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Fourier Analysis of ALS


ALS appears to have interesting cyclic behaviour every 27 weeks (107.8625*cosine), 19 weeks (83.7271*sine), and 18 weeks (74.1971*cosine).

ALS has an average price of 392.15 (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 1/9/2017 for ALS, this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0392.1541   0 
1620.7343 415.0721 (1*2π)/272272 weeks
2244.8534 593.5319 (2*2π)/272136 weeks
3-97.57658 477.7346 (3*2π)/27291 weeks
4-221.5476 214.8192 (4*2π)/27268 weeks
5-131.8927 19.22079 (5*2π)/27254 weeks
615.75169 -2.19086 (6*2π)/27245 weeks
769.67451 90.81128 (7*2π)/27239 weeks
84.90654 160.947 (8*2π)/27234 weeks
9-86.67155 131.1253 (9*2π)/27230 weeks
10-107.8625 40.42332 (10*2π)/27227 weeks
11-49.92227 -17.88243 (11*2π)/27225 weeks
1215.24383 1.72542 (12*2π)/27223 weeks
1320.44108 59.5205 (13*2π)/27221 weeks
14-29.77798 83.72709 (14*2π)/27219 weeks
15-74.19705 48.24311 (15*2π)/27218 weeks
16-65.75093 -6.77836 (16*2π)/27217 weeks
17-18.57171 -25.19924 (17*2π)/27216 weeks
1814.02583 4.42898 (18*2π)/27215 weeks
19.07463 41.70874 (19*2π)/27214 weeks
20-39.48579 42.54772 (20*2π)/27214 weeks
21-58.24334 6.30522 (21*2π)/27213 weeks
22-36.17959 -27.54873 (22*2π)/27212 weeks
231.25643 -25.1711 (23*2π)/27212 weeks
2414.20993 5.85848 (24*2π)/27211 weeks
25-7.71291 27.98116 (25*2π)/27211 weeks
26-36.52839 16.36721 (26*2π)/27210 weeks
27-38.96082 -15.36641 (27*2π)/27210 weeks
28-12.70865 -32.6568 (28*2π)/27210 weeks
2913.23656 -18.90153 (29*2π)/2729 weeks
3012.18771 7.78806 (30*2π)/2729 weeks
31-11.42781 16.52708 (31*2π)/2729 weeks
32-28.84311 -1.91955 (32*2π)/2729 weeks
33-19.82584 -26.38851 (33*2π)/2728 weeks
345.75457 -30.23585 (34*2π)/2728 weeks
3520.3974 -10.76321 (35*2π)/2728 weeks
3610.05365 9.1183 (36*2π)/2728 weeks
37-11.21817 7.35496 (37*2π)/2727 weeks
38-18.07485 -13.14541 (38*2π)/2727 weeks
39-2.26837 -28.89693 (39*2π)/2727 weeks
4019.117 -22.61233 (40*2π)/2727 weeks
4123.57785 -1.8837 (41*2π)/2727 weeks
428.12284 10.25659 (42*2π)/2726 weeks
43-8.31013 1.34842 (43*2π)/2726 weeks
44-6.66674 -17.35161 (44*2π)/2726 weeks
4511.2827 -24.26118 (45*2π)/2726 weeks
4625.81343 -11.7367 (46*2π)/2726 weeks
4721.76909 6.12418 (47*2π)/2726 weeks
485.10118 9.92667 (48*2π)/2726 weeks
49-4.54062 -3.33485 (49*2π)/2726 weeks
503.90065 -17.61132 (50*2π)/2725 weeks
5120.9652 -16.26477 (51*2π)/2725 weeks
5227.87823 -.52902 (52*2π)/2725 weeks
5317.69993 12.46177 (53*2π)/2725 weeks
542.58574 9.1943 (54*2π)/2725 weeks
55-.28076 -5.34924 (55*2π)/2725 weeks
5612.0699 -13.83432 (56*2π)/2725 weeks
5725.55347 -6.18639 (57*2π)/2725 weeks
5825.18834 9.4574 (58*2π)/2725 weeks
5911.73827 16.31653 (59*2π)/2725 weeks
60.38708 7.8587 (60*2π)/2725 weeks
613.45461 -5.29693 (61*2π)/2724 weeks
6216.80169 -7.66398 (62*2π)/2724 weeks
6324.93683 3.71161 (63*2π)/2724 weeks
6418.59383 16.35416 (64*2π)/2724 weeks
654.90094 16.66944 (65*2π)/2724 weeks
66-1.01702 5.17765 (66*2π)/2724 weeks
676.88496 -4.43428 (67*2π)/2724 weeks
6819.01147 -.90919 (68*2π)/2724 weeks
6921.19281 12.04904 (69*2π)/2724 weeks
7010.63282 20.22329 (70*2π)/2724 weeks
71-1.21679 14.98068 (71*2π)/2724 weeks
72-1.72565 2.7936 (72*2π)/2724 weeks
738.78398 -2.30265 (73*2π)/2724 weeks
7417.69422 5.45808 (74*2π)/2724 weeks
7514.40804 17.31885 (75*2π)/2724 weeks
762.16858 20.06346 (76*2π)/2724 weeks
77-5.8545 10.87075 (77*2π)/2724 weeks
78-1.45419 .25619 (78*2π)/2723 weeks
799.52408 .0767 (79*2π)/2723 weeks
8014.01185 10.21795 (80*2π)/2723 weeks
816.45474 18.96651 (81*2π)/2723 weeks
82-5.05241 16.32371 (82*2π)/2723 weeks
83-8.08477 5.19956 (83*2π)/2723 weeks
84.11532 -2.02561 (84*2π)/2723 weeks
859.6683 2.47059 (85*2π)/2723 weeks
869.29342 13.21844 (86*2π)/2723 weeks
87-1.00701 17.77189 (87*2π)/2723 weeks
88-10.09609 10.7195 (88*2π)/2723 weeks
89-8.30319 -.33544 (89*2π)/2723 weeks
901.7752 -3.46208 (90*2π)/2723 weeks
918.36943 4.21273 (91*2π)/2723 weeks
923.81531 13.3998 (92*2π)/2723 weeks
93-6.91149 13.24174 (93*2π)/2723 weeks
94-11.93871 3.4809 (94*2π)/2723 weeks
95-5.89349 -5.38017 (95*2π)/2723 weeks
964.1555 -3.97654 (96*2π)/2723 weeks
976.7781 5.41995 (97*2π)/2723 weeks
98-.95929 11.59217 (98*2π)/2723 weeks
99-10.264 7.05969 (99*2π)/2723 weeks
100-10.62749 -3.53958 (100*2π)/2723 weeks
101-1.64299 -8.77426 (101*2π)/2723 weeks
1026.60882 -3.31335 (102*2π)/2723 weeks
1034.97966 6.12695 (103*2π)/2723 weeks
104-4.50036 8.4281 (104*2π)/2723 weeks
105-10.98276 .56464 (105*2π)/2723 weeks
106-7.03553 -9.06681 (106*2π)/2723 weeks
1073.0649 -10.1625 (107*2π)/2723 weeks
1088.24847 -2.05874 (108*2π)/2723 weeks
1093.11793 5.62075 (109*2π)/2722 weeks
110-6.06044 3.88428 (110*2π)/2722 weeks
111-8.51796 -5.55237 (111*2π)/2722 weeks
112-1.11667 -12.28907 (112*2π)/2722 weeks
1138.16362 -9.00548 (113*2π)/2722 weeks
1149.30225 .32767 (114*2π)/2722 weeks
1151.50439 4.98131 (115*2π)/2722 weeks
116-5.94031 -.3958 (116*2π)/2722 weeks
117-4.19626 -9.8005 (117*2π)/2722 weeks
1185.18396 -12.68613 (118*2π)/2722 weeks
11912.0532 -5.85918 (119*2π)/2722 weeks
1209.13501 2.96385 (120*2π)/2722 weeks
121.18208 3.88853 (121*2π)/2722 weeks
122-4.29155 -4.02168 (122*2π)/2722 weeks
1231.12901 -11.73687 (123*2π)/2722 weeks
12410.7012 -10.48205 (124*2π)/2722 weeks
12514.05309 -1.57532 (125*2π)/2722 weeks
1267.87626 5.09856 (126*2π)/2722 weeks
127-.41375 2.29277 (127*2π)/2722 weeks
128-1.08456 -6.47447 (128*2π)/2722 weeks
1296.90239 -10.92362 (129*2π)/2722 weeks
13014.75286 -5.66945 (130*2π)/2722 weeks
13113.79266 3.7098 (131*2π)/2722 weeks
1325.27846 6.97468 (132*2π)/2722 weeks
133-1.03194 .80944 (133*2π)/2722 weeks
1342.10673 -7.4535 (134*2π)/2722 weeks
13511.23551 -8.09838 (135*2π)/2722 weeks
13616.10493   (136*2π)/2722 weeks
13711.23551 8.09838 (137*2π)/2722 weeks
1382.10673 7.4535 (138*2π)/2722 weeks
139-1.03194 -.80944 (139*2π)/2722 weeks
1405.27846 -6.97468 (140*2π)/2722 weeks
14113.79266 -3.7098 (141*2π)/2722 weeks
14214.75286 5.66945 (142*2π)/2722 weeks
1436.90239 10.92362 (143*2π)/2722 weeks
144-1.08456 6.47447 (144*2π)/2722 weeks
145-.41375 -2.29277 (145*2π)/2722 weeks
1467.87626 -5.09856 (146*2π)/2722 weeks
14714.05309 1.57532 (147*2π)/2722 weeks
14810.7012 10.48205 (148*2π)/2722 weeks
1491.12901 11.73687 (149*2π)/2722 weeks
150-4.29155 4.02168 (150*2π)/2722 weeks
151.18208 -3.88853 (151*2π)/2722 weeks
1529.13501 -2.96385 (152*2π)/2722 weeks
15312.0532 5.85918 (153*2π)/2722 weeks
1545.18396 12.68613 (154*2π)/2722 weeks
155-4.19626 9.8005 (155*2π)/2722 weeks
156-5.94031 .3958 (156*2π)/2722 weeks
1571.50439 -4.98131 (157*2π)/2722 weeks
1589.30225 -.32767 (158*2π)/2722 weeks
1598.16362 9.00548 (159*2π)/2722 weeks
160-1.11667 12.28907 (160*2π)/2722 weeks
161-8.51796 5.55237 (161*2π)/2722 weeks
162-6.06044 -3.88428 (162*2π)/2722 weeks
1633.11793 -5.62075 (163*2π)/2722 weeks
1648.24847 2.05874 (164*2π)/2722 weeks
1653.0649 10.1625 (165*2π)/2722 weeks
166-7.03553 9.06681 (166*2π)/2722 weeks
167-10.98276 -.56464 (167*2π)/2722 weeks
168-4.50036 -8.4281 (168*2π)/2722 weeks
1694.97966 -6.12695 (169*2π)/2722 weeks
1706.60882 3.31335 (170*2π)/2722 weeks
171-1.64299 8.77426 (171*2π)/2722 weeks
172-10.62749 3.53958 (172*2π)/2722 weeks
173-10.264 -7.05969 (173*2π)/2722 weeks
174-.95929 -11.59217 (174*2π)/2722 weeks
1756.7781 -5.41995 (175*2π)/2722 weeks
1764.1555 3.97654 (176*2π)/2722 weeks
177-5.89349 5.38017 (177*2π)/2722 weeks
178-11.93871 -3.4809 (178*2π)/2722 weeks
179-6.91149 -13.24174 (179*2π)/2722 weeks
1803.81531 -13.3998 (180*2π)/2722 weeks
1818.36943 -4.21273 (181*2π)/2722 weeks
1821.7752 3.46208 (182*2π)/2721 weeks
183-8.30319 .33544 (183*2π)/2721 weeks
184-10.09609 -10.7195 (184*2π)/2721 weeks
185-1.00701 -17.77189 (185*2π)/2721 weeks
1869.29342 -13.21844 (186*2π)/2721 weeks
1879.6683 -2.47059 (187*2π)/2721 weeks
188.11532 2.02561 (188*2π)/2721 weeks
189-8.08477 -5.19956 (189*2π)/2721 weeks
190-5.05241 -16.32371 (190*2π)/2721 weeks
1916.45474 -18.96651 (191*2π)/2721 weeks
19214.01185 -10.21795 (192*2π)/2721 weeks
1939.52408 -.0767 (193*2π)/2721 weeks
194-1.45419 -.25619 (194*2π)/2721 weeks
195-5.8545 -10.87075 (195*2π)/2721 weeks
1962.16858 -20.06346 (196*2π)/2721 weeks
19714.40804 -17.31885 (197*2π)/2721 weeks
19817.69422 -5.45808 (198*2π)/2721 weeks
1998.78398 2.30265 (199*2π)/2721 weeks
200-1.72565 -2.7936 (200*2π)/2721 weeks
201-1.21679 -14.98068 (201*2π)/2721 weeks
20210.63282 -20.22329 (202*2π)/2721 weeks
20321.19281 -12.04904 (203*2π)/2721 weeks
20419.01147 .90919 (204*2π)/2721 weeks
2056.88496 4.43428 (205*2π)/2721 weeks
206-1.01702 -5.17765 (206*2π)/2721 weeks
2074.90094 -16.66944 (207*2π)/2721 weeks
20818.59383 -16.35416 (208*2π)/2721 weeks
20924.93683 -3.71161 (209*2π)/2721 weeks
21016.80169 7.66398 (210*2π)/2721 weeks
2113.45461 5.29693 (211*2π)/2721 weeks
212.38708 -7.8587 (212*2π)/2721 weeks
21311.73827 -16.31653 (213*2π)/2721 weeks
21425.18834 -9.4574 (214*2π)/2721 weeks
21525.55347 6.18639 (215*2π)/2721 weeks
21612.0699 13.83432 (216*2π)/2721 weeks
217-.28076 5.34924 (217*2π)/2721 weeks
2182.58574 -9.1943 (218*2π)/2721 weeks
21917.69993 -12.46177 (219*2π)/2721 weeks
22027.87823 .52902 (220*2π)/2721 weeks
22120.9652 16.26477 (221*2π)/2721 weeks
2223.90065 17.61132 (222*2π)/2721 weeks
223-4.54062 3.33485 (223*2π)/2721 weeks
2245.10118 -9.92667 (224*2π)/2721 weeks
22521.76909 -6.12418 (225*2π)/2721 weeks
22625.81343 11.7367 (226*2π)/2721 weeks
22711.2827 24.26118 (227*2π)/2721 weeks
228-6.66674 17.35161 (228*2π)/2721 weeks
229-8.31013 -1.34842 (229*2π)/2721 weeks
2308.12284 -10.25659 (230*2π)/2721 weeks
23123.57785 1.8837 (231*2π)/2721 weeks
23219.117 22.61233 (232*2π)/2721 weeks
233-2.26837 28.89693 (233*2π)/2721 weeks
234-18.07485 13.14541 (234*2π)/2721 weeks
235-11.21817 -7.35496 (235*2π)/2721 weeks
23610.05365 -9.1183 (236*2π)/2721 weeks
23720.3974 10.76321 (237*2π)/2721 weeks
2385.75457 30.23585 (238*2π)/2721 weeks
239-19.82584 26.38851 (239*2π)/2721 weeks
240-28.84311 1.91955 (240*2π)/2721 weeks
241-11.42781 -16.52708 (241*2π)/2721 weeks
24212.18771 -7.78806 (242*2π)/2721 weeks
24313.23656 18.90153 (243*2π)/2721 weeks
244-12.70865 32.6568 (244*2π)/2721 weeks
245-38.96082 15.36641 (245*2π)/2721 weeks
246-36.52839 -16.36721 (246*2π)/2721 weeks
247-7.71291 -27.98116 (247*2π)/2721 weeks
24814.20993 -5.85848 (248*2π)/2721 weeks
2491.25643 25.1711 (249*2π)/2721 weeks
250-36.17959 27.54873 (250*2π)/2721 weeks
251-58.24334 -6.30522 (251*2π)/2721 weeks
252-39.48579 -42.54772 (252*2π)/2721 weeks
253.07463 -41.70874 (253*2π)/2721 weeks
25414.02583 -4.42898 (254*2π)/2721 weeks
255-18.57171 25.19924 (255*2π)/2721 weeks
256-65.75093 6.77836 (256*2π)/2721 weeks
257-74.19705 -48.24311 (257*2π)/2721 weeks
258-29.77798 -83.72709 (258*2π)/2721 weeks
25920.44108 -59.5205 (259*2π)/2721 weeks
26015.24383 -1.72542 (260*2π)/2721 weeks
261-49.92227 17.88243 (261*2π)/2721 weeks
262-107.8625 -40.42332 (262*2π)/2721 weeks
263-86.67155 -131.1253 (263*2π)/2721 weeks
2644.90654 -160.947 (264*2π)/2721 weeks
26569.67451 -90.81128 (265*2π)/2721 weeks
26615.75169 2.19086 (266*2π)/2721 weeks
267-131.8927 -19.22079 (267*2π)/2721 weeks
268-221.5476 -214.8192 (268*2π)/2721 weeks
269-97.57658 -477.7346 (269*2π)/2721 weeks
270244.8534 -593.5319 (270*2π)/2721 weeks

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