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Fourier Analysis of ALS


ALS appears to have interesting cyclic behaviour every 29 weeks (112.651*cosine), 26 weeks (91.8673*cosine), and 18 weeks (81.2544*cosine).

ALS has an average price of 368.34 (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 11/2/2007 to 4/17/2017 for ALS, this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0368.3406   0 
1595.0468 379.0201 (1*2π)/286286 weeks
2261.1411 560.4464 (2*2π)/286143 weeks
3-64.77329 483.3537 (3*2π)/28695 weeks
4-215.746 252.9196 (4*2π)/28672 weeks
5-167.4333 48.25477 (5*2π)/28657 weeks
6-30.86841 -14.11879 (6*2π)/28648 weeks
754.23841 50.12556 (7*2π)/28641 weeks
829.23923 134.5913 (8*2π)/28636 weeks
9-56.88184 146.4618 (9*2π)/28632 weeks
10-112.651 79.68673 (10*2π)/28629 weeks
11-91.86728 1.61284 (11*2π)/28626 weeks
12-26.35879 -20.82876 (12*2π)/28624 weeks
1316.15553 17.92913 (13*2π)/28622 weeks
14-.1637 66.37148 (14*2π)/28620 weeks
15-50.59938 71.88832 (15*2π)/28619 weeks
16-81.25435 30.18657 (16*2π)/28618 weeks
17-63.83162 -16.88307 (17*2π)/28617 weeks
18-19.50949 -26.79603 (18*2π)/28616 weeks
196.85597 2.70791 (19*2π)/28615 weeks
20-7.44541 35.63646 (20*2π)/28614 weeks
21-43.18785 36.41104 (21*2π)/28614 weeks
22-61.82006 4.3973 (22*2π)/28613 weeks
23-44.82994 -28.54857 (23*2π)/28612 weeks
24-10.16171 -32.00112 (24*2π)/28612 weeks
258.28492 -6.70369 (25*2π)/28611 weeks
26-4.87442 18.57678 (26*2π)/28611 weeks
27-32.71014 17.4024 (27*2π)/28611 weeks
28-45.06958 -8.46973 (28*2π)/28610 weeks
29-29.22853 -32.82606 (29*2π)/28610 weeks
30-1.3195 -32.59642 (30*2π)/28610 weeks
3111.59766 -10.54151 (31*2π)/2869 weeks
32-.91674 9.15443 (32*2π)/2869 weeks
33-23.30684 6.24336 (33*2π)/2869 weeks
34-31.06828 -15.62772 (34*2π)/2868 weeks
35-15.74394 -33.94647 (35*2π)/2868 weeks
367.53325 -30.86991 (36*2π)/2868 weeks
3716.41212 -10.84303 (37*2π)/2868 weeks
384.10466 5.00581 (38*2π)/2868 weeks
39-14.61664 .87737 (39*2π)/2867 weeks
40-19.24511 -18.12483 (40*2π)/2867 weeks
41-4.41981 -32.06787 (41*2π)/2867 weeks
4215.38756 -26.888 (42*2π)/2867 weeks
4321.26528 -8.24904 (43*2π)/2867 weeks
449.02307 4.981 (44*2π)/2867 weeks
45-7.20529 .26369 (45*2π)/2866 weeks
46-9.99502 -16.33254 (46*2π)/2866 weeks
473.75207 -26.99105 (47*2π)/2866 weeks
4820.26492 -20.62136 (48*2π)/2866 weeks
4923.5023 -3.74183 (49*2π)/2866 weeks
5011.42016 6.79659 (50*2π)/2866 weeks
51-2.47227 1.23588 (51*2π)/2866 weeks
52-3.39837 -13.47242 (52*2π)/2866 weeks
539.70237 -21.31196 (53*2π)/2865 weeks
5423.56395 -13.74442 (54*2π)/2865 weeks
5524.50369 1.8761 (55*2π)/2865 weeks
5612.32475 10.29183 (56*2π)/2865 weeks
57.07057 4.01712 (57*2π)/2865 weeks
58.39507 -9.27407 (58*2π)/2865 weeks
5912.74458 -15.02522 (59*2π)/2865 weeks
6024.30822 -6.76528 (60*2π)/2865 weeks
6123.37836 7.56965 (61*2π)/2865 weeks
6211.19399 14.08895 (62*2π)/2865 weeks
63.30967 7.22404 (63*2π)/2865 weeks
641.52861 -4.89398 (64*2π)/2864 weeks
6512.98984 -9.05538 (65*2π)/2864 weeks
6622.42262 -.58163 (66*2π)/2864 weeks
6719.93651 12.17417 (67*2π)/2864 weeks
688.02923 16.66489 (68*2π)/2864 weeks
69-1.25856 9.08694 (69*2π)/2864 weeks
701.12438 -1.97446 (70*2π)/2864 weeks
7112.05791 -4.57374 (71*2π)/2864 weeks
7219.70416 4.30902 (72*2π)/2864 weeks
7315.77715 15.84956 (73*2π)/2864 weeks
743.94048 18.64435 (74*2π)/2864 weeks
75-4.16601 10.38888 (75*2π)/2864 weeks
76-.96011 .05465 (76*2π)/2864 weeks
779.42061 -1.50141 (77*2π)/2864 weeks
7815.60035 7.35845 (78*2π)/2864 weeks
7910.69244 17.55 (79*2π)/2864 weeks
80-.73109 18.75648 (80*2π)/2864 weeks
81-7.53848 9.97985 (81*2π)/2864 weeks
82-3.51328 .38592 (82*2π)/2863 weeks
836.37146 -.23365 (83*2π)/2863 weeks
8411.26248 8.48886 (84*2π)/2863 weeks
855.61326 17.31697 (85*2π)/2863 weeks
86-5.1849 17.00504 (86*2π)/2863 weeks
87-10.52293 7.79334 (87*2π)/2863 weeks
88-5.5102 -.96409 (88*2π)/2863 weeks
894.07204 -.52138 (89*2π)/2863 weeks
907.82068 8.29947 (90*2π)/2863 weeks
911.45705 16.05785 (91*2π)/2863 weeks
92-8.88465 14.46912 (92*2π)/2863 weeks
93-13.04042 4.87132 (93*2π)/2863 weeks
94-7.2662 -3.26134 (94*2π)/2863 weeks
952.02699 -2.12034 (95*2π)/2863 weeks
964.9538 6.50489 (96*2π)/2863 weeks
97-1.67119 13.16144 (97*2π)/2863 weeks
98-11.1794 10.52855 (98*2π)/2863 weeks
99-13.98594 .88319 (99*2π)/2863 weeks
100-7.44896 -6.34846 (100*2π)/2863 weeks
1011.50119 -4.32201 (101*2π)/2863 weeks
1023.58447 4.22888 (102*2π)/2863 weeks
103-3.30672 9.90682 (103*2π)/2863 weeks
104-11.98973 6.35706 (104*2π)/2863 weeks
105-13.4708 -3.22443 (105*2π)/2863 weeks
106-6.1929 -9.45979 (106*2π)/2863 weeks
1072.41741 -6.45736 (107*2π)/2863 weeks
1083.64972 2.15296 (108*2π)/2863 weeks
109-3.55055 7.03307 (109*2π)/2863 weeks
110-11.56027 2.74134 (110*2π)/2863 weeks
111-11.95318 -6.7165 (111*2π)/2863 weeks
112-4.1373 -12.07208 (112*2π)/2863 weeks
1134.1177 -8.33068 (113*2π)/2863 weeks
1144.70706 .16981 (114*2π)/2863 weeks
115-2.49143 4.29461 (115*2π)/2862 weeks
116-9.59102 -.46769 (116*2π)/2862 weeks
117-8.86283 -9.42265 (117*2π)/2862 weeks
118-.66836 -13.55883 (118*2π)/2862 weeks
1196.95657 -8.857 (119*2π)/2862 weeks
1206.62775 -.37126 (120*2π)/2862 weeks
121-.81049 3.00232 (121*2π)/2862 weeks
122-7.19106 -2.2739 (122*2π)/2862 weeks
123-5.48079 -10.79156 (123*2π)/2862 weeks
1242.99476 -13.79473 (124*2π)/2862 weeks
1259.95087 -8.20457 (125*2π)/2862 weeks
1268.70009 .23899 (126*2π)/2862 weeks
1271.00678 2.92141 (127*2π)/2862 weeks
128-4.75875 -2.78368 (128*2π)/2862 weeks
129-2.25625 -10.84403 (129*2π)/2862 weeks
1306.31336 -12.81791 (130*2π)/2862 weeks
13112.53716 -6.53191 (131*2π)/2862 weeks
13210.44726 1.71554 (132*2π)/2862 weeks
1332.65954 3.70125 (133*2π)/2862 weeks
134-2.39182 -2.26977 (134*2π)/2862 weeks
135.83956 -9.63559 (135*2π)/2862 weeks
1369.27986 -10.39173 (136*2π)/2862 weeks
13714.44535 -3.36098 (137*2π)/2862 weeks
13811.20084 4.59566 (138*2π)/2862 weeks
1393.0719 5.66695 (139*2π)/2862 weeks
140-1.4127 -.83852 (140*2π)/2862 weeks
1412.49609 -7.79057 (141*2π)/2862 weeks
14210.84873 -7.58867 (142*2π)/2862 weeks
14315.08299   (143*2π)/2862 weeks
14410.84873 7.58867 (144*2π)/2862 weeks
1452.49609 7.79057 (145*2π)/2862 weeks
146-1.4127 .83852 (146*2π)/2862 weeks
1473.0719 -5.66695 (147*2π)/2862 weeks
14811.20084 -4.59566 (148*2π)/2862 weeks
14914.44535 3.36098 (149*2π)/2862 weeks
1509.27986 10.39173 (150*2π)/2862 weeks
151.83956 9.63559 (151*2π)/2862 weeks
152-2.39182 2.26977 (152*2π)/2862 weeks
1532.65954 -3.70125 (153*2π)/2862 weeks
15410.44726 -1.71554 (154*2π)/2862 weeks
15512.53716 6.53191 (155*2π)/2862 weeks
1566.31336 12.81791 (156*2π)/2862 weeks
157-2.25625 10.84403 (157*2π)/2862 weeks
158-4.75875 2.78368 (158*2π)/2862 weeks
1591.00678 -2.92141 (159*2π)/2862 weeks
1608.70009 -.23899 (160*2π)/2862 weeks
1619.95087 8.20457 (161*2π)/2862 weeks
1622.99476 13.79473 (162*2π)/2862 weeks
163-5.48079 10.79156 (163*2π)/2862 weeks
164-7.19106 2.2739 (164*2π)/2862 weeks
165-.81049 -3.00232 (165*2π)/2862 weeks
1666.62775 .37126 (166*2π)/2862 weeks
1676.95657 8.857 (167*2π)/2862 weeks
168-.66836 13.55883 (168*2π)/2862 weeks
169-8.86283 9.42265 (169*2π)/2862 weeks
170-9.59102 .46769 (170*2π)/2862 weeks
171-2.49143 -4.29461 (171*2π)/2862 weeks
1724.70706 -.16981 (172*2π)/2862 weeks
1734.1177 8.33068 (173*2π)/2862 weeks
174-4.1373 12.07208 (174*2π)/2862 weeks
175-11.95318 6.7165 (175*2π)/2862 weeks
176-11.56027 -2.74134 (176*2π)/2862 weeks
177-3.55055 -7.03307 (177*2π)/2862 weeks
1783.64972 -2.15296 (178*2π)/2862 weeks
1792.41741 6.45736 (179*2π)/2862 weeks
180-6.1929 9.45979 (180*2π)/2862 weeks
181-13.4708 3.22443 (181*2π)/2862 weeks
182-11.98973 -6.35706 (182*2π)/2862 weeks
183-3.30672 -9.90682 (183*2π)/2862 weeks
1843.58447 -4.22888 (184*2π)/2862 weeks
1851.50119 4.32201 (185*2π)/2862 weeks
186-7.44896 6.34846 (186*2π)/2862 weeks
187-13.98594 -.88319 (187*2π)/2862 weeks
188-11.1794 -10.52855 (188*2π)/2862 weeks
189-1.67119 -13.16144 (189*2π)/2862 weeks
1904.9538 -6.50489 (190*2π)/2862 weeks
1912.02699 2.12034 (191*2π)/2861 weeks
192-7.2662 3.26134 (192*2π)/2861 weeks
193-13.04042 -4.87132 (193*2π)/2861 weeks
194-8.88465 -14.46912 (194*2π)/2861 weeks
1951.45705 -16.05785 (195*2π)/2861 weeks
1967.82068 -8.29947 (196*2π)/2861 weeks
1974.07204 .52138 (197*2π)/2861 weeks
198-5.5102 .96409 (198*2π)/2861 weeks
199-10.52293 -7.79334 (199*2π)/2861 weeks
200-5.1849 -17.00504 (200*2π)/2861 weeks
2015.61326 -17.31697 (201*2π)/2861 weeks
20211.26248 -8.48886 (202*2π)/2861 weeks
2036.37146 .23365 (203*2π)/2861 weeks
204-3.51328 -.38592 (204*2π)/2861 weeks
205-7.53848 -9.97985 (205*2π)/2861 weeks
206-.73109 -18.75648 (206*2π)/2861 weeks
20710.69244 -17.55 (207*2π)/2861 weeks
20815.60035 -7.35845 (208*2π)/2861 weeks
2099.42061 1.50141 (209*2π)/2861 weeks
210-.96011 -.05465 (210*2π)/2861 weeks
211-4.16601 -10.38888 (211*2π)/2861 weeks
2123.94048 -18.64435 (212*2π)/2861 weeks
21315.77715 -15.84956 (213*2π)/2861 weeks
21419.70416 -4.30902 (214*2π)/2861 weeks
21512.05791 4.57374 (215*2π)/2861 weeks
2161.12438 1.97446 (216*2π)/2861 weeks
217-1.25856 -9.08694 (217*2π)/2861 weeks
2188.02923 -16.66489 (218*2π)/2861 weeks
21919.93651 -12.17417 (219*2π)/2861 weeks
22022.42262 .58163 (220*2π)/2861 weeks
22112.98984 9.05538 (221*2π)/2861 weeks
2221.52861 4.89398 (222*2π)/2861 weeks
223.30967 -7.22404 (223*2π)/2861 weeks
22411.19399 -14.08895 (224*2π)/2861 weeks
22523.37836 -7.56965 (225*2π)/2861 weeks
22624.30822 6.76528 (226*2π)/2861 weeks
22712.74458 15.02522 (227*2π)/2861 weeks
228.39507 9.27407 (228*2π)/2861 weeks
229.07057 -4.01712 (229*2π)/2861 weeks
23012.32475 -10.29183 (230*2π)/2861 weeks
23124.50369 -1.8761 (231*2π)/2861 weeks
23223.56395 13.74442 (232*2π)/2861 weeks
2339.70237 21.31196 (233*2π)/2861 weeks
234-3.39837 13.47242 (234*2π)/2861 weeks
235-2.47227 -1.23588 (235*2π)/2861 weeks
23611.42016 -6.79659 (236*2π)/2861 weeks
23723.5023 3.74183 (237*2π)/2861 weeks
23820.26492 20.62136 (238*2π)/2861 weeks
2393.75207 26.99105 (239*2π)/2861 weeks
240-9.99502 16.33254 (240*2π)/2861 weeks
241-7.20529 -.26369 (241*2π)/2861 weeks
2429.02307 -4.981 (242*2π)/2861 weeks
24321.26528 8.24904 (243*2π)/2861 weeks
24415.38756 26.888 (244*2π)/2861 weeks
245-4.41981 32.06787 (245*2π)/2861 weeks
246-19.24511 18.12483 (246*2π)/2861 weeks
247-14.61664 -.87737 (247*2π)/2861 weeks
2484.10466 -5.00581 (248*2π)/2861 weeks
24916.41212 10.84303 (249*2π)/2861 weeks
2507.53325 30.86991 (250*2π)/2861 weeks
251-15.74394 33.94647 (251*2π)/2861 weeks
252-31.06828 15.62772 (252*2π)/2861 weeks
253-23.30684 -6.24336 (253*2π)/2861 weeks
254-.91674 -9.15443 (254*2π)/2861 weeks
25511.59766 10.54151 (255*2π)/2861 weeks
256-1.3195 32.59642 (256*2π)/2861 weeks
257-29.22853 32.82606 (257*2π)/2861 weeks
258-45.06958 8.46973 (258*2π)/2861 weeks
259-32.71014 -17.4024 (259*2π)/2861 weeks
260-4.87442 -18.57678 (260*2π)/2861 weeks
2618.28492 6.70369 (261*2π)/2861 weeks
262-10.16171 32.00112 (262*2π)/2861 weeks
263-44.82994 28.54857 (263*2π)/2861 weeks
264-61.82006 -4.3973 (264*2π)/2861 weeks
265-43.18785 -36.41104 (265*2π)/2861 weeks
266-7.44541 -35.63646 (266*2π)/2861 weeks
2676.85597 -2.70791 (267*2π)/2861 weeks
268-19.50949 26.79603 (268*2π)/2861 weeks
269-63.83162 16.88307 (269*2π)/2861 weeks
270-81.25435 -30.18657 (270*2π)/2861 weeks
271-50.59938 -71.88832 (271*2π)/2861 weeks
272-.1637 -66.37148 (272*2π)/2861 weeks
27316.15553 -17.92913 (273*2π)/2861 weeks
274-26.35879 20.82876 (274*2π)/2861 weeks
275-91.86728 -1.61284 (275*2π)/2861 weeks
276-112.651 -79.68673 (276*2π)/2861 weeks
277-56.88184 -146.4618 (277*2π)/2861 weeks
27829.23923 -134.5913 (278*2π)/2861 weeks
27954.23841 -50.12556 (279*2π)/2861 weeks
280-30.86841 14.11879 (280*2π)/2861 weeks
281-167.4333 -48.25477 (281*2π)/2861 weeks
282-215.746 -252.9196 (282*2π)/2861 weeks
283-64.77329 -483.3537 (283*2π)/2861 weeks
284261.1411 -560.4464 (284*2π)/2861 weeks



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