weeks
18-.3139 .18871 (18*2π)/20611 weeks
19-.27992 -.09318 (19*2π)/20611 weeks
20.00065 -.45339 (20*2π)/20610 weeks
21-.42852 -.51084 (21*2π)/20610 weeks
22-.03703 -.35393 (22*2π)/2069 weeks
23-.11544 -.30269 (23*2π)/2069 weeks
24-.09894 -.24662 (24*2π)/2069 weeks
25-.22642 -.16786 (25*2π)/2068 weeks
26-.14201 -.33379 (26*2π)/2068 weeks
27-.05128 -.43859 (27*2π)/2068 weeks
28-.01084 -.0817 (28*2π)/2067 weeks
29-.17498 -.18689 (29*2π)/2067 weeks
30.11201 -.19788 (30*2π)/2067 weeks
31-.28576 -.22803 (31*2π)/2067 weeks
32-.37982 -.16727 (32*2π)/2066 weeks
33.00411 .01306 (33*2π)/2066 weeks
34.08127 -.37048 (34*2π)/2066 weeks
35-.14851 -.31388 (35*2π)/2066 weeks
36-.23765 -.14213 (36*2π)/2066 weeks
37-.1029 -.08125 (37*2π)/2066 weeks
38-.08934 -.18593 (38*2π)/2065 weeks
39-.09817 -.21386 (39*2π)/2065 weeks
40-.10144 -.13062 (40*2π)/2065 weeks
41.02435 -.26758 (41*2π)/2065 weeks
42-.11756 -.18699 (42*2π)/2065 weeks
43-.25422 -.04525 (43*2π)/2065 weeks
44-.07541 -.12501 (44*2π)/2065 weeks
45.08366 -.42316 (45*2π)/2065 weeks
46-.14705 -.03113 (46*2π)/2064 weeks
47.00349 -.04407 (47*2π)/2064 weeks
48-.06305 -.15003 (48*2π)/2064 weeks
49.03016 -.2804 (49*2π)/2064 weeks
50-.23169 -.00778 (50*2π)/2064 weeks
51.00369 .00006 (51*2π)/2064 weeks
52.01811 -.10999 (52*2π)/2064 weeks
53-.08273 -.04629 (53*2π)/2064 weeks
54-.06317 -.11699 (54*2π)/2064 weeks
55-.10935 -.06154 (55*2π)/2064 weeks
56-.1521 -.09033 (56*2π)/2064 weeks
57.00119 .03204 (57*2π)/2064 weeks
58-.08664 -.03587 (58*2π)/2064 weeks
59-.02143 -.11065 (59*2π)/2063 weeks
60-.13311 -.10101 (60*2π)/2063 weeks
61-.15291 .07369 (61*2π)/2063 weeks
62-.12354 -.0304 (62*2π)/2063 weeks
63-.12876 -.03607 (63*2π)/2063 weeks
64-.00548 -.05038 (64*2π)/2063 weeks
65-.1451 -.05177 (65*2π)/2063 weeks
66-.25994 -.05797 (66*2π)/2063 weeks
67-.05155 .03348 (67*2π)/2063 weeks
68-.14453 -.19187 (68*2π)/2063 weeks
69-.15785 -.04461 (69*2π)/2063 weeks
70-.08886 .00988 (70*2π)/2063 weeks
71-.12365 -.06687 (71*2π)/2063 weeks
72-.13636 -.11981 (72*2π)/2063 weeks
73-.11975 -.04223 (73*2π)/2063 weeks
74-.10681 -.09964 (74*2π)/2063 weeks
75-.14644 -.12409 (75*2π)/2063 weeks
76-.05783 .02939 (76*2π)/2063 weeks
77-.16501 -.02894 (77*2π)/2063 weeks
78.0028 -.14014 (78*2π)/2063 weeks
79-.19136 -.10225 (79*2π)/2063 weeks
80-.10644 .00561 (80*2π)/2063 weeks
81-.0653 -.05451 (81*2π)/2063 weeks
82-.0203 -.11555 (82*2π)/2063 weeks
83-.14801 -.04795 (83*2π)/2062 weeks
84-.09306 .04482 (84*2π)/2062 weeks
85-.05844 -.07298 (85*2π)/2062 weeks
86-.16582 -.14232 (86*2π)/2062 weeks
87-.06887 -.02077 (87*2π)/2062 weeks
88.03797 -.10085 (88*2π)/2062 weeks
89-.18543 -.02345 (89*2π)/2062 weeks
90-.03418 -.01865 (90*2π)/2062 weeks
91.0462 .01776 (91*2π)/2062 weeks
92-.0565 -.03921 (92*2π)/2062 weeks
93-.20866 -.04838 (93*2π)/2062 weeks
94-.02548 -.06263 (94*2π)/2062 weeks
95-.05774 .11739 (95*2π)/2062 weeks
96.00264 .01713 (96*2π)/2062 weeks
97-.05617 .01808 (97*2π)/2062 weeks
98-.21604 -.01603 (98*2π)/2062 weeks
99-.11219 .07449 (99*2π)/2062 weeks
100-.07671 -.08368 (100*2π)/2062 weeks
101-.08675 .09121 (101*2π)/2062 weeks
102-.11094 .00773 (102*2π)/2062 weeks
103-.12336   (103*2π)/2062 weeks
104-.11094 -.00773 (104*2π)/2062 weeks
105-.08675 -.09121 (105*2π)/2062 weeks
106-.07671 .08368 (106*2π)/2062 weeks
107-.11219 -.07449 (107*2π)/2062 weeks
108-.21604 .01603 (108*2π)/2062 weeks
109-.05617 -.01808 (109*2π)/2062 weeks
110.00264 -.01713 (110*2π)/2062 weeks
111-.05774 -.11739 (111*2π)/2062 weeks
112-.02548 .06263 (112*2π)/2062 weeks
113-.20866 .04838 (113*2π)/2062 weeks
114-.0565 .03921 (114*2π)/2062 weeks
115.0462 -.01776 (115*2π)/2062 weeks
116-.03418 .01865 (116*2π)/2062 weeks
117-.18543 .02345 (117*2π)/2062 weeks
118.03797 .10085 (118*2π)/2062 weeks
119-.06887 .02077 (119*2π)/2062 weeks
120-.16582 .14232 (120*2π)/2062 weeks
121-.05844 .07298 (121*2π)/2062 weeks
122-.09306 -.04482 (122*2π)/2062 weeks
123-.14801 .04795 (123*2π)/2062 weeks
124-.0203 .11555 (124*2π)/2062 weeks
125-.0653 .05451 (125*2π)/2062 weeks
126-.10644 -.00561 (126*2π)/2062 weeks
127-.19136 .10225 (127*2π)/2062 weeks
128.0028 .14014 (128*2π)/2062 weeks
129-.16501 .02894 (129*2π)/2062 weeks
130-.05783 -.02939 (130*2π)/2062 weeks
131-.14644 .12409 (131*2π)/2062 weeks
132-.10681 .09964 (132*2π)/2062 weeks
133-.11975 .04223 (133*2π)/2062 weeks
134-.13636 .11981 (134*2π)/2062 weeks
135-.12365 .06687 (135*2π)/2062 weeks
136-.08886 -.00988 (136*2π)/2062 weeks
137-.15785 .04461 (137*2π)/2062 weeks
138-.14453 .19187 (138*2π)/2061 weeks
139-.05155 -.03348 (139*2π)/2061 weeks
140-.25994 .05797 (140*2π)/2061 weeks
141-.1451 .05177 (141*2π)/2061 weeks
142-.00548 .05038 (142*2π)/2061 weeks
143-.12876 .03607 (143*2π)/2061 weeks
144-.12354 .0304 (144*2π)/2061 weeks
145-.15291 -.07369 (145*2π)/2061 weeks
146-.13311 .10101 (146*2π)/2061 weeks
147-.02143 .11065 (147*2π)/2061 weeks
148-.08664 .03587 (148*2π)/2061 weeks
149.00119 -.03204 (149*2π)/2061 weeks
150-.1521 .09033 (150*2π)/2061 weeks
151-.10935 .06154 (151*2π)/2061 weeks
152-.06317 .11699 (152*2π)/2061 weeks
153-.08273 .04629 (153*2π)/2061 weeks
154.01811 .10999 (154*2π)/2061 weeks
155.00369 -.00006 (155*2π)/2061 weeks
156-.23169 .00778 (156*2π)/2061 weeks
157.03016 .2804 (157*2π)/2061 weeks
158-.06305 .15003 (158*2π)/2061 weeks
159.00349 .04407 (159*2π)/2061 weeks
160-.14705 .03113 (160*2π)/2061 weeks
161.08366 .42316 (161*2π)/2061 weeks
162-.07541 .12501 (162*2π)/2061 weeks
163-.25422 .04525 (163*2π)/2061 weeks
164-.11756 .18699 (164*2π)/2061 weeks
165.02435 .26758 (165*2π)/2061 weeks
166-.10144 .13062 (166*2π)/2061 weeks
167-.09817 .21386 (167*2π)/2061 weeks
168-.08934 .18593 (168*2π)/2061 weeks
169-.1029 .08125 (169*2π)/2061 weeks
170-.23765 .14213 (170*2π)/2061 weeks
171-.14851 .31388 (171*2π)/2061 weeks
172.08127 .37048 (172*2π)/2061 weeks
173.00411 -.01306 (173*2π)/2061 weeks
174-.37982 .16727 (174*2π)/2061 weeks
175-.28576 .22803 (175*2π)/2061 weeks
176.11201 .19788 (176*2π)/2061 weeks
177-.17498 .18689 (177*2π)/2061 weeks
178-.01084 .0817 (178*2π)/2061 weeks
179-.05128 .43859 (179*2π)/2061 weeks
180-.14201 .33379 (180*2π)/2061 weeks
181-.22642 .16786 (181*2π)/2061 weeks
182-.09894 .24662 (182*2π)/2061 weeks
183-.11544 .30269 (183*2π)/2061 weeks
184-.03703 .35393 (184*2π)/2061 weeks
185-.42852 .51084 (185*2π)/2061 weeks
186.00065 .45339 (186*2π)/2061 weeks
187-.27992 .09318 (187*2π)/2061 weeks
188-.3139 -.18871 (188*2π)/2061 weeks
189-.30987 .70093 (189*2π)/2061 weeks
190.22434 .629 (190*2π)/2061 weeks
191-.13039 -.01089 (191*2π)/2061 weeks
192-.15475 .35296 (192*2π)/2061 weeks
193-.34419 .52462 (193*2π)/2061 weeks
194.30392 .59667 (194*2π)/2061 weeks
195-.32286 .51349 (195*2π)/2061 weeks
196-.32359 .80437 (196*2π)/2061 weeks
197-.20804 .92349 (197*2π)/2061 weeks
198-.83962 .02093 (198*2π)/2061 weeks
199.3043 .87363 (199*2π)/2061 weeks
200.53854 .72068 (200*2π)/2061 weeks
201-.43332 .55275 (201*2π)/2061 weeks
202-.25371 2.25333 (202*2π)/2061 weeks
203-1.82662 1.38625 (203*2π)/2061 weeks
2042.8742 5.14612 (204*2π)/2061 weeks