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Fourier Analysis of ALLY (Ally Financial Inc)


ALLY (Ally Financial Inc) appears to have interesting cyclic behaviour every 23 weeks (477.5169*sine), 21 weeks (453.9956*sine), and 23 weeks (145.0868*cosine).

ALLY (Ally Financial Inc) has an average price of 373.31 (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.

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 5/21/2018 for ALLY (Ally Financial Inc), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0373.3138   0 
1699.9572 89.00515 (1*2π)/226226 weeks
2672.8331 173.7788 (2*2π)/226113 weeks
3635.1976 254.0306 (3*2π)/22675 weeks
4582.5523 325.333 (4*2π)/22657 weeks
5520.9899 385.4626 (5*2π)/22645 weeks
6451.2971 433.1308 (6*2π)/22638 weeks
7375.4197 465.9861 (7*2π)/22632 weeks
8296.916 483.95 (8*2π)/22628 weeks
9219.0084 487.7575 (9*2π)/22625 weeks
10145.0868 477.5169 (10*2π)/22623 weeks
1175.52093 453.9956 (11*2π)/22621 weeks
1215.04347 420.1258 (12*2π)/22619 weeks
13-35.79776 377.3265 (13*2π)/22617 weeks
14-74.92799 328.1244 (14*2π)/22616 weeks
15-102.6331 275.3249 (15*2π)/22615 weeks
16-118.3443 221.5385 (16*2π)/22614 weeks
17-122.5381 169.2356 (17*2π)/22613 weeks
18-116.3603 119.9566 (18*2π)/22613 weeks
19-100.756 77.10615 (19*2π)/22612 weeks
20-77.75977 41.11728 (20*2π)/22611 weeks
21-49.78632 13.50363 (21*2π)/22611 weeks
22-18.94625 -5.34464 (22*2π)/22610 weeks
2313.29229 -14.96412 (23*2π)/22610 weeks
2444.18232 -16.42583 (24*2π)/2269 weeks
2571.85802 -10.0864 (25*2π)/2269 weeks
2695.38371 2.67273 (26*2π)/2269 weeks
27113.395 20.03669 (27*2π)/2268 weeks
28124.8873 41.01785 (28*2π)/2268 weeks
29129.6581 63.4356 (29*2π)/2268 weeks
30127.737 85.52219 (30*2π)/2268 weeks
31119.939 105.647 (31*2π)/2267 weeks
32106.9674 122.6583 (32*2π)/2267 weeks
3389.83529 135.4203 (33*2π)/2267 weeks
3469.98474 143.311 (34*2π)/2267 weeks
3548.7261 145.5653 (35*2π)/2266 weeks
3627.64247 142.3428 (36*2π)/2266 weeks
378.30421 134.1311 (37*2π)/2266 weeks
38-8.79226 121.5278 (38*2π)/2266 weeks
39-22.07774 105.5598 (39*2π)/2266 weeks
40-31.02176 86.76371 (40*2π)/2266 weeks
41-35.12309 67.0853 (41*2π)/2266 weeks
42-34.64449 47.44465 (42*2π)/2265 weeks
43-29.4268 29.02924 (43*2π)/2265 weeks
44-20.39255 12.78019 (44*2π)/2265 weeks
45-7.97325 -.19616 (45*2π)/2265 weeks
466.67062 -9.41089 (46*2π)/2265 weeks
4722.38809 -14.3869 (47*2π)/2265 weeks
4838.17714 -15.114 (48*2π)/2265 weeks
4952.95821 -11.79023 (49*2π)/2265 weeks
5066.03088 -4.88516 (50*2π)/2265 weeks
5176.15101 4.91506 (51*2π)/2264 weeks
5283.11237 16.79412 (52*2π)/2264 weeks
5386.21421 29.81945 (53*2π)/2264 weeks
5485.63092 42.96842 (54*2π)/2264 weeks
5581.31247 55.44263 (55*2π)/2264 weeks
5673.93982 66.04353 (56*2π)/2264 weeks
5763.77754 74.10564 (57*2π)/2264 weeks
5851.85693 79.2567 (58*2π)/2264 weeks
5938.94213 81.18153 (59*2π)/2264 weeks
6025.7632 79.3243 (60*2π)/2264 weeks
6113.47856 74.38536 (61*2π)/2264 weeks
622.97079 66.47847 (62*2π)/2264 weeks
63-5.3637 56.10354 (63*2π)/2264 weeks
64-10.87603 44.04409 (64*2π)/2264 weeks
65-13.21062 31.07107 (65*2π)/2263 weeks
66-12.2197 18.04444 (66*2π)/2263 weeks
67-8.29975 5.90158 (67*2π)/2263 weeks
68-1.42694 -4.92233 (68*2π)/2263 weeks
697.67141 -13.36966 (69*2π)/2263 weeks
7018.412 -19.14926 (70*2π)/2263 weeks
7130.06235 -21.9508 (71*2π)/2263 weeks
7241.82774 -21.66217 (72*2π)/2263 weeks
7352.7584 -18.36456 (73*2π)/2263 weeks
7462.24786 -12.49432 (74*2π)/2263 weeks
7569.71375 -4.35451 (75*2π)/2263 weeks
7674.54029 5.2908 (76*2π)/2263 weeks
7776.54722 15.78917 (77*2π)/2263 weeks
7875.70493 26.42422 (78*2π)/2263 weeks
7971.99526 36.31104 (79*2π)/2263 weeks
8065.65123 44.98256 (80*2π)/2263 weeks
8157.18718 51.57005 (81*2π)/2263 weeks
8247.3277 55.63748 (82*2π)/2263 weeks
8336.54499 57.14392 (83*2π)/2263 weeks
8425.76583 55.86379 (84*2π)/2263 weeks
8515.48251 51.7583 (85*2π)/2263 weeks
866.64986 45.13877 (86*2π)/2263 weeks
87-.36557 36.61551 (87*2π)/2263 weeks
88-4.93822 26.59686 (88*2π)/2263 weeks
89-6.97643 15.73255 (89*2π)/2263 weeks
90-6.29423 4.75394 (90*2π)/2263 weeks
91-2.97828 -5.60809 (91*2π)/2262 weeks
922.80331 -14.65678 (92*2π)/2262 weeks
9310.48365 -21.88472 (93*2π)/2262 weeks
9419.53539 -26.80522 (94*2π)/2262 weeks
9529.38786 -29.36395 (95*2π)/2262 weeks
9639.40653 -29.17539 (96*2π)/2262 weeks
9748.87426 -26.4509 (97*2π)/2262 weeks
9857.01854 -21.44232 (98*2π)/2262 weeks
9963.42726 -14.54453 (99*2π)/2262 weeks
10067.64288 -6.2839 (100*2π)/2262 weeks
10169.45445 2.73499 (101*2π)/2262 weeks
10268.71462 11.86739 (102*2π)/2262 weeks
10365.46124 20.3909 (103*2π)/2262 weeks
10460.0492 27.74153 (104*2π)/2262 weeks
10552.76814 33.32127 (105*2π)/2262 weeks
10644.17826 36.75778 (106*2π)/2262 weeks
10734.87829 37.81507 (107*2π)/2262 weeks
10825.58348 36.42296 (108*2π)/2262 weeks
10916.79308 32.4376 (109*2π)/2262 weeks
1109.37117 26.4788 (110*2π)/2262 weeks
1113.58789 18.78078 (111*2π)/2262 weeks
112-.04919 9.68908 (112*2π)/2262 weeks
113-1.35909   (113*2π)/2262 weeks
114-.04919 -9.68908 (114*2π)/2262 weeks
1153.58789 -18.78078 (115*2π)/2262 weeks
1169.37117 -26.4788 (116*2π)/2262 weeks
11716.79308 -32.4376 (117*2π)/2262 weeks
11825.58348 -36.42296 (118*2π)/2262 weeks
11934.87829 -37.81507 (119*2π)/2262 weeks
12044.17826 -36.75778 (120*2π)/2262 weeks
12152.76814 -33.32127 (121*2π)/2262 weeks
12260.0492 -27.74153 (122*2π)/2262 weeks
12365.46124 -20.3909 (123*2π)/2262 weeks
12468.71462 -11.86739 (124*2π)/2262 weeks
12569.45445 -2.73499 (125*2π)/2262 weeks
12667.64288 6.2839 (126*2π)/2262 weeks
12763.42726 14.54453 (127*2π)/2262 weeks
12857.01854 21.44232 (128*2π)/2262 weeks
12948.87426 26.4509 (129*2π)/2262 weeks
13039.40653 29.17539 (130*2π)/2262 weeks
13129.38786 29.36395 (131*2π)/2262 weeks
13219.53539 26.80522 (132*2π)/2262 weeks
13310.48365 21.88472 (133*2π)/2262 weeks
1342.80331 14.65678 (134*2π)/2262 weeks
135-2.97828 5.60809 (135*2π)/2262 weeks
136-6.29423 -4.75394 (136*2π)/2262 weeks
137-6.97643 -15.73255 (137*2π)/2262 weeks
138-4.93822 -26.59686 (138*2π)/2262 weeks
139-.36557 -36.61551 (139*2π)/2262 weeks
1406.64986 -45.13877 (140*2π)/2262 weeks
14115.48251 -51.7583 (141*2π)/2262 weeks
14225.76583 -55.86379 (142*2π)/2262 weeks
14336.54499 -57.14392 (143*2π)/2262 weeks
14447.3277 -55.63748 (144*2π)/2262 weeks
14557.18718 -51.57005 (145*2π)/2262 weeks
14665.65123 -44.98256 (146*2π)/2262 weeks
14771.99526 -36.31104 (147*2π)/2262 weeks
14875.70493 -26.42422 (148*2π)/2262 weeks
14976.54722 -15.78917 (149*2π)/2262 weeks
15074.54029 -5.2908 (150*2π)/2262 weeks
15169.71375 4.35451 (151*2π)/2261 weeks
15262.24786 12.49432 (152*2π)/2261 weeks
15352.7584 18.36456 (153*2π)/2261 weeks
15441.82774 21.66217 (154*2π)/2261 weeks
15530.06235 21.9508 (155*2π)/2261 weeks
15618.412 19.14926 (156*2π)/2261 weeks
1577.67141 13.36966 (157*2π)/2261 weeks
158-1.42694 4.92233 (158*2π)/2261 weeks
159-8.29975 -5.90158 (159*2π)/2261 weeks
160-12.2197 -18.04444 (160*2π)/2261 weeks
161-13.21062 -31.07107 (161*2π)/2261 weeks
162-10.87603 -44.04409 (162*2π)/2261 weeks
163-5.3637 -56.10354 (163*2π)/2261 weeks
1642.97079 -66.47847 (164*2π)/2261 weeks
16513.47856 -74.38536 (165*2π)/2261 weeks
16625.7632 -79.3243 (166*2π)/2261 weeks
16738.94213 -81.18153 (167*2π)/2261 weeks
16851.85693 -79.2567 (168*2π)/2261 weeks
16963.77754 -74.10564 (169*2π)/2261 weeks
17073.93982 -66.04353 (170*2π)/2261 weeks
17181.31247 -55.44263 (171*2π)/2261 weeks
17285.63092 -42.96842 (172*2π)/2261 weeks
17386.21421 -29.81945 (173*2π)/2261 weeks
17483.11237 -16.79412 (174*2π)/2261 weeks
17576.15101 -4.91506 (175*2π)/2261 weeks
17666.03088 4.88516 (176*2π)/2261 weeks
17752.95821 11.79023 (177*2π)/2261 weeks
17838.17714 15.114 (178*2π)/2261 weeks
17922.38809 14.3869 (179*2π)/2261 weeks
1806.67062 9.41089 (180*2π)/2261 weeks
181-7.97325 .19616 (181*2π)/2261 weeks
182-20.39255 -12.78019 (182*2π)/2261 weeks
183-29.4268 -29.02924 (183*2π)/2261 weeks
184-34.64449 -47.44465 (184*2π)/2261 weeks
185-35.12309 -67.0853 (185*2π)/2261 weeks
186-31.02176 -86.76371 (186*2π)/2261 weeks
187-22.07774 -105.5598 (187*2π)/2261 weeks
188-8.79226 -121.5278 (188*2π)/2261 weeks
1898.30421 -134.1311 (189*2π)/2261 weeks
19027.64247 -142.3428 (190*2π)/2261 weeks
19148.7261 -145.5653 (191*2π)/2261 weeks
19269.98474 -143.311 (192*2π)/2261 weeks
19389.83529 -135.4203 (193*2π)/2261 weeks
194106.9674 -122.6583 (194*2π)/2261 weeks
195119.939 -105.647 (195*2π)/2261 weeks
196127.737 -85.52219 (196*2π)/2261 weeks
197129.6581 -63.4356 (197*2π)/2261 weeks
198124.8873 -41.01785 (198*2π)/2261 weeks
199113.395 -20.03669 (199*2π)/2261 weeks
20095.38371 -2.67273 (200*2π)/2261 weeks
20171.85802 10.0864 (201*2π)/2261 weeks
20244.18232 16.42583 (202*2π)/2261 weeks
20313.29229 14.96412 (203*2π)/2261 weeks
204-18.94625 5.34464 (204*2π)/2261 weeks
205-49.78632 -13.50363 (205*2π)/2261 weeks
206-77.75977 -41.11728 (206*2π)/2261 weeks
207-100.756 -77.10615 (207*2π)/2261 weeks
208-116.3603 -119.9566 (208*2π)/2261 weeks
209-122.5381 -169.2356 (209*2π)/2261 weeks
210-118.3443 -221.5385 (210*2π)/2261 weeks
211-102.6331 -275.3249 (211*2π)/2261 weeks
212-74.92799 -328.1244 (212*2π)/2261 weeks
213-35.79776 -377.3265 (213*2π)/2261 weeks
21415.04347 -420.1258 (214*2π)/2261 weeks
21575.52093 -453.9956 (215*2π)/2261 weeks
216145.0868 -477.5169 (216*2π)/2261 weeks
217219.0084 -487.7575 (217*2π)/2261 weeks
218296.916 -483.95 (218*2π)/2261 weeks
219375.4197 -465.9861 (219*2π)/2261 weeks
220451.2971 -433.1308 (220*2π)/2261 weeks
221520.9899 -385.4626 (221*2π)/2261 weeks
222582.5523 -325.333 (222*2π)/2261 weeks
223635.1976 -254.0306 (223*2π)/2261 weeks
224672.8331 -173.7788 (224*2π)/2261 weeks



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