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Fourier Analysis of ALSN (Allison Transmission Holdings, )


ALSN (Allison Transmission Holdings, ) appears to have interesting cyclic behaviour every 25 weeks (.5907*sine), 18 weeks (.4321*cosine), and 18 weeks (.244*sine).

ALSN (Allison Transmission Holdings, ) has an average price of 25.29 (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 3/15/2012 to 11/21/2016 for ALSN (Allison Transmission Holdings, ), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
025.28639   0 
1-3.45692 -3.79463 (1*2π)/246246 weeks
21.19386 -1.03872 (2*2π)/246123 weeks
3.68348 -1.66753 (3*2π)/24682 weeks
4.10607 -1.75879 (4*2π)/24662 weeks
5.44655 -.62216 (5*2π)/24649 weeks
6-.21144 -.44741 (6*2π)/24641 weeks
7.24289 -.08756 (7*2π)/24635 weeks
8.51111 -.34171 (8*2π)/24631 weeks
9.51659 -.15441 (9*2π)/24627 weeks
10.39684 -.5907 (10*2π)/24625 weeks
11-.1719 -.02515 (11*2π)/24622 weeks
12.22556 -.10013 (12*2π)/24621 weeks
13-.07737 -.04798 (13*2π)/24619 weeks
14.4321 -.24396 (14*2π)/24618 weeks
15.19409 -.34044 (15*2π)/24616 weeks
16.02995 -.13161 (16*2π)/24615 weeks
17-.0589 -.21467 (17*2π)/24614 weeks
18-.05958 -.12145 (18*2π)/24614 weeks
19.12077 -.27781 (19*2π)/24613 weeks
20-.05256 -.09068 (20*2π)/24612 weeks
21.17394 -.10698 (21*2π)/24612 weeks
22.07195 -.04963 (22*2π)/24611 weeks
23-.07515 -.04646 (23*2π)/24611 weeks
24-.09559 -.18604 (24*2π)/24610 weeks
25.1792 .11933 (25*2π)/24610 weeks
26-.14452 -.23264 (26*2π)/2469 weeks
27.09576 -.21613 (27*2π)/2469 weeks
28.00715 -.15624 (28*2π)/2469 weeks
29-.07558 .03228 (29*2π)/2468 weeks
30-.03816 -.24535 (30*2π)/2468 weeks
31-.1265 -.10852 (31*2π)/2468 weeks
32.07678 -.17918 (32*2π)/2468 weeks
33-.16826 -.13672 (33*2π)/2467 weeks
34.02878 -.21523 (34*2π)/2467 weeks
35-.09024 -.24415 (35*2π)/2467 weeks
36.07524 -.05555 (36*2π)/2467 weeks
37.00227 .00503 (37*2π)/2467 weeks
38-.07989 -.05317 (38*2π)/2466 weeks
39.02472 -.02528 (39*2π)/2466 weeks
40-.12422 -.18293 (40*2π)/2466 weeks
41-.01349 -.16295 (41*2π)/2466 weeks
42-.0595 -.18402 (42*2π)/2466 weeks
43-.14264 -.0749 (43*2π)/2466 weeks
44-.12995 -.07178 (44*2π)/2466 weeks
45-.07049 .09599 (45*2π)/2465 weeks
46-.02931 -.1074 (46*2π)/2465 weeks
47.03629 -.07712 (47*2π)/2465 weeks
48-.11119 -.03981 (48*2π)/2465 weeks
49-.12565 .02153 (49*2π)/2465 weeks
50-.04725 -.04825 (50*2π)/2465 weeks
51-.06192 -.06066 (51*2π)/2465 weeks
52-.05714 -.14611 (52*2π)/2465 weeks
53-.1302 -.11269 (53*2π)/2465 weeks
54-.02302 .04981 (54*2π)/2465 weeks
55-.09146 -.09181 (55*2π)/2464 weeks
56.09097 -.09405 (56*2π)/2464 weeks
57-.05733 -.12551 (57*2π)/2464 weeks
58.00494 -.13167 (58*2π)/2464 weeks
59-.11873 -.06548 (59*2π)/2464 weeks
60-.09266 -.03031 (60*2π)/2464 weeks
61.03528 -.03457 (61*2π)/2464 weeks
62.00931 -.11847 (62*2π)/2464 weeks
63-.11481 -.03563 (63*2π)/2464 weeks
64-.03979 -.10764 (64*2π)/2464 weeks
65-.02412 -.02386 (65*2π)/2464 weeks
66-.03381 -.06819 (66*2π)/2464 weeks
67-.02637 -.06012 (67*2π)/2464 weeks
68-.06944 .00358 (68*2π)/2464 weeks
69-.03535 .01902 (69*2π)/2464 weeks
70-.09565 -.0075 (70*2π)/2464 weeks
71-.10413 -.10845 (71*2π)/2463 weeks
72-.14832 -.04556 (72*2π)/2463 weeks
73-.10163 -.01799 (73*2π)/2463 weeks
74-.00587 -.04015 (74*2π)/2463 weeks
75-.05779 -.05334 (75*2π)/2463 weeks
76-.03622 -.08489 (76*2π)/2463 weeks
77.00631 .02595 (77*2π)/2463 weeks
78.01438 -.0616 (78*2π)/2463 weeks
79.03924 -.0513 (79*2π)/2463 weeks
80-.03941 .01945 (80*2π)/2463 weeks
81-.06325 -.00383 (81*2π)/2463 weeks
82.01689 -.01114 (82*2π)/2463 weeks
83-.09184 -.01042 (83*2π)/2463 weeks
84-.08862 .00923 (84*2π)/2463 weeks
85-.01772 .012 (85*2π)/2463 weeks
86.04384 -.04635 (86*2π)/2463 weeks
87-.05219 -.06848 (87*2π)/2463 weeks
88.02508 .04874 (88*2π)/2463 weeks
89-.03503 .06557 (89*2π)/2463 weeks
90-.00832 -.0298 (90*2π)/2463 weeks
91-.01649 -.03297 (91*2π)/2463 weeks
92-.00865 -.09892 (92*2π)/2463 weeks
93.04466 .01953 (93*2π)/2463 weeks
94-.00742 .00449 (94*2π)/2463 weeks
95.00145 -.03473 (95*2π)/2463 weeks
96.00286 .04729 (96*2π)/2463 weeks
97.0054 .04358 (97*2π)/2463 weeks
98-.07785 -.00079 (98*2π)/2463 weeks
99-.04224 .03691 (99*2π)/2462 weeks
100-.07043 -.00869 (100*2π)/2462 weeks
101-.04691 .01448 (101*2π)/2462 weeks
102.01885 -.05209 (102*2π)/2462 weeks
103-.09575 -.04205 (103*2π)/2462 weeks
104-.01883 -.04396 (104*2π)/2462 weeks
105-.03344 -.04341 (105*2π)/2462 weeks
106-.0082 .01265 (106*2π)/2462 weeks
107-.07744 -.01515 (107*2π)/2462 weeks
108-.046 -.0312 (108*2π)/2462 weeks
109-.01528 -.05249 (109*2π)/2462 weeks
110-.08032 -.0395 (110*2π)/2462 weeks
111-.04454 .07302 (111*2π)/2462 weeks
112-.06335 -.0986 (112*2π)/2462 weeks
113-.00431 .02309 (113*2π)/2462 weeks
114-.05844 -.07978 (114*2π)/2462 weeks
115-.02983 -.03008 (115*2π)/2462 weeks
116-.12484 -.02036 (116*2π)/2462 weeks
117-.05686 -.10115 (117*2π)/2462 weeks
118-.03167 .03445 (118*2π)/2462 weeks
119.01129 -.00596 (119*2π)/2462 weeks
120-.01632 -.03318 (120*2π)/2462 weeks
121-.11758 -.01658 (121*2π)/2462 weeks
122-.0401 -.0277 (122*2π)/2462 weeks
123-.02072   (123*2π)/2462 weeks
124-.0401 .0277 (124*2π)/2462 weeks
125-.11758 .01658 (125*2π)/2462 weeks
126-.01632 .03318 (126*2π)/2462 weeks
127.01129 .00596 (127*2π)/2462 weeks
128-.03167 -.03445 (128*2π)/2462 weeks
129-.05686 .10115 (129*2π)/2462 weeks
130-.12484 .02036 (130*2π)/2462 weeks
131-.02983 .03008 (131*2π)/2462 weeks
132-.05844 .07978 (132*2π)/2462 weeks
133-.00431 -.02309 (133*2π)/2462 weeks
134-.06335 .0986 (134*2π)/2462 weeks
135-.04454 -.07302 (135*2π)/2462 weeks
136-.08032 .0395 (136*2π)/2462 weeks
137-.01528 .05249 (137*2π)/2462 weeks
138-.046 .0312 (138*2π)/2462 weeks
139-.07744 .01515 (139*2π)/2462 weeks
140-.0082 -.01265 (140*2π)/2462 weeks
141-.03344 .04341 (141*2π)/2462 weeks
142-.01883 .04396 (142*2π)/2462 weeks
143-.09575 .04205 (143*2π)/2462 weeks
144.01885 .05209 (144*2π)/2462 weeks
145-.04691 -.01448 (145*2π)/2462 weeks
146-.07043 .00869 (146*2π)/2462 weeks
147-.04224 -.03691 (147*2π)/2462 weeks
148-.07785 .00079 (148*2π)/2462 weeks
149.0054 -.04358 (149*2π)/2462 weeks
150.00286 -.04729 (150*2π)/2462 weeks
151.00145 .03473 (151*2π)/2462 weeks
152-.00742 -.00449 (152*2π)/2462 weeks
153.04466 -.01953 (153*2π)/2462 weeks
154-.00865 .09892 (154*2π)/2462 weeks
155-.01649 .03297 (155*2π)/2462 weeks
156-.00832 .0298 (156*2π)/2462 weeks
157-.03503 -.06557 (157*2π)/2462 weeks
158.02508 -.04874 (158*2π)/2462 weeks
159-.05219 .06848 (159*2π)/2462 weeks
160.04384 .04635 (160*2π)/2462 weeks
161-.01772 -.012 (161*2π)/2462 weeks
162-.08862 -.00923 (162*2π)/2462 weeks
163-.09184 .01042 (163*2π)/2462 weeks
164.01689 .01114 (164*2π)/2462 weeks
165-.06325 .00383 (165*2π)/2461 weeks
166-.03941 -.01945 (166*2π)/2461 weeks
167.03924 .0513 (167*2π)/2461 weeks
168.01438 .0616 (168*2π)/2461 weeks
169.00631 -.02595 (169*2π)/2461 weeks
170-.03622 .08489 (170*2π)/2461 weeks
171-.05779 .05334 (171*2π)/2461 weeks
172-.00587 .04015 (172*2π)/2461 weeks
173-.10163 .01799 (173*2π)/2461 weeks
174-.14832 .04556 (174*2π)/2461 weeks
175-.10413 .10845 (175*2π)/2461 weeks
176-.09565 .0075 (176*2π)/2461 weeks
177-.03535 -.01902 (177*2π)/2461 weeks
178-.06944 -.00358 (178*2π)/2461 weeks
179-.02637 .06012 (179*2π)/2461 weeks
180-.03381 .06819 (180*2π)/2461 weeks
181-.02412 .02386 (181*2π)/2461 weeks
182-.03979 .10764 (182*2π)/2461 weeks
183-.11481 .03563 (183*2π)/2461 weeks
184.00931 .11847 (184*2π)/2461 weeks
185.03528 .03457 (185*2π)/2461 weeks
186-.09266 .03031 (186*2π)/2461 weeks
187-.11873 .06548 (187*2π)/2461 weeks
188.00494 .13167 (188*2π)/2461 weeks
189-.05733 .12551 (189*2π)/2461 weeks
190.09097 .09405 (190*2π)/2461 weeks
191-.09146 .09181 (191*2π)/2461 weeks
192-.02302 -.04981 (192*2π)/2461 weeks
193-.1302 .11269 (193*2π)/2461 weeks
194-.05714 .14611 (194*2π)/2461 weeks
195-.06192 .06066 (195*2π)/2461 weeks
196-.04725 .04825 (196*2π)/2461 weeks
197-.12565 -.02153 (197*2π)/2461 weeks
198-.11119 .03981 (198*2π)/2461 weeks
199.03629 .07712 (199*2π)/2461 weeks
200-.02931 .1074 (200*2π)/2461 weeks
201-.07049 -.09599 (201*2π)/2461 weeks
202-.12995 .07178 (202*2π)/2461 weeks
203-.14264 .0749 (203*2π)/2461 weeks
204-.0595 .18402 (204*2π)/2461 weeks
205-.01349 .16295 (205*2π)/2461 weeks
206-.12422 .18293 (206*2π)/2461 weeks
207.02472 .02528 (207*2π)/2461 weeks
208-.07989 .05317 (208*2π)/2461 weeks
209.00227 -.00503 (209*2π)/2461 weeks
210.07524 .05555 (210*2π)/2461 weeks
211-.09024 .24415 (211*2π)/2461 weeks
212.02878 .21523 (212*2π)/2461 weeks
213-.16826 .13672 (213*2π)/2461 weeks
214.07678 .17918 (214*2π)/2461 weeks
215-.1265 .10852 (215*2π)/2461 weeks
216-.03816 .24535 (216*2π)/2461 weeks
217-.07558 -.03228 (217*2π)/2461 weeks
218.00715 .15624 (218*2π)/2461 weeks
219.09576 .21613 (219*2π)/2461 weeks
220-.14452 .23264 (220*2π)/2461 weeks
221.1792 -.11933 (221*2π)/2461 weeks
222-.09559 .18604 (222*2π)/2461 weeks
223-.07515 .04646 (223*2π)/2461 weeks
224.07195 .04963 (224*2π)/2461 weeks
225.17394 .10698 (225*2π)/2461 weeks
226-.05256 .09068 (226*2π)/2461 weeks
227.12077 .27781 (227*2π)/2461 weeks
228-.05958 .12145 (228*2π)/2461 weeks
229-.0589 .21467 (229*2π)/2461 weeks
230.02995 .13161 (230*2π)/2461 weeks
231.19409 .34044 (231*2π)/2461 weeks
232.4321 .24396 (232*2π)/2461 weeks
233-.07737 .04798 (233*2π)/2461 weeks
234.22556 .10013 (234*2π)/2461 weeks
235-.1719 .02515 (235*2π)/2461 weeks
236.39684 .5907 (236*2π)/2461 weeks
237.51659 .15441 (237*2π)/2461 weeks
238.51111 .34171 (238*2π)/2461 weeks
239.24289 .08756 (239*2π)/2461 weeks
240-.21144 .44741 (240*2π)/2461 weeks
241.44655 .62216 (241*2π)/2461 weeks
242.10607 1.75879 (242*2π)/2461 weeks
243.68348 1.66753 (243*2π)/2461 weeks
2441.19386 1.03872 (244*2π)/2461 weeks

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