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Fourier Analysis of ALS


ALS appears to have interesting cyclic behaviour every 27 weeks (110.4445*cosine), 18 weeks (85.487*cosine), and 17 weeks (60.5899*cosine).

ALS has an average price of 395.69 (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 12/5/2016 for ALS, this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0395.6879   0 
1618.8892 428.7771 (1*2π)/267267 weeks
2226.5662 604.7847 (2*2π)/267134 weeks
3-120.8685 472.821 (3*2π)/26789 weeks
4-232.5067 198.2613 (4*2π)/26767 weeks
5-127.2521 8.62691 (5*2π)/26753 weeks
621.45966 3.66045 (6*2π)/26745 weeks
760.76505 104.3989 (7*2π)/26738 weeks
8-17.41689 164.3484 (8*2π)/26733 weeks
9-105.6747 117.8022 (9*2π)/26730 weeks
10-110.4445 22.71456 (10*2π)/26727 weeks
11-41.67809 -22.87532 (11*2π)/26724 weeks
1216.49261 11.68013 (12*2π)/26722 weeks
135.11012 69.23545 (13*2π)/26721 weeks
14-52.01103 78.04694 (14*2π)/26719 weeks
15-85.48695 29.48613 (15*2π)/26718 weeks
16-60.58992 -21.49394 (16*2π)/26717 weeks
17-10.11106 -23.59178 (17*2π)/26716 weeks
189.09656 15.65576 (18*2π)/26715 weeks
19-19.25589 44.58361 (19*2π)/26714 weeks
20-57.34406 28.49027 (20*2π)/26713 weeks
21-60.06113 -13.92679 (21*2π)/26713 weeks
22-25.44355 -36.14767 (22*2π)/26712 weeks
236.93744 -17.687 (23*2π)/26712 weeks
243.25538 15.41246 (24*2π)/26711 weeks
25-27.5325 23.15203 (25*2π)/26711 weeks
26-47.01941 -2.85913 (26*2π)/26710 weeks
27-32.32316 -32.52729 (27*2π)/26710 weeks
28-.50507 -33.67105 (28*2π)/26710 weeks
2913.3733 -8.20477 (29*2π)/2679 weeks
30-3.2366 12.35842 (30*2π)/2679 weeks
31-27.74627 4.22377 (31*2π)/2679 weeks
32-30.08043 -22.37856 (32*2π)/2678 weeks
33-7.0479 -36.83043 (33*2π)/2678 weeks
3415.63877 -23.86259 (34*2π)/2678 weeks
3514.04537 .02169 (35*2π)/2678 weeks
36-6.99711 6.97233 (36*2π)/2677 weeks
37-20.88873 -10.11061 (37*2π)/2677 weeks
38-10.49228 -30.54741 (38*2π)/2677 weeks
3912.87415 -30.70826 (39*2π)/2677 weeks
4023.622 -10.94298 (40*2π)/2677 weeks
4111.55048 5.91517 (41*2π)/2677 weeks
42-7.26364 1.48466 (42*2π)/2676 weeks
43-9.96863 -17.54716 (43*2π)/2676 weeks
446.84866 -28.14256 (44*2π)/2676 weeks
4524.13154 -17.88969 (45*2π)/2676 weeks
4623.06743 1.35137 (46*2π)/2676 weeks
476.51902 7.98853 (47*2π)/2676 weeks
48-5.10827 -4.22083 (48*2π)/2676 weeks
492.08257 -19.65894 (49*2π)/2675 weeks
5019.83524 -19.53668 (50*2π)/2675 weeks
5127.98613 -3.52529 (51*2π)/2675 weeks
5217.99244 10.50068 (52*2π)/2675 weeks
532.28661 7.55829 (53*2π)/2675 weeks
54-.63186 -7.37068 (54*2π)/2675 weeks
5512.38013 -15.7234 (55*2π)/2675 weeks
5626.0077 -7.06619 (56*2π)/2675 weeks
5724.61863 9.20015 (57*2π)/2675 weeks
5810.19061 15.21729 (58*2π)/2675 weeks
59-.50434 5.41516 (59*2π)/2675 weeks
604.42143 -7.51554 (60*2π)/2674 weeks
6118.46988 -7.72735 (61*2π)/2674 weeks
6224.80656 5.44664 (62*2π)/2674 weeks
6315.92682 17.19523 (63*2π)/2674 weeks
642.06639 14.71134 (64*2π)/2674 weeks
65-1.09924 1.9311 (65*2π)/2674 weeks
669.33438 -5.43083 (66*2π)/2674 weeks
6720.43121 1.6901 (67*2π)/2674 weeks
6818.70293 15.37756 (68*2π)/2674 weeks
695.71239 20.24332 (69*2π)/2674 weeks
70-4.05469 11.33396 (70*2π)/2674 weeks
71-.16629 -.37016 (71*2π)/2674 weeks
7211.80441 -.97466 (72*2π)/2674 weeks
7317.07396 10.25563 (73*2π)/2674 weeks
748.87923 20.30638 (74*2π)/2674 weeks
75-3.86167 17.73157 (75*2π)/2674 weeks
76-7.16714 5.82012 (76*2π)/2674 weeks
771.7809 -1.48247 (77*2π)/2673 weeks
7811.57944 4.09231 (78*2π)/2673 weeks
7910.0962 15.70257 (79*2π)/2673 weeks
80-1.49288 19.56319 (80*2π)/2673 weeks
81-10.27356 11.07007 (81*2π)/2673 weeks
82-6.74542 -.01411 (82*2π)/2673 weeks
834.19394 -1.07866 (83*2π)/2673 weeks
849.11323 8.67083 (84*2π)/2673 weeks
851.74859 17.42843 (85*2π)/2673 weeks
86-9.84808 14.62894 (86*2π)/2673 weeks
87-12.7905 3.1568 (87*2π)/2673 weeks
88-4.33034 -4.16605 (88*2π)/2673 weeks
895.12936 .45786 (89*2π)/2673 weeks
904.22573 10.87268 (90*2π)/2673 weeks
91-6.17946 14.29053 (91*2π)/2673 weeks
92-14.18462 6.18187 (92*2π)/2673 weeks
93-10.77028 -4.57893 (93*2π)/2673 weeks
94-.20863 -6.16045 (94*2π)/2673 weeks
955.04431 2.47098 (95*2π)/2673 weeks
96-1.11622 10.49693 (96*2π)/2673 weeks
97-11.41712 7.90963 (97*2π)/2673 weeks
98-13.79508 -2.85116 (98*2π)/2673 weeks
99-5.45046 -9.85574 (99*2π)/2673 weeks
1003.97242 -5.60863 (100*2π)/2673 weeks
1013.691 4.27304 (101*2π)/2673 weeks
102-5.70634 7.69883 (102*2π)/2673 weeks
103-13.0325 .16146 (103*2π)/2673 weeks
104-9.5518 -10.09871 (104*2π)/2673 weeks
105.92907 -11.75682 (105*2π)/2673 weeks
1066.60348 -3.53186 (106*2π)/2673 weeks
1071.41258 4.43483 (107*2π)/2672 weeks
108-7.99647 2.47478 (108*2π)/2672 weeks
109-10.12465 -7.4069 (109*2π)/2672 weeks
110-2.01249 -13.96444 (110*2π)/2672 weeks
1117.36964 -9.85899 (111*2π)/2672 weeks
1127.65687 -.15771 (112*2π)/2672 weeks
113-.86573 3.62787 (113*2π)/2672 weeks
114-7.64717 -3.00194 (114*2π)/2672 weeks
115-4.22403 -12.3612 (115*2π)/2672 weeks
1165.94911 -13.57726 (116*2π)/2672 weeks
11711.5732 -5.25996 (117*2π)/2672 weeks
1186.68757 2.9332 (118*2π)/2672 weeks
119-2.43832 1.57262 (119*2π)/2672 weeks
120-4.64882 -7.58327 (120*2π)/2672 weeks
1213.10123 -13.691 (121*2π)/2672 weeks
12212.26757 -9.48678 (122*2π)/2672 weeks
12312.7026 .3169 (123*2π)/2672 weeks
1244.47878 4.58067 (124*2π)/2672 weeks
125-2.29459 -1.25614 (125*2π)/2672 weeks
126.71423 -9.90008 (126*2π)/2672 weeks
12710.31862 -10.76936 (127*2π)/2672 weeks
12815.58272 -2.36829 (128*2π)/2672 weeks
12910.59786 5.97412 (129*2π)/2672 weeks
1301.39553 5.00842 (130*2π)/2672 weeks
131-1.11679 -3.63918 (131*2π)/2672 weeks
1326.13104 -9.36252 (132*2π)/2672 weeks
13314.77525 -4.96167 (133*2π)/2672 weeks
13414.77525 4.96167 (134*2π)/2672 weeks
1356.13104 9.36252 (135*2π)/2672 weeks
136-1.11679 3.63918 (136*2π)/2672 weeks
1371.39553 -5.00842 (137*2π)/2672 weeks
13810.59786 -5.97412 (138*2π)/2672 weeks
13915.58272 2.36829 (139*2π)/2672 weeks
14010.31862 10.76936 (140*2π)/2672 weeks
141.71423 9.90008 (141*2π)/2672 weeks
142-2.29459 1.25614 (142*2π)/2672 weeks
1434.47878 -4.58067 (143*2π)/2672 weeks
14412.7026 -.3169 (144*2π)/2672 weeks
14512.26757 9.48678 (145*2π)/2672 weeks
1463.10123 13.691 (146*2π)/2672 weeks
147-4.64882 7.58327 (147*2π)/2672 weeks
148-2.43832 -1.57262 (148*2π)/2672 weeks
1496.68757 -2.9332 (149*2π)/2672 weeks
15011.5732 5.25996 (150*2π)/2672 weeks
1515.94911 13.57726 (151*2π)/2672 weeks
152-4.22403 12.3612 (152*2π)/2672 weeks
153-7.64717 3.00194 (153*2π)/2672 weeks
154-.86573 -3.62787 (154*2π)/2672 weeks
1557.65687 .15771 (155*2π)/2672 weeks
1567.36964 9.85899 (156*2π)/2672 weeks
157-2.01249 13.96444 (157*2π)/2672 weeks
158-10.12465 7.4069 (158*2π)/2672 weeks
159-7.99647 -2.47478 (159*2π)/2672 weeks
1601.41258 -4.43483 (160*2π)/2672 weeks
1616.60348 3.53186 (161*2π)/2672 weeks
162.92907 11.75682 (162*2π)/2672 weeks
163-9.5518 10.09871 (163*2π)/2672 weeks
164-13.0325 -.16146 (164*2π)/2672 weeks
165-5.70634 -7.69883 (165*2π)/2672 weeks
1663.691 -4.27304 (166*2π)/2672 weeks
1673.97242 5.60863 (167*2π)/2672 weeks
168-5.45046 9.85574 (168*2π)/2672 weeks
169-13.79508 2.85116 (169*2π)/2672 weeks
170-11.41712 -7.90963 (170*2π)/2672 weeks
171-1.11622 -10.49693 (171*2π)/2672 weeks
1725.04431 -2.47098 (172*2π)/2672 weeks
173-.20863 6.16045 (173*2π)/2672 weeks
174-10.77028 4.57893 (174*2π)/2672 weeks
175-14.18462 -6.18187 (175*2π)/2672 weeks
176-6.17946 -14.29053 (176*2π)/2672 weeks
1774.22573 -10.87268 (177*2π)/2672 weeks
1785.12936 -.45786 (178*2π)/2672 weeks
179-4.33034 4.16605 (179*2π)/2671 weeks
180-12.7905 -3.1568 (180*2π)/2671 weeks
181-9.84808 -14.62894 (181*2π)/2671 weeks
1821.74859 -17.42843 (182*2π)/2671 weeks
1839.11323 -8.67083 (183*2π)/2671 weeks
1844.19394 1.07866 (184*2π)/2671 weeks
185-6.74542 .01411 (185*2π)/2671 weeks
186-10.27356 -11.07007 (186*2π)/2671 weeks
187-1.49288 -19.56319 (187*2π)/2671 weeks
18810.0962 -15.70257 (188*2π)/2671 weeks
18911.57944 -4.09231 (189*2π)/2671 weeks
1901.7809 1.48247 (190*2π)/2671 weeks
191-7.16714 -5.82012 (191*2π)/2671 weeks
192-3.86167 -17.73157 (192*2π)/2671 weeks
1938.87923 -20.30638 (193*2π)/2671 weeks
19417.07396 -10.25563 (194*2π)/2671 weeks
19511.80441 .97466 (195*2π)/2671 weeks
196-.16629 .37016 (196*2π)/2671 weeks
197-4.05469 -11.33396 (197*2π)/2671 weeks
1985.71239 -20.24332 (198*2π)/2671 weeks
19918.70293 -15.37756 (199*2π)/2671 weeks
20020.43121 -1.6901 (200*2π)/2671 weeks
2019.33438 5.43083 (201*2π)/2671 weeks
202-1.09924 -1.9311 (202*2π)/2671 weeks
2032.06639 -14.71134 (203*2π)/2671 weeks
20415.92682 -17.19523 (204*2π)/2671 weeks
20524.80656 -5.44664 (205*2π)/2671 weeks
20618.46988 7.72735 (206*2π)/2671 weeks
2074.42143 7.51554 (207*2π)/2671 weeks
208-.50434 -5.41516 (208*2π)/2671 weeks
20910.19061 -15.21729 (209*2π)/2671 weeks
21024.61863 -9.20015 (210*2π)/2671 weeks
21126.0077 7.06619 (211*2π)/2671 weeks
21212.38013 15.7234 (212*2π)/2671 weeks
213-.63186 7.37068 (213*2π)/2671 weeks
2142.28661 -7.55829 (214*2π)/2671 weeks
21517.99244 -10.50068 (215*2π)/2671 weeks
21627.98613 3.52529 (216*2π)/2671 weeks
21719.83524 19.53668 (217*2π)/2671 weeks
2182.08257 19.65894 (218*2π)/2671 weeks
219-5.10827 4.22083 (219*2π)/2671 weeks
2206.51902 -7.98853 (220*2π)/2671 weeks
22123.06743 -1.35137 (221*2π)/2671 weeks
22224.13154 17.88969 (222*2π)/2671 weeks
2236.84866 28.14256 (223*2π)/2671 weeks
224-9.96863 17.54716 (224*2π)/2671 weeks
225-7.26364 -1.48466 (225*2π)/2671 weeks
22611.55048 -5.91517 (226*2π)/2671 weeks
22723.622 10.94298 (227*2π)/2671 weeks
22812.87415 30.70826 (228*2π)/2671 weeks
229-10.49228 30.54741 (229*2π)/2671 weeks
230-20.88873 10.11061 (230*2π)/2671 weeks
231-6.99711 -6.97233 (231*2π)/2671 weeks
23214.04537 -.02169 (232*2π)/2671 weeks
23315.63877 23.86259 (233*2π)/2671 weeks
234-7.0479 36.83043 (234*2π)/2671 weeks
235-30.08043 22.37856 (235*2π)/2671 weeks
236-27.74627 -4.22377 (236*2π)/2671 weeks
237-3.2366 -12.35842 (237*2π)/2671 weeks
23813.3733 8.20477 (238*2π)/2671 weeks
239-.50507 33.67105 (239*2π)/2671 weeks
240-32.32316 32.52729 (240*2π)/2671 weeks
241-47.01941 2.85913 (241*2π)/2671 weeks
242-27.5325 -23.15203 (242*2π)/2671 weeks
2433.25538 -15.41246 (243*2π)/2671 weeks
2446.93744 17.687 (244*2π)/2671 weeks
245-25.44355 36.14767 (245*2π)/2671 weeks
246-60.06113 13.92679 (246*2π)/2671 weeks
247-57.34406 -28.49027 (247*2π)/2671 weeks
248-19.25589 -44.58361 (248*2π)/2671 weeks
2499.09656 -15.65576 (249*2π)/2671 weeks
250-10.11106 23.59178 (250*2π)/2671 weeks
251-60.58992 21.49394 (251*2π)/2671 weeks
252-85.48695 -29.48613 (252*2π)/2671 weeks
253-52.01103 -78.04694 (253*2π)/2671 weeks
2545.11012 -69.23545 (254*2π)/2671 weeks
25516.49261 -11.68013 (255*2π)/2671 weeks
256-41.67809 22.87532 (256*2π)/2671 weeks
257-110.4445 -22.71456 (257*2π)/2671 weeks
258-105.6747 -117.8022 (258*2π)/2671 weeks
259-17.41689 -164.3484 (259*2π)/2671 weeks
26060.76505 -104.3989 (260*2π)/2671 weeks
26121.45966 -3.66045 (261*2π)/2671 weeks
262-127.2521 -8.62691 (262*2π)/2671 weeks
263-232.5067 -198.2613 (263*2π)/2671 weeks
264-120.8685 -472.821 (264*2π)/2671 weeks
265226.5662 -604.7847 (265*2π)/2671 weeks

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