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Fourier Analysis of XOM (Exxon Mobil Corporation Common )


XOM (Exxon Mobil Corporation Common ) appears to have interesting cyclic behaviour every 205 weeks (2.6299*sine), 224 weeks (2.4044*sine), and 246 weeks (2.3049*sine).

XOM (Exxon Mobil Corporation Common ) has an average price of 23.69 (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 1/2/1970 to 3/20/2017 for XOM (Exxon Mobil Corporation Common ), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
023.69112   0 
116.29302 -27.11615 (1*2π)/24642,464 weeks
21.95896 -15.84486 (2*2π)/24641,232 weeks
3.1648 -9.83567 (3*2π)/2464821 weeks
4-.23102 -6.30273 (4*2π)/2464616 weeks
51.94158 -5.89235 (5*2π)/2464493 weeks
6-.73082 -7.1815 (6*2π)/2464411 weeks
7-2.70163 -3.73656 (7*2π)/2464352 weeks
8-.87584 -1.75968 (8*2π)/2464308 weeks
9.33624 -1.57226 (9*2π)/2464274 weeks
10.75744 -2.30486 (10*2π)/2464246 weeks
11.50679 -2.40439 (11*2π)/2464224 weeks
12.09264 -2.62987 (12*2π)/2464205 weeks
13-.53683 -1.96877 (13*2π)/2464190 weeks
14-.00159 -.84605 (14*2π)/2464176 weeks
15.99558 -1.22278 (15*2π)/2464164 weeks
16.8983 -2.03674 (16*2π)/2464154 weeks
17.27079 -2.00671 (17*2π)/2464145 weeks
18.16426 -1.6916 (18*2π)/2464137 weeks
19.34522 -1.55689 (19*2π)/2464130 weeks
20.39993 -1.83743 (20*2π)/2464123 weeks
21-.00803 -1.93638 (21*2π)/2464117 weeks
22-.20112 -1.65388 (22*2π)/2464112 weeks
23-.26795 -1.31229 (23*2π)/2464107 weeks
24.09796 -1.35433 (24*2π)/2464103 weeks
25-.10445 -1.54282 (25*2π)/246499 weeks
26-.31006 -1.45701 (26*2π)/246495 weeks
27-.52879 -1.32525 (27*2π)/246491 weeks
28-.58286 -.9055 (28*2π)/246488 weeks
29-.4319 -.732 (29*2π)/246485 weeks
30-.23892 -.52404 (30*2π)/246482 weeks
31.17479 -.54928 (31*2π)/246479 weeks
32.2116 -.98923 (32*2π)/246477 weeks
33-.08312 -1.12814 (33*2π)/246475 weeks
34-.34877 -.92096 (34*2π)/246472 weeks
35-.27716 -.75362 (35*2π)/246470 weeks
36-.29859 -.61599 (36*2π)/246468 weeks
37-.18755 -.47159 (37*2π)/246467 weeks
38.08231 -.51152 (38*2π)/246465 weeks
39.01723 -.68065 (39*2π)/246463 weeks
40.05411 -.73101 (40*2π)/246462 weeks
41-.15929 -.89286 (41*2π)/246460 weeks
42-.43131 -.63674 (42*2π)/246459 weeks
43-.27942 -.37241 (43*2π)/246457 weeks
44-.13537 -.24829 (44*2π)/246456 weeks
45.0912 -.29162 (45*2π)/246455 weeks
46.14737 -.43935 (46*2π)/246454 weeks
47.16706 -.47242 (47*2π)/246452 weeks
48.15597 -.717 (48*2π)/246451 weeks
49-.12048 -.64241 (49*2π)/246450 weeks
50-.10737 -.4798 (50*2π)/246449 weeks
51-.04433 -.47279 (51*2π)/246448 weeks
52-.07207 -.38353 (52*2π)/246447 weeks
53.10392 -.30864 (53*2π)/246446 weeks
54.22986 -.49767 (54*2π)/246446 weeks
55.12564 -.65611 (55*2π)/246445 weeks
56-.06564 -.67513 (56*2π)/246444 weeks
57-.08994 -.50255 (57*2π)/246443 weeks
58-.07925 -.54543 (58*2π)/246442 weeks
59-.12948 -.4522 (59*2π)/246442 weeks
60-.06906 -.42175 (60*2π)/246441 weeks
61-.14589 -.41793 (61*2π)/246440 weeks
62-.04182 -.19248 (62*2π)/246440 weeks
63.23172 -.33359 (63*2π)/246439 weeks
64.13001 -.60707 (64*2π)/246439 weeks
65-.03535 -.56406 (65*2π)/246438 weeks
66-.12537 -.54922 (66*2π)/246437 weeks
67-.18507 -.40889 (67*2π)/246437 weeks
68-.14308 -.267 (68*2π)/246436 weeks
69.10202 -.27724 (69*2π)/246436 weeks
70.02154 -.47455 (70*2π)/246435 weeks
71-.07815 -.35794 (71*2π)/246435 weeks
72.05436 -.3191 (72*2π)/246434 weeks
73.05062 -.42575 (73*2π)/246434 weeks
74.06617 -.38113 (74*2π)/246433 weeks
75.11535 -.56456 (75*2π)/246433 weeks
76-.13055 -.60335 (76*2π)/246432 weeks
77-.18224 -.48054 (77*2π)/246432 weeks
78-.20651 -.40529 (78*2π)/246432 weeks
79-.20103 -.28481 (79*2π)/246431 weeks
80-.06256 -.28772 (80*2π)/246431 weeks
81-.07438 -.28245 (81*2π)/246430 weeks
82.03085 -.36402 (82*2π)/246430 weeks
83-.12298 -.44603 (83*2π)/246430 weeks
84-.17992 -.27663 (84*2π)/246429 weeks
85-.03583 -.25106 (85*2π)/246429 weeks
86.03043 -.34191 (86*2π)/246429 weeks
87-.06714 -.46445 (87*2π)/246428 weeks
88-.2208 -.39671 (88*2π)/246428 weeks
89-.2025 -.22738 (89*2π)/246428 weeks
90-.03564 -.22679 (90*2π)/246427 weeks
91-.07168 -.38833 (91*2π)/246427 weeks
92-.18026 -.3223 (92*2π)/246427 weeks
93-.19527 -.32636 (93*2π)/246426 weeks
94-.28552 -.18855 (94*2π)/246426 weeks
95-.13353 -.07688 (95*2π)/246426 weeks
96-.07956 -.16797 (96*2π)/246426 weeks
97-.07206 -.09236 (97*2π)/246425 weeks
98.02297 -.21838 (98*2π)/246425 weeks
99-.14587 -.22796 (99*2π)/246425 weeks
100-.10009 -.00107 (100*2π)/246425 weeks
101.13245 -.05964 (101*2π)/246424 weeks
102.19779 -.22355 (102*2π)/246424 weeks
103.0814 -.36821 (103*2π)/246424 weeks
104-.01292 -.33485 (104*2π)/246424 weeks
105-.04969 -.3033 (105*2π)/246423 weeks
106-.04921 -.29583 (106*2π)/246423 weeks
107-.05904 -.31063 (107*2π)/246423 weeks
108-.1489 -.26408 (108*2π)/246423 weeks
109-.0748 -.17029 (109*2π)/246423 weeks
110-.00477 -.25603 (110*2π)/246422 weeks
111-.1251 -.31197 (111*2π)/246422 weeks
112-.17377 -.18699 (112*2π)/246422 weeks
113-.11797 -.10279 (113*2π)/246422 weeks
114.0133 -.06529 (114*2π)/246422 weeks
115.10925 -.22068 (115*2π)/246421 weeks
116.00984 -.33719 (116*2π)/246421 weeks
117-.11467 -.32747 (117*2π)/246421 weeks
118-.16419 -.25856 (118*2π)/246421 weeks
119-.19088 -.18597 (119*2π)/246421 weeks
120-.15691 -.09768 (120*2π)/246421 weeks
121-.06821 -.08912 (121*2π)/246420 weeks
122-.04784 -.13582 (122*2π)/246420 weeks
123-.08668 -.12781 (123*2π)/246420 weeks
124-.07632 -.08937 (124*2π)/246420 weeks
125-.02073 -.04897 (125*2π)/246420 weeks
126.06064 -.10951 (126*2π)/246420 weeks
127-.02843 -.16009 (127*2π)/246419 weeks
128.01201 -.04673 (128*2π)/246419 weeks
129.13355 -.16194 (129*2π)/246419 weeks
130-.01524 -.24668 (130*2π)/246419 weeks
131-.00751 -.09861 (131*2π)/246419 weeks
132.08687 -.15143 (132*2π)/246419 weeks
133.07364 -.22242 (133*2π)/246419 weeks
134.04016 -.27063 (134*2π)/246418 weeks
135-.07396 -.28132 (135*2π)/246418 weeks
136-.101 -.12621 (136*2π)/246418 weeks
137.04138 -.11966 (137*2π)/246418 weeks
138.03968 -.22988 (138*2π)/246418 weeks
139-.03514 -.21955 (139*2π)/246418 weeks
140-.03028 -.17784 (140*2π)/246418 weeks
141-.02462 -.17637 (141*2π)/246417 weeks
142.02383 -.15145 (142*2π)/246417 weeks
143.03729 -.24572 (143*2π)/246417 weeks
144-.04259 -.26468 (144*2π)/246417 weeks
145-.08215 -.23183 (145*2π)/246417 weeks
146-.12536 -.17448 (146*2π)/246417 weeks
147-.04184 -.08571 (147*2π)/246417 weeks
148.04256 -.1778 (148*2π)/246417 weeks
149-.02799 -.23123 (149*2π)/246417 weeks
150-.05097 -.22442 (150*2π)/246416 weeks
151-.12915 -.24163 (151*2π)/246416 weeks
152-.16501 -.1129 (152*2π)/246416 weeks
153-.08141 -.07641 (153*2π)/246416 weeks
154-.05281 -.07504 (154*2π)/246416 weeks
155.00383 -.0693 (155*2π)/246416 weeks
156.04019 -.14573 (156*2π)/246416 weeks
157-.0366 -.18333 (157*2π)/246416 weeks
158-.06997 -.12206 (158*2π)/246416 weeks
159-.00693 -.07422 (159*2π)/246415 weeks
160.03645 -.13909 (160*2π)/246415 weeks
161.00055 -.184