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Fourier Analysis of MSI (Motorola Solutions, Inc. Common)


MSI (Motorola Solutions, Inc. Common) appears to have interesting cyclic behaviour every 123 weeks (4.6965*sine), 209 weeks (4.3352*sine), and 174 weeks (4.3039*cosine).

MSI (Motorola Solutions, Inc. Common) has an average price of 35.68 (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 1/3/1977 to 1/17/2017 for MSI (Motorola Solutions, Inc. Common), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
035.6825   0 
1-13.43026 -24.10564 (1*2π)/20892,089 weeks
211.15253 -1.61769 (2*2π)/20891,045 weeks
3-.59902 -7.82751 (3*2π)/2089696 weeks
46.77263 -6.77533 (4*2π)/2089522 weeks
5-.85426 -10.88673 (5*2π)/2089418 weeks
6-8.15443 -.8836 (6*2π)/2089348 weeks
77.53139 2.14734 (7*2π)/2089298 weeks
8-1.19923 -7.63516 (8*2π)/2089261 weeks
9.34868 -.24477 (9*2π)/2089232 weeks
10-.19041 -4.33522 (10*2π)/2089209 weeks
11-1.40291 .38386 (11*2π)/2089190 weeks
124.30391 -2.29242 (12*2π)/2089174 weeks
13-2.16375 -2.39106 (13*2π)/2089161 weeks
141.7923 -.96617 (14*2π)/2089149 weeks
15-1.30942 -3.23488 (15*2π)/2089139 weeks
16.88755 1.03485 (16*2π)/2089131 weeks
17.73935 -4.69651 (17*2π)/2089123 weeks
18-1.42916 .82956 (18*2π)/2089116 weeks
192.49137 -3.17509 (19*2π)/2089110 weeks
20-3.04686 -.53599 (20*2π)/2089104 weeks
211.51316 .06672 (21*2π)/208999 weeks
22.78756 -1.9876 (22*2π)/208995 weeks
23-.859 -1.54046 (23*2π)/208991 weeks
24.34617 -.87607 (24*2π)/208987 weeks
25-.87332 -.94304 (25*2π)/208984 weeks
26.58056 -.47774 (26*2π)/208980 weeks
27-.03613 -1.02609 (27*2π)/208977 weeks
28.2302 -.15616 (28*2π)/208975 weeks
29.43248 -1.84164 (29*2π)/208972 weeks
30-.81705 -.31221 (30*2π)/208970 weeks
311.04175 -.53171 (31*2π)/208967 weeks
32-.55146 -.96001 (32*2π)/208965 weeks
33.3836 -.37681 (33*2π)/208963 weeks
34-.03182 -1.24241 (34*2π)/208961 weeks
35.08724 -.34325 (35*2π)/208960 weeks
36.09426 -1.23425 (36*2π)/208958 weeks
37-.7711 -.02079 (37*2π)/208956 weeks
38.49883 -.45625 (38*2π)/208955 weeks
39.69311 -.49745 (39*2π)/208954 weeks
40-.07791 -.93351 (40*2π)/208952 weeks
41-.03327 -1.03149 (41*2π)/208951 weeks
42.13734 .12254 (42*2π)/208950 weeks
431.06979 -1.25858 (43*2π)/208949 weeks
44-.77316 -1.12958 (44*2π)/208947 weeks
45.18814 -1.06191 (45*2π)/208946 weeks
46-1.17775 .04091 (46*2π)/208945 weeks
471.10253 -.6321 (47*2π)/208944 weeks
48-.79131 -.90019 (48*2π)/208944 weeks
49.14783 .10663 (49*2π)/208943 weeks
50.22309 -1.07049 (50*2π)/208942 weeks
51-.53025 -.26727 (51*2π)/208941 weeks
52.63193 -.4614 (52*2π)/208940 weeks
53-.6522 -.90633 (53*2π)/208939 weeks
54.39635 .15974 (54*2π)/208939 weeks
55-.61426 -.89511 (55*2π)/208938 weeks
56.47435 .20097 (56*2π)/208937 weeks
57.00314 -.68713 (57*2π)/208937 weeks
58-.03417 -.48731 (58*2π)/208936 weeks
59-.11542 -.12225 (59*2π)/208935 weeks
60.2399 -.71969 (60*2π)/208935 weeks
61-.1394 .22933 (61*2π)/208934 weeks
62.64866 -.94653 (62*2π)/208934 weeks
63-.07093 -.27156 (63*2π)/208933 weeks
64.29317 -1.15207 (64*2π)/208933 weeks
65-.72885 .11396 (65*2π)/208932 weeks
661.135 -.6757 (66*2π)/208932 weeks
67-.89553 -1.11826 (67*2π)/208931 weeks
68.05048 .0375 (68*2π)/208931 weeks
69-.24733 -.69281 (69*2π)/208930 weeks
70-.10873 -.09972 (70*2π)/208930 weeks
71.14379 -.77874 (71*2π)/208929 weeks
72-.68304 -.29606 (72*2π)/208929 weeks
73.22869 -.02166 (73*2π)/208929 weeks
74-.12256 -.87602 (74*2π)/208928 weeks
75-.21758 .21803 (75*2π)/208928 weeks
76.13767 -.68041 (76*2π)/208927 weeks
77-.52305 -.0219 (77*2π)/208927 weeks
78.54019 -.36507 (78*2π)/208927 weeks
79-.64473 -.61498 (79*2π)/208926 weeks
80.19767 .07579 (80*2π)/208926 weeks
81-.5607 -.46953 (81*2π)/208926 weeks
82.30745 .17143 (82*2π)/208925 weeks
83-.04495 -.66171 (83*2π)/208925 weeks
84-.22956 .00427 (84*2π)/208925 weeks
85.04781 -.03264 (85*2π)/208925 weeks
86.05793 -.60817 (86*2π)/208924 weeks
87-.29156 .19368 (87*2π)/208924 weeks
88.23585 -.44528 (88*2π)/208924 weeks
89-.36848 -.03248 (89*2π)/208923 weeks
90.49587 -.097 (90*2π)/208923 weeks
91-.09297 -.44078 (91*2π)/208923 weeks
92-.02835 .15494 (92*2π)/208923 weeks
93.49722 -.61837 (93*2π)/208922 weeks
94-.27376 -.13975 (94*2π)/208922 weeks
95.34284 -.26751 (95*2π)/208922 weeks
96-.22973 -.43812 (96*2π)/208922 weeks
97-.04197 -.15696 (97*2π)/208922 weeks
98.16642 -.50829 (98*2π)/208921 weeks
99-.3422 .07719 (99*2π)/208921 weeks
100.59959 -.16455 (100*2π)/208921 weeks
101-.10428 -.61814 (101*2π)/208921 weeks
102-.00357 -.15649 (102*2π)/208920 weeks
103-.11843 -.4317 (103*2π)/208920 weeks
104.07519 .12942 (104*2π)/208920 weeks
105.47549 -.54417 (105*2π)/208920 weeks
106-.27181 -.36944 (106*2π)/208920 weeks
107.02812 -.18113 (107*2π)/208920 weeks
108.11579 -.31764 (108*2π)/208919 weeks
109-.03304 -.46439 (109*2π)/208919 weeks
110.05795 -.2971 (110*2π)/208919 weeks
111-.19918 -.31881 (111*2π)/208919 weeks
112.24026 -.32131 (112*2π)/208919 weeks
113-.26194 -.40635 (113*2π)/208918 weeks
114.1362 -.09941 (114*2π)/208918 weeks
115-.02681 -.67733 (115*2π)/208918 weeks
116-.15778 -.2381 (116*2π)/208918 weeks
117-.02602 -.44724 (117*2π)/208918 weeks
118-.49261 -.13363 (118*2π)/208918 weeks
119.19052 -.15928 (119*2π)/208918 weeks
120-.06285 -.38921 (120*2π)/208917 weeks
121-.13903 -.25639 (121*2π)/208917 weeks
122-.27766 -.19808 (122*2π)/208917 weeks
123-.01276 .05982 (123*2π)/208917 weeks
124.23883 -.43141 (124*2π)/208917 weeks
125-.25323 -.26493 (125*2π)/208917 weeks
126.05701 -.24668 (126*2π)/208917 weeks
127-.3114 -.29276 (127*2π)/208916 weeks
128-.02109 -.08734 (128*2π)/208916 weeks
129-.11501 -.17113 (129*2π)/208916 weeks
130.12151 -.32351 (130*2π)/208916 weeks
131-.28505 -.41988 (131*2π)/208916 weeks
132-.29447 .15014 (132*2π)/208916 weeks
133.26643 -.12206 (133*2π)/208916 weeks
134-.22589 -.36016 (134*2π)/208916 weeks
135-.10952 -.09159 (135*2π)/208915 weeks
136-.02068 -.25689 (136*2π)/208915 weeks
137-.12183 .05719 (137*2π)/208915 weeks
138.15045 -.36247 (138*2π)/208915 weeks
139-.23786 -.09132 (139*2π)/208915 weeks
140.13182 -.22671 (140*2π)/208915 weeks
141-.3204 -.20101 (141*2π)/208915 weeks
142.15607 -.03401 (142*2π)/208915 weeks
143-.02878 -.38442 (143*2π)/208915 weeks
144-.2582 .01312 (144*2π)/208915 weeks
145.2279 -.13877 (145*2π)/208914 weeks
146-.17259 -.3759 (146*2π)/208914 weeks
147.05138 .11745 (147*2π)/208914 weeks
148.01428 -.60453 (148*2π)/208914 weeks
149-.29225 .02769 (149*2π)/208914 weeks
150.16389 -.25282 (150*2π)/208914 weeks
151-.24048 -.08739 (151*2π)/208914 weeks
152.11416 -.21162 (152*2π)/208914 weeks
153-.14925 -.27725 (153*2π)/208914 weeks
154-.08037 -.10751 (154*2π)/208914 weeks
155-.07377 -.14944 (155*2π)/208913 weeks
156-.1128 -.18248 (156*2π)/208913 weeks
157-.06222 -.20533 (157*2π)/208913 weeks
158-.05748 -.01789 (158*2π)/208913 weeks
159.00651 -.32179 (159*2π)/208913 weeks
160-.26329 -.08557 (160*2π)/208913 weeks
161-.07011 -.14414 (161*2π)/208913 weeks
162-.05299 -.07857 (162*2π)/208913 weeks
163-.20765 -.13039 (163*2π)/208913 weeks
164.05654 -.03632 (164*2π)/208913 weeks
165-.12662 -.07906 (165*2π)/208913 weeks
166.09023 -.04735 (166*2π)/208913 weeks
167-.07486 -.29593 (167*2π)/208913 weeks
168-.01748 .10809 (168*2π)/208912 weeks
169.03263 -.32043 (169*2π)/208912 weeks
170-.22072 -.00773 (170*2π)/208912 weeks
171.20119 -.12746 (171*2π)/208912 weeks
172-.19409 -.22599 (172*2π)/208912 weeks
173.10319 -.04027 (173*2π)/208912 weeks
174-.21507 -.30161 (174*2π)/208912 weeks
175-.00771 .1232 (175*2π)/208912 weeks
176.18482 -.26584 (176*2π)/208912 weeks
177-.38478 -.15457 (177*2π)/208912 weeks
178.22144 .01256 (178*2π)/208912 weeks
179-.17902 -.28689 (179*2π)/208912 weeks
180.04946 .18075 (180*2π)/208912 weeks
181.04949 -.33118 (181*2π)/208912 weeks
182-.06482 -.12497 (182*2π)/208911 weeks
183-.0912 -.17314 (183*2π)/208911 weeks
184-.01529 -.02928 (184*2π)/208911 weeks
185-.01966 -.0393 (185*2π)/208911 weeks
186.1036 -.28487 (186*2π)/208911 weeks
187-.25959 -.11259 (187*2π)/208911 weeks
188.00475 -.0249 (188*2π)/208911 weeks
189.0406 -.05643 (189*2π)/208911 weeks
190.05016 -.20455 (190*2π)/208911 weeks
191.02452 -.18922 (191*2π)/208911 weeks
192-.1925 -.12936 (192*2π)/208911 weeks
193.04849 -.08032 (193*2π)/208911 weeks
194-.01108 -.13656 (194*2π)/208911 weeks
195.02272 -.24374 (195*2π)/208911 weeks
196-.16862 -.09888 (196*2π)/208911 weeks
197-.04507 -.12915 (197*2π)/208911 weeks
198.08364 -.07955 (198*2π)/208911 weeks
199-.15863 -.20509 (199*2π)/208910 weeks
200-.01028 -.05239 (200*2π)/208910 weeks
201-.12706 -.18322 (201*2π)/208910 weeks
202-.04678 .02921 (202*2π)/208910 weeks
203.06444 -.18593 (203*2π)/208910 weeks
204-.14568 -.06223 (204*2π)/208910 weeks
205.1079 -.15712 (205*2π)/208910 weeks
206-.17874 -.05916 (206*2π)/208910 weeks
207.10031 -.11652 (207*2π)/208910 weeks
208-.09455 -.12345 (208*2π)/208910 weeks
209-.03896 -.06053 (209*2π)/208910 weeks
210.08162 -.08912 (210*2π)/208910 weeks
211-.07152 -.13399 (211*2π)/208910 weeks
212.1027 -.1992 (212*2π)/208910 weeks
213-.20954 -.11101 (213*2π)/208910 weeks
214.07914 -.05882 (214*2π)/208910 weeks
215-.08359 -.22526 (215*2π)/208910 weeks
216-.01691 -.11728 (216*2π)/208910 weeks
217-.13671 .00931 (217*2π)/208910 weeks
218.11572 -.14575 (218*2π)/208910 weeks
219-.08978 -.19156 (219*2π)/208910 weeks
220-.01581 -.03308 (220*2π)/20899 weeks
221.00639 -.11732 (221*2π)/20899 weeks
222-.03413 -.14952 (222*2π)/20899 weeks
223-.01211 -.19555 (223*2π)/20899 weeks
224-.1616 -.14335 (224*2π)/20899 weeks
225.03427 .02859 (225*2π)/20899 weeks
226.00779 -.29972 (226*2π)/20899 weeks
227-.19989 -.04649 (227*2π)/20899 weeks
228.05478 -.02907 (228*2π)/20899 weeks
229-.07385 -.17157 (229*2π)/20899 weeks
230.04489 -.09059 (230*2π)/20899 weeks
231-.20136 -.24296 (231*2π)/20899 weeks
232-.07571 .13823 (232*2π)/20899 weeks
233.13708 -.22488 (233*2π)/20899 weeks
234-.15871 -.14302 (234*2π)/20899 weeks
235-.05298 -.103 (235*2π)/20899 weeks
236-.11132 .02906 (236*2π)/20899 weeks
237.09463 -.06927 (237*2π)/20899 weeks
238.01117 -.23309 (238*2π)/20899 weeks
239-.2222 -.01693 (239*2π)/20899 weeks
240.17421 -.05297 (240*2π)/20899 weeks
241-.1975 -.23479 (241*2π)/20899 weeks
242.06972 .00932 (242*2π)/20899 weeks
243-.13759 -.2439 (243*2π)/20899 weeks
244-.0968 .03627 (244*2π)/20899 weeks
245.03111 -.1567 (245*2π)/20899 weeks
246-.15892 -.04412 (246*2π)/20898 weeks
247.11711 .00763 (247*2π)/20898 weeks
248-.1277 -.21648 (248*2π)/20898 weeks
249-.009 .02781 (249*2π)/20898 weeks
250-.06635 -.07021 (250*2π)/20898 weeks
251.09939 -.0748 (251*2π)/20898 weeks
252-.06696 -.11502 (252*2π)/20898 weeks
253.05525 -.09253 (253*2π)/20898 weeks
254-.07715 -.15369 (254*2π)/20898 weeks
255.00853 -.12607 (255*2π)/20898 weeks
256-.05403 -.09862 (256*2π)/20898 weeks
257-.08102 -.13979 (257*2π)/20898 weeks
258-.00258 -.09675 (258*2π)/20898 weeks
259-.18528 -.04595 (259*2π)/20898 weeks
260.13265 .01291 (260*2π)/20898 weeks
261-.03514 -.27894 (261*2π)/20898 weeks
262-.07251 -.0457 (262*2π)/20898 weeks
263-.10049 -.14424 (263*2π)/20898 weeks
264-.0037 .08957 (264*2π)/20898 weeks
265.02714 -.23072 (265*2π)/20898 weeks
266-.14754 -.04033 (266*2π)/20898 weeks
267-.00879 -.04482 (267*2π)/20898 weeks
268.10462 -.09897 (268*2π)/20898 weeks
269-.11617 -.13108 (269*2π)/20898 weeks
270.03681 -.09234 (270*2π)/20898 weeks
271-.16055 -.04707 (271*2π)/20898 weeks
272.19064 -.10191 (272*2π)/20898 weeks
273-.15239 -.24643 (273*2π)/20898 weeks
274-.03463 .0081 (274*2π)/20898 weeks
275.01635 -.16875 (275*2π)/20898 weeks
276-.06657 -.10078 (276*2π)/20898 weeks
277-.01607 -.10933 (277*2π)/20898 weeks
278-.05421 -.14204 (278*2π)/20898 weeks
279-.07707 -.10236 (279*2π)/20897 weeks
280-.05583 -.1951 (280*2π)/20897 weeks
281-.20389 -.01226 (281*2π)/20897 weeks
282.00609 .01472 (282*2π)/20897 weeks
283.01979 -.1832 (283*2π)/20897 weeks
284-.15495 -.05626 (284*2π)/20897 weeks
285-.0287 -.04147 (285*2π)/20897 weeks
286-.03953 -.06978 (286*2π)/20897 weeks
287-.05831 -.16464 (287*2π)/20897 weeks
288-.12674 .08939 (288*2π)/20897 weeks
289.08532 -.1402 (289*2π)/20897 weeks
290-.06536 -.10307 (290*2π)/20897 weeks
291-.03081 -.13449 (291*2π)/20897 weeks
292-.1202 -.04205 (292*2π)/20897 weeks
293-.0398 -.0183 (293*2π)/20897 weeks
294-.02502 -.12595 (294*2π)/20897 weeks
295-.0484 -.04994 (295*2π)/20897 weeks
296-.02988 -.08134 (296*2π)/20897 weeks
297-.05841 -.12984 (297*2π)/20897 weeks
298-.071 -.08164 (298*2π)/20897 weeks
299-.06867 -.04509 (299*2π)/20897 weeks
300-.09341 -.04747 (300*2π)/20897 weeks
301-.04148 -.05847 (301*2π)/20897 weeks
302-.07058 -.04255 (302*2π)/20897 weeks
303-.01127 .03964 (303*2π)/20897 weeks
304.03978 -.1234 (304*2π)/20897 weeks
305-.1075 -.03604 (305*2π)/20897 weeks
306.08084