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Fourier Analysis of 3M

3M appears to have interesting cyclic behaviour every 18 weeks (.0345*cosine), 17 weeks (.0331*sine), and 17 weeks (.0269*cosine).

3M has an average price of .4 (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 5/20/2013 to 3/20/2017 for 3M, this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0.3974   0
1.21469 .49796 (1*2π)/201201 weeks
2-.11631 .21397 (2*2π)/201101 weeks
3-.03895 .03354 (3*2π)/20167 weeks
4.03901 .06602 (4*2π)/20150 weeks
5-.02789 .09914 (5*2π)/20140 weeks
6-.04814 .04801 (6*2π)/20134 weeks
7-.05066 .00599 (7*2π)/20129 weeks
8-.00049 -.01877 (8*2π)/20125 weeks
9.01179 -.00042 (9*2π)/20122 weeks
10.02629 -.00622 (10*2π)/20120 weeks
11.0345 .01787 (11*2π)/20118 weeks
12.02692 .03311 (12*2π)/20117 weeks
13.00765 .0319 (13*2π)/20115 weeks
14.00676 .02517 (14*2π)/20114 weeks
15.00355 .02828 (15*2π)/20113 weeks
16.00444 .02638 (16*2π)/20113 weeks
17-.00371 .02622 (17*2π)/20112 weeks
18-.00937 .02304 (18*2π)/20111 weeks
19-.0191 .01171 (19*2π)/20111 weeks
20-.00665 -.00212 (20*2π)/20110 weeks
21-.00232 .00021 (21*2π)/20110 weeks
22-.00232 -.00178 (22*2π)/2019 weeks
23.00612 -.00867 (23*2π)/2019 weeks
24.01724 -.00244 (24*2π)/2018 weeks
25.01836 .00859 (25*2π)/2018 weeks
26.01277 .01613 (26*2π)/2018 weeks
27.00757 .0132 (27*2π)/2017 weeks
28.01105 .01736 (28*2π)/2017 weeks
29-.00222 .02496 (29*2π)/2017 weeks
30-.01725 .00626 (30*2π)/2017 weeks
31.00594 -.007 (31*2π)/2016 weeks
32.00616 .01514 (32*2π)/2016 weeks
33-.00896 .00542 (33*2π)/2016 weeks
34.00122 -.00208 (34*2π)/2016 weeks
35.005 .00258 (35*2π)/2016 weeks
36-.00057 .00104 (36*2π)/2016 weeks
37.00971 -.00511 (37*2π)/2015 weeks
38.01326 .00334 (38*2π)/2015 weeks
39.01242 .00977 (39*2π)/2015 weeks
40.00562 .01087 (40*2π)/2015 weeks
41.00296 .00858 (41*2π)/2015 weeks
42.00023 .00672 (42*2π)/2015 weeks
43.0054 .00418 (43*2π)/2015 weeks
44.00356 .0064 (44*2π)/2015 weeks
45.00586 .00434 (45*2π)/2014 weeks
46.00154 .01163 (46*2π)/2014 weeks
47-.0015 .00158 (47*2π)/2014 weeks
48.00424 .00293 (48*2π)/2014 weeks
49.00249 .00553 (49*2π)/2014 weeks
50.00041 .00155 (50*2π)/2014 weeks
51.00656 .00146 (51*2π)/2014 weeks
52.00334 .0062 (52*2π)/2014 weeks
53-.00085 .00069 (53*2π)/2014 weeks
54.00597 -.00314 (54*2π)/2014 weeks
55.01207 .00551 (55*2π)/2014 weeks
56.00336 .0096 (56*2π)/2014 weeks
57.00153 .00322 (57*2π)/2014 weeks
58.00555 .00379 (58*2π)/2013 weeks
59.00318 .00877 (59*2π)/2013 weeks
60-.00435 .00299 (60*2π)/2013 weeks
61.00435 -.00509 (61*2π)/2013 weeks
62.00922 .00463 (62*2π)/2013 weeks
63-.00003 .00609 (63*2π)/2013 weeks
64.00441 -.00154 (64*2π)/2013 weeks
65.00569 .00476 (65*2π)/2013 weeks
66.00363 .00427 (66*2π)/2013 weeks
67.00225 .00401 (67*2π)/2013 weeks
68.0018 .00254 (68*2π)/2013 weeks
69.00028 -.00151 (69*2π)/2013 weeks
70.00739 -.00097 (70*2π)/2013 weeks
71.00714 .00387 (71*2π)/2013 weeks
72.00679 .00439 (72*2π)/2013 weeks
73.00357 .00875 (73*2π)/2013 weeks
74-.00176 .00736 (74*2π)/2013 weeks
75-.00365 .00198 (75*2π)/2013 weeks
76-.00297 .00013 (76*2π)/2013 weeks
77-.00297 -.006 (77*2π)/2013 weeks
78.00702 -.00595 (78*2π)/2013 weeks
79.00762 .00074 (79*2π)/2013 weeks
80.00356 -.00002 (80*2π)/2013 weeks
81.00588 -.00197 (81*2π)/2012 weeks
82.00866 .00392 (82*2π)/2012 weeks
83.00312 .00445 (83*2π)/2012 weeks
84.00326 .00129 (84*2π)/2012 weeks
85.00352 .00249 (85*2π)/2012 weeks
86.00117 .00316 (86*2π)/2012 weeks
87.0004 -.00006 (87*2π)/2012 weeks
88.00461 -.0036 (88*2π)/2012 weeks
89.00718 .00263 (89*2π)/2012 weeks
90.00264 .00707 (90*2π)/2012 weeks
91-.00192 .00116 (91*2π)/2012 weeks
92-.0001 -.00248 (92*2π)/2012 weeks
93.00187 -.00074 (93*2π)/2012 weeks
94.00009 -.00371 (94*2π)/2012 weeks
95.00562 -.00798 (95*2π)/2012 weeks
96.01366 -.00039 (96*2π)/2012 weeks
97.00411 .00707 (97*2π)/2012 weeks
98.00224 .00232 (98*2π)/2012 weeks
99.00383 .00452 (99*2π)/2012 weeks
100-.00187 .00186 (100*2π)/2012 weeks
101-.00187 -.00186 (101*2π)/2012 weeks
102.00383 -.00452 (102*2π)/2012 weeks
103.00224 -.00232 (103*2π)/2012 weeks
104.00411 -.00707 (104*2π)/2012 weeks
105.01366 .00039 (105*2π)/2012 weeks
106.00562 .00798 (106*2π)/2012 weeks
107.00009 .00371 (107*2π)/2012 weeks
108.00187 .00074 (108*2π)/2012 weeks
109-.0001 .00248 (109*2π)/2012 weeks
110-.00192 -.00116 (110*2π)/2012 weeks
111.00264 -.00707 (111*2π)/2012 weeks
112.00718 -.00263 (112*2π)/2012 weeks
113.00461 .0036 (113*2π)/2012 weeks
114.0004 .00006 (114*2π)/2012 weeks
115.00117 -.00316 (115*2π)/2012 weeks
116.00352 -.00249 (116*2π)/2012 weeks
117.00326 -.00129 (117*2π)/2012 weeks
118.00312 -.00445 (118*2π)/2012 weeks
119.00866 -.00392 (119*2π)/2012 weeks
120.00588 .00197 (120*2π)/2012 weeks
121.00356 .00002 (121*2π)/2012 weeks
122.00762 -.00074 (122*2π)/2012 weeks
123.00702 .00595 (123*2π)/2012 weeks
124-.00297 .006 (124*2π)/2012 weeks
125-.00297 -.00013 (125*2π)/2012 weeks
126-.00365 -.00198 (126*2π)/2012 weeks
127-.00176 -.00736 (127*2π)/2012 weeks
128.00357 -.00875 (128*2π)/2012 weeks
129.00679 -.00439 (129*2π)/2012 weeks
130.00714 -.00387 (130*2π)/2012 weeks
131.00739 .00097 (131*2π)/2012 weeks
132.00028 .00151 (132*2π)/2012 weeks
133.0018 -.00254 (133*2π)/2012 weeks
134.00225 -.00401 (134*2π)/2012 weeks
135.00363 -.00427 (135*2π)/2011 weeks
136.00569 -.00476 (136*2π)/2011 weeks
137.00441 .00154 (137*2π)/2011 weeks
138-.00003 -.00609 (138*2π)/2011 weeks
139.00922 -.00463 (139*2π)/2011 weeks
140.00435 .00509 (140*2π)/2011 weeks
141-.00435 -.00299 (141*2π)/2011 weeks
142.00318 -.00877 (142*2π)/2011 weeks
143.00555 -.00379 (143*2π)/2011 weeks
144.00153 -.00322 (144*2π)/2011 weeks
145.00336 -.0096 (145*2π)/2011 weeks
146.01207 -.00551 (146*2π)/2011 weeks
147.00597 .00314 (147*2π)/2011 weeks
148-.00085 -.00069 (148*2π)/2011 weeks
149.00334 -.0062 (149*2π)/2011 weeks
150.00656 -.00146 (150*2π)/2011 weeks
151.00041 -.00155 (151*2π)/2011 weeks
152.00249 -.00553 (152*2π)/2011 weeks
153.00424 -.00293 (153*2π)/2011 weeks
154-.0015 -.00158 (154*2π)/2011 weeks
155.00154 -.01163 (155*2π)/2011 weeks
156.00586 -.00434 (156*2π)/2011 weeks
157.00356 -.0064 (157*2π)/2011 weeks
158.0054 -.00418 (158*2π)/2011 weeks
159.00023 -.00672 (159*2π)/2011 weeks
160.00296 -.00858 (160*2π)/2011 weeks
161.00562 -.01087 (161*2π)/2011 weeks
162.01242 -.00977 (162*2π)/2011 weeks
163.01326 -.00334 (163*2π)/2011 weeks
164.00971 .00511 (164*2π)/2011 weeks
165-.00057 -.00104 (165*2π)/2011 weeks
166.005 -.00258 (166*2π)/2011 weeks
167.00122 .00208 (167*2π)/2011 weeks
168-.00896 -.00542 (168*2π)/2011 weeks
169.00616 -.01514 (169*2π)/2011 weeks
170.00594 .007 (170*2π)/2011 weeks
171-.01725 -.00626 (171*2π)/2011 weeks
172-.00222 -.02496 (172*2π)/2011 weeks
173.01105 -.01736 (173*2π)/2011 weeks
174.00757 -.0132 (174*2π)/2011 weeks
175.01277 -.01613 (175*2π)/2011 weeks
176.01836 -.00859 (176*2π)/2011 weeks
177.01724 .00244 (177*2π)/2011 weeks
178.00612 .00867 (178*2π)/2011 weeks
179-.00232 .00178 (179*2π)/2011 weeks
180-.00232 -.00021 (180*2π)/2011 weeks
181-.00665 .00212 (181*2π)/2011 weeks
182-.0191 -.01171 (182*2π)/2011 weeks
183-.00937 -.02304 (183*2π)/2011 weeks
184-.00371 -.02622 (184*2π)/2011 weeks
185.00444 -.02638 (185*2π)/2011 weeks
186.00355 -.02828 (186*2π)/2011 weeks
187.00676 -.02517 (187*2π)/2011 weeks
188.00765 -.0319 (188*2π)/2011 weeks
189.02692 -.03311 (189*2π)/2011 weeks
190.0345 -.01787 (190*2π)/2011 weeks
191.02629 .00622 (191*2π)/2011 weeks
192.01179 .00042 (192*2π)/2011 weeks
193-.00049 .01877 (193*2π)/2011 weeks
194-.05066 -.00599 (194*2π)/2011 weeks
195-.04814 -.04801 (195*2π)/2011 weeks
196-.02789 -.09914 (196*2π)/2011 weeks
197.03901 -.06602 (197*2π)/2011 weeks
198-.03895 -.03354 (198*2π)/2011 weeks
199-.11631 -.21397 (199*2π)/2011 weeks

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