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# Fourier Analysis of CVRR (CVR Refining)

CVRR (CVR Refining) appears to have interesting cyclic behaviour every 28 weeks (.6134*sine), 28 weeks (.5461*cosine), and 16 weeks (.283*cosine).

CVRR (CVR Refining) has an average price of 13.97 (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 1/17/2013 to 4/16/2018 for CVRR (CVR Refining), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
013.96765   0
1.08717 4.7854 (1*2π)/275275 weeks
22.18151 .5068 (2*2π)/275138 weeks
3-.08127 .04284 (3*2π)/27592 weeks
41.41147 1.45766 (4*2π)/27569 weeks
5-.47667 -.40154 (5*2π)/27555 weeks
6-.61564 -.28608 (6*2π)/27546 weeks
7-.08474 -.11834 (7*2π)/27539 weeks
8-.49713 .38755 (8*2π)/27534 weeks
9-.06064 -.05533 (9*2π)/27531 weeks
10-.54608 .61344 (10*2π)/27528 weeks
11.08832 -.08512 (11*2π)/27525 weeks
12.02085 .33551 (12*2π)/27523 weeks
13-.01601 .43309 (13*2π)/27521 weeks
14-.02664 -.48119 (14*2π)/27520 weeks
15-.10494 .38984 (15*2π)/27518 weeks
16.1191 .14383 (16*2π)/27517 weeks
17.283 .08971 (17*2π)/27516 weeks
18.07997 .1651 (18*2π)/27515 weeks
19.00835 .03284 (19*2π)/27514 weeks
20.19432 -.00722 (20*2π)/27514 weeks
21-.00095 .02203 (21*2π)/27513 weeks
22-.23259 -.11896 (22*2π)/27513 weeks
23.24534 -.05906 (23*2π)/27512 weeks
24-.19392 -.13816 (24*2π)/27511 weeks
25-.02224 -.06049 (25*2π)/27511 weeks
26-.01322 -.08605 (26*2π)/27511 weeks
27.05847 -.04583 (27*2π)/27510 weeks
28.03611 -.06967 (28*2π)/27510 weeks
29-.13312 -.00155 (29*2π)/2759 weeks
30-.00837 .02113 (30*2π)/2759 weeks
31-.01331 -.00563 (31*2π)/2759 weeks
32.04167 .12031 (32*2π)/2759 weeks
33.15184 .0936 (33*2π)/2758 weeks
34-.04553 -.02784 (34*2π)/2758 weeks
35.05977 -.03206 (35*2π)/2758 weeks
36.03009 .03944 (36*2π)/2758 weeks
37.07393 .05634 (37*2π)/2757 weeks
38-.04309 .02626 (38*2π)/2757 weeks
39-.0738 .10427 (39*2π)/2757 weeks
40-.01225 -.06988 (40*2π)/2757 weeks
41-.09584 -.00071 (41*2π)/2757 weeks
42.00227 .01618 (42*2π)/2757 weeks
43-.08289 -.00059 (43*2π)/2756 weeks
44-.14434 .06016 (44*2π)/2756 weeks
45-.11568 -.02436 (45*2π)/2756 weeks
46-.09097 -.00063 (46*2π)/2756 weeks
47-.13051 -.07669 (47*2π)/2756 weeks
48.00581 -.18684 (48*2π)/2756 weeks
49.06443 -.05957 (49*2π)/2756 weeks
50.00546 -.10237 (50*2π)/2756 weeks
51-.0551 -.07844 (51*2π)/2755 weeks
52-.03861 .03633 (52*2π)/2755 weeks
53-.03491 -.17206 (53*2π)/2755 weeks
54-.05419 .08613 (54*2π)/2755 weeks
55-.01809 -.02831 (55*2π)/2755 weeks
56-.00671 -.11974 (56*2π)/2755 weeks
57.01327 .04314 (57*2π)/2755 weeks
58-.10928 -.01408 (58*2π)/2755 weeks
59.07339 -.04311 (59*2π)/2755 weeks
60-.05933 -.06149 (60*2π)/2755 weeks
61-.0769 -.06537 (61*2π)/2755 weeks
62.03284 -.02998 (62*2π)/2754 weeks
63-.04107 -.03505 (63*2π)/2754 weeks
64-.00907 -.0175 (64*2π)/2754 weeks
65-.0141 .05192 (65*2π)/2754 weeks
66.01223 -.05576 (66*2π)/2754 weeks
67-.05558 -.06162 (67*2π)/2754 weeks
68-.01922 .00507 (68*2π)/2754 weeks
69.04797 -.07629 (69*2π)/2754 weeks
70.06579 -.02656 (70*2π)/2754 weeks
71-.08827 .00065 (71*2π)/2754 weeks
72.07453 .06469 (72*2π)/2754 weeks
73-.05219 .00824 (73*2π)/2754 weeks
74-.06966 .03574 (74*2π)/2754 weeks
75-.03876 .04441 (75*2π)/2754 weeks
76-.01303 .02145 (76*2π)/2754 weeks
77-.00782 -.01677 (77*2π)/2754 weeks
78-.01563 .0693 (78*2π)/2754 weeks
79.0038 .02151 (79*2π)/2753 weeks
80-.05242 -.01782 (80*2π)/2753 weeks
81.03697 -.04387 (81*2π)/2753 weeks
82-.018 -.05964 (82*2π)/2753 weeks
83.00589 -.01838 (83*2π)/2753 weeks
84.01916 -.00244 (84*2π)/2753 weeks
85.02876 -.03946 (85*2π)/2753 weeks
86.00192 -.02455 (86*2π)/2753 weeks
87.02026 .01725 (87*2π)/2753 weeks
88-.01041 .01537 (88*2π)/2753 weeks
89.02597 -.01511 (89*2π)/2753 weeks
90.01277 -.05511 (90*2π)/2753 weeks
91.03629 .00015 (91*2π)/2753 weeks
92.01479 -.04785 (92*2π)/2753 weeks
93-.06993 .01709 (93*2π)/2753 weeks
94-.04169 .00605 (94*2π)/2753 weeks
95-.04761 -.01539 (95*2π)/2753 weeks
96-.01552 -.1306 (96*2π)/2753 weeks
97.01532 -.01116 (97*2π)/2753 weeks
98.01979 .03759 (98*2π)/2753 weeks
99-.01104 -.056 (99*2π)/2753 weeks
100-.03981 .01084 (100*2π)/2753 weeks
101.00731 -.00988 (101*2π)/2753 weeks
102.00956 .00332 (102*2π)/2753 weeks
103-.02833 -.00925 (103*2π)/2753 weeks
104.01231 -.02838 (104*2π)/2753 weeks
105-.01758 .04667 (105*2π)/2753 weeks
106.00302 -.00805 (106*2π)/2753 weeks
107.06001 .04786 (107*2π)/2753 weeks
108.06004 .06145 (108*2π)/2753 weeks
109.02911 .00587 (109*2π)/2753 weeks
110.04071 .09243 (110*2π)/2753 weeks
111.03986 .01514 (111*2π)/2752 weeks
112.01402 .03107 (112*2π)/2752 weeks
113-.06974 .02381 (113*2π)/2752 weeks
114.00275 .02315 (114*2π)/2752 weeks
115.09596 -.05013 (115*2π)/2752 weeks
116-.07189 .01468 (116*2π)/2752 weeks
117.00102 .02457 (117*2π)/2752 weeks
118-.02933 -.0279 (118*2π)/2752 weeks
119.04671 -.05987 (119*2π)/2752 weeks
120-.04416 -.03028 (120*2π)/2752 weeks
121.00656 .07979 (121*2π)/2752 weeks
122.01549 -.03991 (122*2π)/2752 weeks
123.03713 .03737 (123*2π)/2752 weeks
124-.08984 .04935 (124*2π)/2752 weeks
125-.07784 -.02885 (125*2π)/2752 weeks
126-.03707 -.00258 (126*2π)/2752 weeks
127-.0274 -.04674 (127*2π)/2752 weeks
128-.05144 .00886 (128*2π)/2752 weeks
129.01285 -.07793 (129*2π)/2752 weeks
130-.00062 .01416 (130*2π)/2752 weeks
131.03009 -.09105 (131*2π)/2752 weeks
132-.02132 -.04072 (132*2π)/2752 weeks
133.00029 -.0234 (133*2π)/2752 weeks
134.02116 -.04259 (134*2π)/2752 weeks
135-.00844 -.03149 (135*2π)/2752 weeks
136-.02246 .08813 (136*2π)/2752 weeks
137.02521 .00345 (137*2π)/2752 weeks
138.02521 -.00345 (138*2π)/2752 weeks
139-.02246 -.08813 (139*2π)/2752 weeks
140-.00844 .03149 (140*2π)/2752 weeks
141.02116 .04259 (141*2π)/2752 weeks
142.00029 .0234 (142*2π)/2752 weeks
143-.02132 .04072 (143*2π)/2752 weeks
144.03009 .09105 (144*2π)/2752 weeks
145-.00062 -.01416 (145*2π)/2752 weeks
146.01285 .07793 (146*2π)/2752 weeks
147-.05144 -.00886 (147*2π)/2752 weeks
148-.0274 .04674 (148*2π)/2752 weeks
149-.03707 .00258 (149*2π)/2752 weeks
150-.07784 .02885 (150*2π)/2752 weeks
151-.08984 -.04935 (151*2π)/2752 weeks
152.03713 -.03737 (152*2π)/2752 weeks
153.01549 .03991 (153*2π)/2752 weeks
154.00656 -.07979 (154*2π)/2752 weeks
155-.04416 .03028 (155*2π)/2752 weeks
156.04671 .05987 (156*2π)/2752 weeks
157-.02933 .0279 (157*2π)/2752 weeks
158.00102 -.02457 (158*2π)/2752 weeks
159-.07189 -.01468 (159*2π)/2752 weeks
160.09596 .05013 (160*2π)/2752 weeks
161.00275 -.02315 (161*2π)/2752 weeks
162-.06974 -.02381 (162*2π)/2752 weeks
163.01402 -.03107 (163*2π)/2752 weeks
164.03986 -.01514 (164*2π)/2752 weeks
165.04071 -.09243 (165*2π)/2752 weeks
166.02911 -.00587 (166*2π)/2752 weeks
167.06004 -.06145 (167*2π)/2752 weeks
168.06001 -.04786 (168*2π)/2752 weeks
169.00302 .00805 (169*2π)/2752 weeks
170-.01758 -.04667 (170*2π)/2752 weeks
171.01231 .02838 (171*2π)/2752 weeks
172-.02833 .00925 (172*2π)/2752 weeks
173.00956 -.00332 (173*2π)/2752 weeks
174.00731 .00988 (174*2π)/2752 weeks
175-.03981 -.01084 (175*2π)/2752 weeks
176-.01104 .056 (176*2π)/2752 weeks
177.01979 -.03759 (177*2π)/2752 weeks
178.01532 .01116 (178*2π)/2752 weeks
179-.01552 .1306 (179*2π)/2752 weeks
180-.04761 .01539 (180*2π)/2752 weeks
181-.04169 -.00605 (181*2π)/2752 weeks
182-.06993 -.01709 (182*2π)/2752 weeks
183.01479 .04785 (183*2π)/2752 weeks
184.03629 -.00015 (184*2π)/2751 weeks
185.01277 .05511 (185*2π)/2751 weeks
186.02597 .01511 (186*2π)/2751 weeks
187-.01041 -.01537 (187*2π)/2751 weeks
188.02026 -.01725 (188*2π)/2751 weeks
189.00192 .02455 (189*2π)/2751 weeks
190.02876 .03946 (190*2π)/2751 weeks
191.01916 .00244 (191*2π)/2751 weeks
192.00589 .01838 (192*2π)/2751 weeks
193-.018 .05964 (193*2π)/2751 weeks
194.03697 .04387 (194*2π)/2751 weeks
195-.05242 .01782 (195*2π)/2751 weeks
196.0038 -.02151 (196*2π)/2751 weeks
197-.01563 -.0693 (197*2π)/2751 weeks
198-.00782 .01677 (198*2π)/2751 weeks
199-.01303 -.02145 (199*2π)/2751 weeks
200-.03876 -.04441 (200*2π)/2751 weeks
201-.06966 -.03574 (201*2π)/2751 weeks
202-.05219 -.00824 (202*2π)/2751 weeks
203.07453 -.06469 (203*2π)/2751 weeks
204-.08827 -.00065 (204*2π)/2751 weeks
205.06579 .02656 (205*2π)/2751 weeks
206.04797 .07629 (206*2π)/2751 weeks
207-.01922 -.00507 (207*2π)/2751 weeks
208-.05558 .06162 (208*2π)/2751 weeks
209.01223 .05576 (209*2π)/2751 weeks
210-.0141 -.05192 (210*2π)/2751 weeks
211-.00907 .0175 (211*2π)/2751 weeks
212-.04107 .03505 (212*2π)/2751 weeks
213.03284 .02998 (213*2π)/2751 weeks
214-.0769 .06537 (214*2π)/2751 weeks
215-.05933 .06149 (215*2π)/2751 weeks
216.07339 .04311 (216*2π)/2751 weeks
217-.10928 .01408 (217*2π)/2751 weeks
218.01327 -.04314 (218*2π)/2751 weeks
219-.00671 .11974 (219*2π)/2751 weeks
220-.01809 .02831 (220*2π)/2751 weeks
221-.05419 -.08613 (221*2π)/2751 weeks
222-.03491 .17206 (222*2π)/2751 weeks
223-.03861 -.03633 (223*2π)/2751 weeks
224-.0551 .07844 (224*2π)/2751 weeks
225.00546 .10237 (225*2π)/2751 weeks
226.06443 .05957 (226*2π)/2751 weeks
227.00581 .18684 (227*2π)/2751 weeks
228-.13051 .07669 (228*2π)/2751 weeks
229-.09097 .00063 (229*2π)/2751 weeks
230-.11568 .02436 (230*2π)/2751 weeks
231-.14434 -.06016 (231*2π)/2751 weeks
232-.08289 .00059 (232*2π)/2751 weeks
233.00227 -.01618 (233*2π)/2751 weeks
234-.09584 .00071 (234*2π)/2751 weeks
235-.01225 .06988 (235*2π)/2751 weeks
236-.0738 -.10427 (236*2π)/2751 weeks
237-.04309 -.02626 (237*2π)/2751 weeks
238.07393 -.05634 (238*2π)/2751 weeks
239.03009 -.03944 (239*2π)/2751 weeks
240.05977 .03206 (240*2π)/2751 weeks
241-.04553 .02784 (241*2π)/2751 weeks
242.15184 -.0936 (242*2π)/2751 weeks
243.04167 -.12031 (243*2π)/2751 weeks
244-.01331 .00563 (244*2π)/2751 weeks
245-.00837 -.02113 (245*2π)/2751 weeks
246-.13312 .00155 (246*2π)/2751 weeks
247.03611 .06967 (247*2π)/2751 weeks
248.05847 .04583 (248*2π)/2751 weeks
249-.01322 .08605 (249*2π)/2751 weeks
250-.02224 .06049 (250*2π)/2751 weeks
251-.19392 .13816 (251*2π)/2751 weeks
252.24534 .05906 (252*2π)/2751 weeks
253-.23259 .11896 (253*2π)/2751 weeks
254-.00095 -.02203 (254*2π)/2751 weeks
255.19432 .00722 (255*2π)/2751 weeks
256.00835 -.03284 (256*2π)/2751 weeks
257.07997 -.1651 (257*2π)/2751 weeks
258.283 -.08971 (258*2π)/2751 weeks
259.1191 -.14383 (259*2π)/2751 weeks
260-.10494 -.38984 (260*2π)/2751 weeks
261-.02664 .48119 (261*2π)/2751 weeks
262-.01601 -.43309 (262*2π)/2751 weeks
263.02085 -.33551 (263*2π)/2751 weeks
264.08832 .08512 (264*2π)/2751 weeks
265-.54608 -.61344 (265*2π)/2751 weeks
266-.06064 .05533 (266*2π)/2751 weeks
267-.49713 -.38755 (267*2π)/2751 weeks
268-.08474 .11834 (268*2π)/2751 weeks
269-.61564 .28608 (269*2π)/2751 weeks
270-.47667 .40154 (270*2π)/2751 weeks
2711.41147 -1.45766 (271*2π)/2751 weeks
272-.08127 -.04284 (272*2π)/2751 weeks
2732.18151 -.5068 (273*2π)/2751 weeks