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Fourier Analysis of ALLY (Ally Financial Inc)


ALLY (Ally Financial Inc) appears to have interesting cyclic behaviour every 21 weeks (502.0395*sine), 19 weeks (462.7275*sine), and 8 weeks (142.2929*cosine).

ALLY (Ally Financial Inc) has an average price of 407.02 (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 1/16/2018 for ALLY (Ally Financial Inc), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0407.0214   0 
1764.9525 107.2017 (1*2π)/208208 weeks
2732.0038 207.0619 (2*2π)/208104 weeks
3683.6766 301.1083 (3*2π)/20869 weeks
4617.7749 381.0257 (4*2π)/20852 weeks
5540.028 446.5554 (5*2π)/20842 weeks
6452.3668 495.285 (6*2π)/20835 weeks
7359.6805 524.7623 (7*2π)/20830 weeks
8266.5395 535.1372 (8*2π)/20826 weeks
9176.6592 526.7873 (9*2π)/20823 weeks
1092.27933 502.0395 (10*2π)/20821 weeks
1119.38231 462.7275 (11*2π)/20819 weeks
12-41.21606 411.7927 (12*2π)/20817 weeks
13-86.71251 352.8217 (13*2π)/20816 weeks
14-117.2072 289.4673 (14*2π)/20815 weeks
15-132.3504 225.4533 (15*2π)/20814 weeks
16-133.2076 164.2795 (16*2π)/20813 weeks
17-120.3737 108.382 (17*2π)/20812 weeks
18-97.34438 61.14169 (18*2π)/20812 weeks
19-66.19978 24.36912 (19*2π)/20811 weeks
20-30.21738 -1.17912 (20*2π)/20810 weeks
218.21554 -15.27122 (21*2π)/20810 weeks
2245.238 -18.31191 (22*2π)/2089 weeks
2378.51395 -11.18054 (23*2π)/2089 weeks
24106.305 4.20437 (24*2π)/2089 weeks
25126.9509 25.5386 (25*2π)/2088 weeks
26138.9888 51.00399 (26*2π)/2088 weeks
27142.2929 77.80681 (27*2π)/2088 weeks
28137.1855 103.3667 (28*2π)/2087 weeks
29124.8671 125.8242 (29*2π)/2087 weeks
30106.5068 143.4972 (30*2π)/2087 weeks
3183.93499 155.0132 (31*2π)/2087 weeks
3258.80584 159.5527 (32*2π)/2087 weeks
3333.51622 156.9519 (33*2π)/2086 weeks
3410.20217 147.7299 (34*2π)/2086 weeks
35-10.16715 132.8291 (35*2π)/2086 weeks
36-25.67737 113.5417 (36*2π)/2086 weeks
37-35.33807 90.87802 (37*2π)/2086 weeks
38-38.84036 67.33696 (38*2π)/2085 weeks
39-36.37412 44.12499 (39*2π)/2085 weeks
40-28.24647 23.22905 (40*2π)/2085 weeks
41-15.27061 5.64982 (41*2π)/2085 weeks
421.14425 -7.21205 (42*2π)/2085 weeks
4319.61115 -14.70533 (43*2π)/2085 weeks
4438.55008 -16.74125 (44*2π)/2085 weeks
4556.44649 -13.47776 (45*2π)/2085 weeks
4672.1643 -5.54511 (46*2π)/2085 weeks
4784.12847 6.19655 (47*2π)/2084 weeks
4891.93804 20.59683 (48*2π)/2084 weeks
4994.78516 36.20926 (49*2π)/2084 weeks
5092.88812 51.73684 (50*2π)/2084 weeks
5186.2035 65.75307 (51*2π)/2084 weeks
5275.73605 77.24167 (52*2π)/2084 weeks
5362.4584 85.01067 (53*2π)/2084 weeks
5447.42262 88.69092 (54*2π)/2084 weeks
5531.54799 87.83212 (55*2π)/2084 weeks
5616.74318 82.68965 (56*2π)/2084 weeks
573.95639 73.57907 (57*2π)/2084 weeks
58-6.05098 61.29906 (58*2π)/2084 weeks
59-12.3826 46.83957 (59*2π)/2084 weeks
60-14.58524 31.30938 (60*2π)/2083 weeks
61-12.49806 15.9951 (61*2π)/2083 weeks
62-6.73311 1.89527 (62*2π)/2083 weeks
632.7204 -9.87169 (63*2π)/2083 weeks
6414.64553 -18.47299 (64*2π)/2083 weeks
6528.16637 -23.37178 (65*2π)/2083 weeks
6642.19544 -24.28228 (66*2π)/2083 weeks
6755.5197 -21.16841 (67*2π)/2083 weeks
6867.12019 -14.6196 (68*2π)/2083 weeks
6976.20981 -5.08659 (69*2π)/2083 weeks
7081.91825 6.43827 (70*2π)/2083 weeks
7183.96726 18.98531 (71*2π)/2083 weeks
7282.27041 31.59271 (72*2π)/2083 weeks
7377.02908 43.07309 (73*2π)/2083 weeks
7468.46032 52.56432 (74*2π)/2083 weeks
7557.48715 59.12156 (75*2π)/2083 weeks
7645.15325 62.45273 (76*2π)/2083 weeks
7732.25242 62.08905 (77*2π)/2083 weeks
7819.70026 58.18739 (78*2π)/2083 weeks
798.75262 50.85117 (79*2π)/2083 weeks
80.12293 40.95262 (80*2π)/2083 weeks
81-5.44726 29.04959 (81*2π)/2083 weeks
82-7.71249 16.09464 (82*2π)/2083 weeks
83-6.43644 3.08147 (83*2π)/2083 weeks
84-1.78218 -9.00748 (84*2π)/2082 weeks
855.86013 -19.14752 (85*2π)/2082 weeks
8615.78507 -26.72335 (86*2π)/2082 weeks
8727.05605 -31.25296 (87*2π)/2082 weeks
8839.06406 -32.44602 (88*2π)/2082 weeks
8950.61306 -30.24987 (89*2π)/2082 weeks
9060.74986 -24.89122 (90*2π)/2082 weeks
9168.77853 -17.00573 (91*2π)/2082 weeks
9274.03485 -7.26681 (92*2π)/2082 weeks
9376.18106 3.47381 (93*2π)/2082 weeks
9475.01896 14.31951 (94*2π)/2082 weeks
9570.65635 24.24853 (95*2π)/2082 weeks
9663.54147 32.52802 (96*2π)/2082 weeks
9754.25317 38.34536 (97*2π)/2082 weeks
9843.58916 41.23491 (98*2π)/2082 weeks
9932.43094 40.9105 (99*2π)/2082 weeks
10021.54833 37.42085 (100*2π)/2082 weeks
10112.25021 30.96764 (101*2π)/2082 weeks
1024.90137 22.18797 (102*2π)/2082 weeks
103.18502 11.52042 (103*2π)/2082 weeks
104-1.48779   (104*2π)/2082 weeks
105.18502 -11.52042 (105*2π)/2082 weeks
1064.90137 -22.18797 (106*2π)/2082 weeks
10712.25021 -30.96764 (107*2π)/2082 weeks
10821.54833 -37.42085 (108*2π)/2082 weeks
10932.43094 -40.9105 (109*2π)/2082 weeks
11043.58916 -41.23491 (110*2π)/2082 weeks
11154.25317 -38.34536 (111*2π)/2082 weeks
11263.54147 -32.52802 (112*2π)/2082 weeks
11370.65635 -24.24853 (113*2π)/2082 weeks
11475.01896 -14.31951 (114*2π)/2082 weeks
11576.18106 -3.47381 (115*2π)/2082 weeks
11674.03485 7.26681 (116*2π)/2082 weeks
11768.77853 17.00573 (117*2π)/2082 weeks
11860.74986 24.89122 (118*2π)/2082 weeks
11950.61306 30.24987 (119*2π)/2082 weeks
12039.06406 32.44602 (120*2π)/2082 weeks
12127.05605 31.25296 (121*2π)/2082 weeks
12215.78507 26.72335 (122*2π)/2082 weeks
1235.86013 19.14752 (123*2π)/2082 weeks
124-1.78218 9.00748 (124*2π)/2082 weeks
125-6.43644 -3.08147 (125*2π)/2082 weeks
126-7.71249 -16.09464 (126*2π)/2082 weeks
127-5.44726 -29.04959 (127*2π)/2082 weeks
128.12293 -40.95262 (128*2π)/2082 weeks
1298.75262 -50.85117 (129*2π)/2082 weeks
13019.70026 -58.18739 (130*2π)/2082 weeks
13132.25242 -62.08905 (131*2π)/2082 weeks
13245.15325 -62.45273 (132*2π)/2082 weeks
13357.48715 -59.12156 (133*2π)/2082 weeks
13468.46032 -52.56432 (134*2π)/2082 weeks
13577.02908 -43.07309 (135*2π)/2082 weeks
13682.27041 -31.59271 (136*2π)/2082 weeks
13783.96726 -18.98531 (137*2π)/2082 weeks
13881.91825 -6.43827 (138*2π)/2082 weeks
13976.20981 5.08659 (139*2π)/2081 weeks
14067.12019 14.6196 (140*2π)/2081 weeks
14155.5197 21.16841 (141*2π)/2081 weeks
14242.19544 24.28228 (142*2π)/2081 weeks
14328.16637 23.37178 (143*2π)/2081 weeks
14414.64553 18.47299 (144*2π)/2081 weeks
1452.7204 9.87169 (145*2π)/2081 weeks
146-6.73311 -1.89527 (146*2π)/2081 weeks
147-12.49806 -15.9951 (147*2π)/2081 weeks
148-14.58524 -31.30938 (148*2π)/2081 weeks
149-12.3826 -46.83957 (149*2π)/2081 weeks
150-6.05098 -61.29906 (150*2π)/2081 weeks
1513.95639 -73.57907 (151*2π)/2081 weeks
15216.74318 -82.68965 (152*2π)/2081 weeks
15331.54799 -87.83212 (153*2π)/2081 weeks
15447.42262 -88.69092 (154*2π)/2081 weeks
15562.4584 -85.01067 (155*2π)/2081 weeks
15675.73605 -77.24167 (156*2π)/2081 weeks
15786.2035 -65.75307 (157*2π)/2081 weeks
15892.88812 -51.73684 (158*2π)/2081 weeks
15994.78516 -36.20926 (159*2π)/2081 weeks
16091.93804 -20.59683 (160*2π)/2081 weeks
16184.12847 -6.19655 (161*2π)/2081 weeks
16272.1643 5.54511 (162*2π)/2081 weeks
16356.44649 13.47776 (163*2π)/2081 weeks
16438.55008 16.74125 (164*2π)/2081 weeks
16519.61115 14.70533 (165*2π)/2081 weeks
1661.14425 7.21205 (166*2π)/2081 weeks
167-15.27061 -5.64982 (167*2π)/2081 weeks
168-28.24647 -23.22905 (168*2π)/2081 weeks
169-36.37412 -44.12499 (169*2π)/2081 weeks
170-38.84036 -67.33696 (170*2π)/2081 weeks
171-35.33807 -90.87802 (171*2π)/2081 weeks
172-25.67737 -113.5417 (172*2π)/2081 weeks
173-10.16715 -132.8291 (173*2π)/2081 weeks
17410.20217 -147.7299 (174*2π)/2081 weeks
17533.51622 -156.9519 (175*2π)/2081 weeks
17658.80584 -159.5527 (176*2π)/2081 weeks
17783.93499 -155.0132 (177*2π)/2081 weeks
178106.5068 -143.4972 (178*2π)/2081 weeks
179124.8671 -125.8242 (179*2π)/2081 weeks
180137.1855 -103.3667 (180*2π)/2081 weeks
181142.2929 -77.80681 (181*2π)/2081 weeks
182138.9888 -51.00399 (182*2π)/2081 weeks
183126.9509 -25.5386 (183*2π)/2081 weeks
184106.305 -4.20437 (184*2π)/2081 weeks
18578.51395 11.18054 (185*2π)/2081 weeks
18645.238 18.31191 (186*2π)/2081 weeks
1878.21554 15.27122 (187*2π)/2081 weeks
188-30.21738 1.17912 (188*2π)/2081 weeks
189-66.19978 -24.36912 (189*2π)/2081 weeks
190-97.34438 -61.14169 (190*2π)/2081 weeks
191-120.3737 -108.382 (191*2π)/2081 weeks
192-133.2076 -164.2795 (192*2π)/2081 weeks
193-132.3504 -225.4533 (193*2π)/2081 weeks
194-117.2072 -289.4673 (194*2π)/2081 weeks
195-86.71251 -352.8217 (195*2π)/2081 weeks
196-41.21606 -411.7927 (196*2π)/2081 weeks
19719.38231 -462.7275 (197*2π)/2081 weeks
19892.27933 -502.0395 (198*2π)/2081 weeks
199176.6592 -526.7873 (199*2π)/2081 weeks
200266.5395 -535.1372 (200*2π)/2081 weeks
201359.6805 -524.7623 (201*2π)/2081 weeks
202452.3668 -495.285 (202*2π)/2081 weeks
203540.028 -446.5554 (203*2π)/2081 weeks
204617.7749 -381.0257 (204*2π)/2081 weeks
205683.6766 -301.1083 (205*2π)/2081 weeks
206732.0038 -207.0619 (206*2π)/2081 weeks



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