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Fourier Analysis of MUSA (Murphy USA Inc. Common Stock)


MUSA (Murphy USA Inc. Common Stock) appears to have interesting cyclic behaviour every 17 weeks (1.5506*sine), 11 weeks (1.19*sine), and 14 weeks (1.1159*sine).

MUSA (Murphy USA Inc. Common Stock) has an average price of 57.99 (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 8/19/2013 to 3/20/2017 for MUSA (Murphy USA Inc. Common Stock), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
057.99474   0 
1-3.97732 -8.23494 (1*2π)/188188 weeks
2-1.05303 -10.42612 (2*2π)/18894 weeks
3-.46104 .84494 (3*2π)/18863 weeks
4-1.38845 -2.17239 (4*2π)/18847 weeks
52.05611 1.18462 (5*2π)/18838 weeks
6-.22819 -1.98117 (6*2π)/18831 weeks
7-.81198 -1.94178 (7*2π)/18827 weeks
8-.41923 -1.56022 (8*2π)/18824 weeks
9-.20129 -.93273 (9*2π)/18821 weeks
10.58589 -.6643 (10*2π)/18819 weeks
11.39473 -1.55056 (11*2π)/18817 weeks
12-.9365 -.62969 (12*2π)/18816 weeks
13.15805 -1.1159 (13*2π)/18814 weeks
14.79145 -.64599 (14*2π)/18813 weeks
15-.37831 -.97138 (15*2π)/18813 weeks
16-.99851 .27049 (16*2π)/18812 weeks
17-.06131 -1.19 (17*2π)/18811 weeks
18-.27751 -.53925 (18*2π)/18810 weeks
19-.65489 -.08942 (19*2π)/18810 weeks
20-.00713 -.00065 (20*2π)/1889 weeks
21.07284 -.12572 (21*2π)/1889 weeks
22-.10531 -.37326 (22*2π)/1889 weeks
23-.13886 -.78186 (23*2π)/1888 weeks
24.14188 -.73637 (24*2π)/1888 weeks
25-.23289 -.47055 (25*2π)/1888 weeks
26.01338 -.89571 (26*2π)/1887 weeks
27-.265 -.388 (27*2π)/1887 weeks
28-.24577 -.56407 (28*2π)/1887 weeks
29-.13627 -.20224 (29*2π)/1886 weeks
30-.04657 -.1139 (30*2π)/1886 weeks
31-.27128 -.37716 (31*2π)/1886 weeks
32-.32383 -.02867 (32*2π)/1886 weeks
33.12372 -.34547 (33*2π)/1886 weeks
34-.20237 -.60582 (34*2π)/1886 weeks
35-.37398 -.38735 (35*2π)/1885 weeks
36-.32436 -.61039 (36*2π)/1885 weeks
37-.3745 -.17031 (37*2π)/1885 weeks
38-.0943 -.14736 (38*2π)/1885 weeks
39-.28019 -.44254 (39*2π)/1885 weeks
40-.26397 -.09632 (40*2π)/1885 weeks
41.1419 -.23183 (41*2π)/1885 weeks
42-.33482 -.27424 (42*2π)/1884 weeks
43.01184 -.29734 (43*2π)/1884 weeks
44-.27364 -.36121 (44*2π)/1884 weeks
45-.27391 -.48773 (45*2π)/1884 weeks
46-.14187 -.1833 (46*2π)/1884 weeks
47-.30096 -.24702 (47*2π)/1884 weeks
48-.52039 .02519 (48*2π)/1884 weeks
49.0767 -.02388 (49*2π)/1884 weeks
50-.14799 -.17282 (50*2π)/1884 weeks
51-.16874 -.22407 (51*2π)/1884 weeks
52-.16437 -.27286 (52*2π)/1884 weeks
53-.14113 -.25115 (53*2π)/1884 weeks
54-.15324 -.31275 (54*2π)/1883 weeks
55-.35068 -.27124 (55*2π)/1883 weeks
56-.15458 .0038 (56*2π)/1883 weeks
57-.38526 -.16785 (57*2π)/1883 weeks
58-.23611 .05649 (58*2π)/1883 weeks
59-.26434 -.20521 (59*2π)/1883 weeks
60-.09384 -.0336 (60*2π)/1883 weeks
61-.11652 .0054 (61*2π)/1883 weeks
62-.15134 -.35407 (62*2π)/1883 weeks
63-.23968 -.11665 (63*2π)/1883 weeks
64-.33953 -.16369 (64*2π)/1883 weeks
65-.23794 .00495 (65*2π)/1883 weeks
66-.20131 -.05083 (66*2π)/1883 weeks
67-.22829 -.02903 (67*2π)/1883 weeks
68-.16227 -.01969 (68*2π)/1883 weeks
69-.07772 .04375 (69*2π)/1883 weeks
70-.28064 -.21187 (70*2π)/1883 weeks
71-.01608 .01314 (71*2π)/1883 weeks
72-.24094 -.18954 (72*2π)/1883 weeks
73-.17456 .06328 (73*2π)/1883 weeks
74-.00798 -.17606 (74*2π)/1883 weeks
75-.18268 -.17336 (75*2π)/1883 weeks
76-.03442 .15488 (76*2π)/1882 weeks
77.02262 -.03331 (77*2π)/1882 weeks
78-.10786 -.12338 (78*2π)/1882 weeks
79-.20004 -.05288 (79*2π)/1882 weeks
80-.24885 -.1094 (80*2π)/1882 weeks
81-.24229 -.06127 (81*2π)/1882 weeks
82-.1986 -.0675 (82*2π)/1882 weeks
83-.09883 -.14463 (83*2π)/1882 weeks
84-.1987 .02391 (84*2π)/1882 weeks
85-.2776 -.12841 (85*2π)/1882 weeks
86-.17705 -.04699 (86*2π)/1882 weeks
87-.0898 .01672 (87*2π)/1882 weeks
88-.07649 .09728 (88*2π)/1882 weeks
89-.20168 -.06162 (89*2π)/1882 weeks
90-.24414 .04826 (90*2π)/1882 weeks
91-.00494 -.11051 (91*2π)/1882 weeks
92-.40584 .12008 (92*2π)/1882 weeks
93-.12576 .06571 (93*2π)/1882 weeks
94-.21096   (94*2π)/1882 weeks
95-.12576 -.06571 (95*2π)/1882 weeks
96-.40584 -.12008 (96*2π)/1882 weeks
97-.00494 .11051 (97*2π)/1882 weeks
98-.24414 -.04826 (98*2π)/1882 weeks
99-.20168 .06162 (99*2π)/1882 weeks
100-.07649 -.09728 (100*2π)/1882 weeks
101-.0898 -.01672 (101*2π)/1882 weeks
102-.17705 .04699 (102*2π)/1882 weeks
103-.2776 .12841 (103*2π)/1882 weeks
104-.1987 -.02391 (104*2π)/1882 weeks
105-.09883 .14463 (105*2π)/1882 weeks
106-.1986 .0675 (106*2π)/1882 weeks
107-.24229 .06127 (107*2π)/1882 weeks
108-.24885 .1094 (108*2π)/1882 weeks
109-.20004 .05288 (109*2π)/1882 weeks
110-.10786 .12338 (110*2π)/1882 weeks
111.02262 .03331 (111*2π)/1882 weeks
112-.03442 -.15488 (112*2π)/1882 weeks
113-.18268 .17336 (113*2π)/1882 weeks
114-.00798 .17606 (114*2π)/1882 weeks
115-.17456 -.06328 (115*2π)/1882 weeks
116-.24094 .18954 (116*2π)/1882 weeks
117-.01608 -.01314 (117*2π)/1882 weeks
118-.28064 .21187 (118*2π)/1882 weeks
119-.07772 -.04375 (119*2π)/1882 weeks
120-.16227 .01969 (120*2π)/1882 weeks
121-.22829 .02903 (121*2π)/1882 weeks
122-.20131 .05083 (122*2π)/1882 weeks
123-.23794 -.00495 (123*2π)/1882 weeks
124-.33953 .16369 (124*2π)/1882 weeks
125-.23968 .11665 (125*2π)/1882 weeks
126-.15134 .35407 (126*2π)/1881 weeks
127-.11652 -.0054 (127*2π)/1881 weeks
128-.09384 .0336 (128*2π)/1881 weeks
129-.26434 .20521 (129*2π)/1881 weeks
130-.23611 -.05649 (130*2π)/1881 weeks
131-.38526 .16785 (131*2π)/1881 weeks
132-.15458 -.0038 (132*2π)/1881 weeks
133-.35068 .27124 (133*2π)/1881 weeks
134-.15324 .31275 (134*2π)/1881 weeks
135-.14113 .25115 (135*2π)/1881 weeks
136-.16437 .27286 (136*2π)/1881 weeks
137-.16874 .22407 (137*2π)/1881 weeks
138-.14799 .17282 (138*2π)/1881 weeks
139.0767 .02388 (139*2π)/1881 weeks
140-.52039 -.02519 (140*2π)/1881 weeks
141-.30096 .24702 (141*2π)/1881 weeks
142-.14187 .1833 (142*2π)/1881 weeks
143-.27391 .48773 (143*2π)/1881 weeks
144-.27364 .36121 (144*2π)/1881 weeks
145.01184 .29734 (145*2π)/1881 weeks
146-.33482 .27424 (146*2π)/1881 weeks
147.1419 .23183 (147*2π)/1881 weeks
148-.26397 .09632 (148*2π)/1881 weeks
149-.28019 .44254 (149*2π)/1881 weeks
150-.0943 .14736 (150*2π)/1881 weeks
151-.3745 .17031 (151*2π)/1881 weeks
152-.32436 .61039 (152*2π)/1881 weeks
153-.37398 .38735 (153*2π)/1881 weeks
154-.20237 .60582 (154*2π)/1881 weeks
155.12372 .34547 (155*2π)/1881 weeks
156-.32383 .02867 (156*2π)/1881 weeks
157-.27128 .37716 (157*2π)/1881 weeks
158-.04657 .1139 (158*2π)/1881 weeks
159-.13627 .20224 (159*2π)/1881 weeks
160-.24577 .56407 (160*2π)/1881 weeks
161-.265 .388 (161*2π)/1881 weeks
162.01338 .89571 (162*2π)/1881 weeks
163-.23289 .47055 (163*2π)/1881 weeks
164.14188 .73637 (164*2π)/1881 weeks
165-.13886 .78186 (165*2π)/1881 weeks
166-.10531 .37326 (166*2π)/1881 weeks
167.07284 .12572 (167*2π)/1881 weeks
168-.00713 .00065 (168*2π)/1881 weeks
169-.65489 .08942 (169*2π)/1881 weeks
170-.27751 .53925 (170*2π)/1881 weeks
171-.06131 1.19 (171*2π)/1881 weeks
172-.99851 -.27049 (172*2π)/1881 weeks
173-.37831 .97138 (173*2π)/1881 weeks
174.79145 .64599 (174*2π)/1881 weeks
175.15805 1.1159 (175*2π)/1881 weeks
176-.9365 .62969 (176*2π)/1881 weeks
177.39473 1.55056 (177*2π)/1881 weeks
178.58589 .6643 (178*2π)/1881 weeks
179-.20129 .93273 (179*2π)/1881 weeks
180-.41923 1.56022 (180*2π)/1881 weeks
181-.81198 1.94178 (181*2π)/1881 weeks
182-.22819 1.98117 (182*2π)/1881 weeks
1832.05611 -1.18462 (183*2π)/1881 weeks
184-1.38845 2.17239 (184*2π)/1881 weeks
185-.46104 -.84494 (185*2π)/1881 weeks
186-1.05303 10.42612 (186*2π)/1881 weeks

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