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Fourier Analysis of DTE (DTE Energy Company Common Stock)

DTE (DTE Energy Company Common Stock) appears to have interesting cyclic behaviour every 246 weeks (3.3272*sine), 224 weeks (3.0889*sine), and 164 weeks (.7384*cosine).

DTE (DTE Energy Company Common Stock) has an average price of 17.31 (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 1/2/1970 to 3/13/2017 for DTE (DTE Energy Company Common Stock), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
017.31333   0
112.05678 -16.62214 (1*2π)/24632,463 weeks
26.38987 -9.84732 (2*2π)/24631,232 weeks
34.41628 -8.48595 (3*2π)/2463821 weeks
42.89825 -8.1933 (4*2π)/2463616 weeks
51.08354 -6.58269 (5*2π)/2463493 weeks
6.29408 -5.76881 (6*2π)/2463411 weeks
7-.07256 -3.74353 (7*2π)/2463352 weeks
8.31149 -3.43841 (8*2π)/2463308 weeks
9.69825 -2.96303 (9*2π)/2463274 weeks
10.59294 -3.32723 (10*2π)/2463246 weeks
11-.07909 -3.08887 (11*2π)/2463224 weeks
12-.04305 -2.12968 (12*2π)/2463205 weeks
13.35039 -2.10785 (13*2π)/2463189 weeks
14.23188 -2.02595 (14*2π)/2463176 weeks
15.73835 -1.65827 (15*2π)/2463164 weeks
16.51247 -2.72084 (16*2π)/2463154 weeks
17-.43131 -1.90963 (17*2π)/2463145 weeks
18.06577 -1.46687 (18*2π)/2463137 weeks
19.14523 -1.33593 (19*2π)/2463130 weeks
20.63344 -1.41269 (20*2π)/2463123 weeks
21.36445 -1.91199 (21*2π)/2463117 weeks
22.10556 -1.67327 (22*2π)/2463112 weeks
23.09079 -1.54818 (23*2π)/2463107 weeks
24.11936 -1.63227 (24*2π)/2463103 weeks
25-.1315 -1.47443 (25*2π)/246399 weeks
26-.00534 -1.2917 (26*2π)/246395 weeks
27-.02849 -1.37489 (27*2π)/246391 weeks
28-.04937 -1.35753 (28*2π)/246388 weeks
29-.24237 -1.33458 (29*2π)/246385 weeks
30-.35044 -1.22304 (30*2π)/246382 weeks
31-.44612 -.89539 (31*2π)/246379 weeks
32-.14052 -.68841 (32*2π)/246377 weeks
33.01875 -.81861 (33*2π)/246375 weeks
34-.04758 -.96324 (34*2π)/246372 weeks
35-.17242 -.82896 (35*2π)/246370 weeks
36-.13983 -.73568 (36*2π)/246368 weeks
37-.04322 -.62193 (37*2π)/246367 weeks
38.05123 -.72141 (38*2π)/246365 weeks
39.03751 -.65468 (39*2π)/246363 weeks
40.14204 -.84284 (40*2π)/246362 weeks
41-.12182 -.83197 (41*2π)/246360 weeks
42-.09716 -.63959 (42*2π)/246359 weeks
43-.03868 -.66669 (43*2π)/246357 weeks
44-.01537 -.57521 (44*2π)/246356 weeks
45.03524 -.63425 (45*2π)/246355 weeks
46-.01296 -.5738 (46*2π)/246354 weeks
47.06386 -.5786 (47*2π)/246352 weeks
48.07703 -.55304 (48*2π)/246351 weeks
49.11835 -.64929 (49*2π)/246350 weeks
50.09456 -.62811 (50*2π)/246349 weeks
51.09747 -.75154 (51*2π)/246348 weeks
52-.13646 -.78448 (52*2π)/246347 weeks
53-.15069 -.50171 (53*2π)/246346 weeks
54.00201 -.58771 (54*2π)/246346 weeks
55-.12001 -.54175 (55*2π)/246345 weeks
56-.04323 -.45874 (56*2π)/246344 weeks
57-.05247 -.49899 (57*2π)/246343 weeks
58-.04533 -.44267 (58*2π)/246342 weeks
59-.03283 -.35544 (59*2π)/246342 weeks
60.11391 -.3716 (60*2π)/246341 weeks
61.11313 -.48645 (61*2π)/246340 weeks
62.05747 -.42755 (62*2π)/246340 weeks
63.15383 -.44851 (63*2π)/246339 weeks
64.14323 -.51847 (64*2π)/246338 weeks
65.13256 -.53924 (65*2π)/246338 weeks
66.08661 -.58221 (66*2π)/246337 weeks
67.04955 -.61354 (67*2π)/246337 weeks
68-.04733 -.51156 (68*2π)/246336 weeks
69.0818 -.4866 (69*2π)/246336 weeks
70.02238 -.59937 (70*2π)/246335 weeks
71-.03787 -.49217 (71*2π)/246335 weeks
72.07333 -.51599 (72*2π)/246334 weeks
73-.03746 -.6616 (73*2π)/246334 weeks
74-.14739 -.4936 (74*2π)/246333 weeks
75-.08265 -.51024 (75*2π)/246333 weeks
76-.12373 -.45993 (76*2π)/246332 weeks
77-.13088 -.44237 (77*2π)/246332 weeks
78-.16577 -.35458 (78*2π)/246332 weeks
79-.06044 -.25446 (79*2π)/246331 weeks
80.05362 -.33299 (80*2π)/246331 weeks
81.01261 -.36658 (81*2π)/246330 weeks
82.08194 -.39671 (82*2π)/246330 weeks
83-.02049 -.47683 (83*2π)/246330 weeks
84-.05774 -.37607 (84*2π)/246329 weeks
85.01578 -.36084 (85*2π)/246329 weeks
86.06176 -.41818 (86*2π)/246329 weeks
87-.02331 -.49658 (87*2π)/246328 weeks
88-.08662 -.43453 (88*2π)/246328 weeks
89-.07554 -.37782 (89*2π)/246328 weeks
90-.07545 -.38192 (90*2π)/246327 weeks
91-.05036 -.31855 (91*2π)/246327 weeks
92.03234 -.3849 (92*2π)/246327 weeks
93-.06849 -.45166 (93*2π)/246326 weeks
94-.14545 -.35935 (94*2π)/246326 weeks
95-.06694 -.24731 (95*2π)/246326 weeks
96.04242 -.33435 (96*2π)/246326 weeks
97-.02777 -.39388 (97*2π)/246325 weeks
98-.03023 -.37513 (98*2π)/246325 weeks
99-.07542 -.42778 (99*2π)/246325 weeks
100-.11773 -.31933 (100*2π)/246325 weeks
101-.07261 -.32837 (101*2π)/246324 weeks
102-.06255 -.33305 (102*2π)/246324 weeks
103-.10381 -.32787 (103*2π)/246324 weeks
104-.07859 -.28735 (104*2π)/246324 weeks
105-.05337 -.29491 (105*2π)/246323 weeks
106-.06359 -.33159 (106*2π)/246323 weeks
107-.09852 -.32 (107*2π)/246323 weeks
108-.11055 -.26874 (108*2π)/246323 weeks
109-.05345 -.22922 (109*2π)/246323 weeks
110.01682 -.29941 (110*2π)/246322 weeks
111-.07651 -.36171 (111*2π)/246322 weeks
112-.10331 -.30219 (112*2π)/246322 weeks
113-.12143 -.2877 (113*2π)/246322 weeks
114-.09949 -.23098 (114*2π)/246322 weeks
115-.07012 -.23907 (115*2π)/246321 weeks
116-.06787 -.27484 (116*2π)/246321 weeks
117-.11834 -.26474 (117*2π)/246321 weeks
118-.12218 -.21022 (118*2π)/246321 weeks
119-.06902 -.18546 (119*2π)/246321 weeks
120-.05932 -.19535 (120*2π)/246321 weeks
121-.04465 -.20513 (121*2π)/246320 weeks
122-.0616 -.20254 (122*2π)/246320 weeks
123-.01364 -.17913 (123*2π)/246320 weeks
124-.04179 -.25052 (124*2π)/246320 weeks
125-.07434 -.16427 (125*2π)/246320 weeks
126.00178 -.16892 (126*2π)/246320 weeks
127.00535 -.19906 (127*2π)/246319 weeks
128-.00093 -.19314 (128*2π)/246319 weeks
129.033 -.18726 (129*2π)/246319 weeks
130.05219 -.25195 (130*2π)/246319 weeks
131.00214 -.26748 (131*2π)/246319 weeks
132.00007 -.23846 (132*2π)/246319 weeks
133.00987 -.2967 (133*2π)/246319 weeks
134-.0538 -.28508 (134*2π)/246318 weeks
135-.09484 -.26644 (135*2π)/246318 weeks
136-.08692 -.1771 (136*2π)/246318 weeks
137-.00556 -.18128 (137*2π)/246318 weeks
138-.00964 -.23225 (138*2π)/246318 weeks
139-.05596 -.21656 (139*2π)/246318 weeks
140-.01745 -.19358 (140*2π)/246318 weeks
141-.03606 -.20819 (141*2π)/246317 weeks
142-.02291 -.16437 (142*2π)/246317 weeks
143.05041 -.1897 (143*2π)/246317 weeks
144.02322 -.26696 (144*2π)/246317 weeks
145-.02673 -.25227 (145*2π)/246317 weeks
146-.01827 -.25229 (146*2π)/246317 weeks
147-.07694 -.22765 (147*2π)/246317 weeks
148-.01602 -.17204 (148*2π)/246317 weeks
149.02195 -.21345 (149*2π)/246317 weeks
150-.00299 -.2702 (150*2π)/246316 weeks
151-.04326 -.25462 (151*2π)/246316 weeks
152-.0619 -.24611 (152*2π)/246316 weeks
153-.07525 -.19622 (153*2π)/246316 weeks
154-.00419 -.199 (154*2π)/246316 weeks
155-.01335 -.2326 (155*2π)/246316 weeks
156-.01769 -.2641 (156*2π)/246316 weeks
157-.06482 -.28366 (157*2π)/246316 weeks
158-.12442 -.25597 (158*2π)/246316 weeks
159-.10928 -.1893 (159*2π)/246315 weeks
160-.08511 -.20029