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Fourier Analysis of ALLY (Ally Financial Inc. Common Stoc)


ALLY (Ally Financial Inc. Common Stoc) appears to have interesting cyclic behaviour every 13 weeks (.4134*sine), 12 weeks (.2613*sine), and 6 weeks (.246*cosine).

ALLY (Ally Financial Inc. Common Stoc) has an average price of 20.86 (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 1/28/2014 to 2/21/2017 for ALLY (Ally Financial Inc. Common Stoc), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
020.85625   0 
11.19245 2.87661 (1*2π)/161161 weeks
21.39168 .61602 (2*2π)/16181 weeks
3-.22819 .49449 (3*2π)/16154 weeks
4.58831 .33684 (4*2π)/16140 weeks
5.116 .6369 (5*2π)/16132 weeks
6.18615 .33342 (6*2π)/16127 weeks
7.65045 .28042 (7*2π)/16123 weeks
8-.22005 .05323 (8*2π)/16120 weeks
9-.22215 .27996 (9*2π)/16118 weeks
10.13293 .03386 (10*2π)/16116 weeks
11.11001 .18739 (11*2π)/16115 weeks
12.01423 .41344 (12*2π)/16113 weeks
13-.09371 -.2613 (13*2π)/16112 weeks
14-.00408 -.21615 (14*2π)/16112 weeks
15.10355 .02325 (15*2π)/16111 weeks
16.16112 -.20778 (16*2π)/16110 weeks
17.09521 -.04432 (17*2π)/1619 weeks
18-.10896 -.0447 (18*2π)/1619 weeks
19-.12715 -.24915 (19*2π)/1618 weeks
20.13316 -.0217 (20*2π)/1618 weeks
21.05619 .16573 (21*2π)/1618 weeks
22-.0193 -.02023 (22*2π)/1617 weeks
23.11174 .01937 (23*2π)/1617 weeks
24.19679 .14617 (24*2π)/1617 weeks
25-.04012 .13735 (25*2π)/1616 weeks
26.01753 -.11366 (26*2π)/1616 weeks
27-.06099 .12396 (27*2π)/1616 weeks
28-.24597 .21013 (28*2π)/1616 weeks
29-.0178 -.02359 (29*2π)/1616 weeks
30-.12614 .00623 (30*2π)/1615 weeks
31-.13055 .05758 (31*2π)/1615 weeks
32.0039 -.05225 (32*2π)/1615 weeks
33.10262 -.00121 (33*2π)/1615 weeks
34.04528 .06613 (34*2π)/1615 weeks
35-.08554 .02021 (35*2π)/1615 weeks
36-.02755 .09697 (36*2π)/1614 weeks
37.05422 -.00633 (37*2π)/1614 weeks
38-.00868 -.01341 (38*2π)/1614 weeks
39.05123 .12682 (39*2π)/1614 weeks
40.0502 .10382 (40*2π)/1614 weeks
41.05144 .00601 (41*2π)/1614 weeks
42.11264 .2001 (42*2π)/1614 weeks
43.01298 .01466 (43*2π)/1614 weeks
44.06685 -.03356 (44*2π)/1614 weeks
45.01783 .00791 (45*2π)/1614 weeks
46-.00931 -.00983 (46*2π)/1614 weeks
47.08839 -.03837 (47*2π)/1613 weeks
48-.12426 -.00523 (48*2π)/1613 weeks
49-.00127 -.02242 (49*2π)/1613 weeks
50.00193 -.04528 (50*2π)/1613 weeks
51.06252 -.07347 (51*2π)/1613 weeks
52.04406 .03903 (52*2π)/1613 weeks
53.05548 -.0307 (53*2π)/1613 weeks
54.0003 .01593 (54*2π)/1613 weeks
55-.00238 -.06333 (55*2π)/1613 weeks
56.03253 -.05705 (56*2π)/1613 weeks
57.06555 .09157 (57*2π)/1613 weeks
58-.05323 .00425 (58*2π)/1613 weeks
59.03161 .05039 (59*2π)/1613 weeks
60.05033 .14767 (60*2π)/1613 weeks
61-.05611 .00907 (61*2π)/1613 weeks
62-.05215 .04057 (62*2π)/1613 weeks
63-.03029 .05877 (63*2π)/1613 weeks
64-.05671 .00558 (64*2π)/1613 weeks
65-.0337 -.07519 (65*2π)/1612 weeks
66.03397 -.01635 (66*2π)/1612 weeks
67-.01375 .08723 (67*2π)/1612 weeks
68.01649 -.04105 (68*2π)/1612 weeks
69.07797 -.02289 (69*2π)/1612 weeks
70.02111 .01611 (70*2π)/1612 weeks
71-.00313 .0163 (71*2π)/1612 weeks
72.02542 -.00974 (72*2π)/1612 weeks
73.01576 .03837 (73*2π)/1612 weeks
74.03719 .02541 (74*2π)/1612 weeks
75.00443 .02504 (75*2π)/1612 weeks
76-.00375 .02583 (76*2π)/1612 weeks
77.00375 .08415 (77*2π)/1612 weeks
78.05875 -.09357 (78*2π)/1612 weeks
79.07302 .06587 (79*2π)/1612 weeks
80.03997 .04371 (80*2π)/1612 weeks
81.03997 -.04371 (81*2π)/1612 weeks
82.07302 -.06587 (82*2π)/1612 weeks
83.05875 .09357 (83*2π)/1612 weeks
84.00375 -.08415 (84*2π)/1612 weeks
85-.00375 -.02583 (85*2π)/1612 weeks
86.00443 -.02504 (86*2π)/1612 weeks
87.03719 -.02541 (87*2π)/1612 weeks
88.01576 -.03837 (88*2π)/1612 weeks
89.02542 .00974 (89*2π)/1612 weeks
90-.00313 -.0163 (90*2π)/1612 weeks
91.02111 -.01611 (91*2π)/1612 weeks
92.07797 .02289 (92*2π)/1612 weeks
93.01649 .04105 (93*2π)/1612 weeks
94-.01375 -.08723 (94*2π)/1612 weeks
95.03397 .01635 (95*2π)/1612 weeks
96-.0337 .07519 (96*2π)/1612 weeks
97-.05671 -.00558 (97*2π)/1612 weeks
98-.03029 -.05877 (98*2π)/1612 weeks
99-.05215 -.04057 (99*2π)/1612 weeks
100-.05611 -.00907 (100*2π)/1612 weeks
101.05033 -.14767 (101*2π)/1612 weeks
102.03161 -.05039 (102*2π)/1612 weeks
103-.05323 -.00425 (103*2π)/1612 weeks
104.06555 -.09157 (104*2π)/1612 weeks
105.03253 .05705 (105*2π)/1612 weeks
106-.00238 .06333 (106*2π)/1612 weeks
107.0003 -.01593 (107*2π)/1612 weeks
108.05548 .0307 (108*2π)/1611 weeks
109.04406 -.03903 (109*2π)/1611 weeks
110.06252 .07347 (110*2π)/1611 weeks
111.00193 .04528 (111*2π)/1611 weeks
112-.00127 .02242 (112*2π)/1611 weeks
113-.12426 .00523 (113*2π)/1611 weeks
114.08839 .03837 (114*2π)/1611 weeks
115-.00931 .00983 (115*2π)/1611 weeks
116.01783 -.00791 (116*2π)/1611 weeks
117.06685 .03356 (117*2π)/1611 weeks
118.01298 -.01466 (118*2π)/1611 weeks
119.11264 -.2001 (119*2π)/1611 weeks
120.05144 -.00601 (120*2π)/1611 weeks
121.0502 -.10382 (121*2π)/1611 weeks
122.05123 -.12682 (122*2π)/1611 weeks
123-.00868 .01341 (123*2π)/1611 weeks
124.05422 .00633 (124*2π)/1611 weeks
125-.02755 -.09697 (125*2π)/1611 weeks
126-.08554 -.02021 (126*2π)/1611 weeks
127.04528 -.06613 (127*2π)/1611 weeks
128.10262 .00121 (128*2π)/1611 weeks
129.0039 .05225 (129*2π)/1611 weeks
130-.13055 -.05758 (130*2π)/1611 weeks
131-.12614 -.00623 (131*2π)/1611 weeks
132-.0178 .02359 (132*2π)/1611 weeks
133-.24597 -.21013 (133*2π)/1611 weeks
134-.06099 -.12396 (134*2π)/1611 weeks
135.01753 .11366 (135*2π)/1611 weeks
136-.04012 -.13735 (136*2π)/1611 weeks
137.19679 -.14617 (137*2π)/1611 weeks
138.11174 -.01937 (138*2π)/1611 weeks
139-.0193 .02023 (139*2π)/1611 weeks
140.05619 -.16573 (140*2π)/1611 weeks
141.13316 .0217 (141*2π)/1611 weeks
142-.12715 .24915 (142*2π)/1611 weeks
143-.10896 .0447 (143*2π)/1611 weeks
144.09521 .04432 (144*2π)/1611 weeks
145.16112 .20778 (145*2π)/1611 weeks
146.10355 -.02325 (146*2π)/1611 weeks
147-.00408 .21615 (147*2π)/1611 weeks
148-.09371 .2613 (148*2π)/1611 weeks
149.01423 -.41344 (149*2π)/1611 weeks
150.11001 -.18739 (150*2π)/1611 weeks
151.13293 -.03386 (151*2π)/1611 weeks
152-.22215 -.27996 (152*2π)/1611 weeks
153-.22005 -.05323 (153*2π)/1611 weeks
154.65045 -.28042 (154*2π)/1611 weeks
155.18615 -.33342 (155*2π)/1611 weeks
156.116 -.6369 (156*2π)/1611 weeks
157.58831 -.33684 (157*2π)/1611 weeks
158-.22819 -.49449 (158*2π)/1611 weeks
1591.39168 -.61602 (159*2π)/1611 weeks

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