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# Fourier Analysis of TM (Toyota Motor Corporation Common)

TM (Toyota Motor Corporation Common) appears to have interesting cyclic behaviour every 163 weeks (5.7926*sine), 141 weeks (3.3715*sine), and 177 weeks (3.0065*cosine).

TM (Toyota Motor Corporation Common) has an average price of 49.8 (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.

## Fourier Analysis

Using data from 8/18/1976 to 3/20/2017 for TM (Toyota Motor Corporation Common), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
049.79751   0
19.60597 -39.93444 (1*2π)/21182,118 weeks
23.39019 -14.28928 (2*2π)/21181,059 weeks
33.66036 -8.62682 (3*2π)/2118706 weeks
46.62648 -7.02282 (4*2π)/2118530 weeks
5-2.60263 -15.0455 (5*2π)/2118424 weeks
6-7.72723 -8.20526 (6*2π)/2118353 weeks
7.28509 -.80968 (7*2π)/2118303 weeks
8-.25106 -5.65858 (8*2π)/2118265 weeks
9-1.26547 -2.97097 (9*2π)/2118235 weeks
10-.46545 -2.30089 (10*2π)/2118212 weeks
11-2.2626 .00154 (11*2π)/2118193 weeks
123.0065 -.34806 (12*2π)/2118177 weeks
13-.52034 -5.79259 (13*2π)/2118163 weeks
14-1.00241 -2.55713 (14*2π)/2118151 weeks
15-1.09325 -3.37148 (15*2π)/2118141 weeks
16.73398 -.82104 (16*2π)/2118132 weeks
17.56031 -1.6009 (17*2π)/2118125 weeks
18-.7691 .05585 (18*2π)/2118118 weeks
19.78935 -.2144 (19*2π)/2118111 weeks
20-.09317 -1.03751 (20*2π)/2118106 weeks
211.09174 -.06148 (21*2π)/2118101 weeks
222.07983 -2.37014 (22*2π)/211896 weeks
231.03354 -2.85337 (23*2π)/211892 weeks
24.60022 -2.29377 (24*2π)/211888 weeks
25.18867 -1.42727 (25*2π)/211885 weeks
26-.05904 -1.46015 (26*2π)/211881 weeks
27-.278 -1.84817 (27*2π)/211878 weeks
28-.48597 -1.73365 (28*2π)/211876 weeks
29-.59091 -2.43834 (29*2π)/211873 weeks
30-1.69163 -1.46143 (30*2π)/211871 weeks
31-.14026 -.15977 (31*2π)/211868 weeks
32.63161 -.31445 (32*2π)/211866 weeks
33.94171 -.98734 (33*2π)/211864 weeks
34-.12744 -2.13001 (34*2π)/211862 weeks
35-1.2394 -.74506 (35*2π)/211861 weeks
36.40495 -1.14976 (36*2π)/211859 weeks
37-.59881 -1.94825 (37*2π)/211857 weeks
38-.65855 -1.01109 (38*2π)/211856 weeks
39-.29723 -.5625 (39*2π)/211854 weeks
40.19031 -.311 (40*2π)/211853 weeks
41.64186 -.96946 (41*2π)/211852 weeks
42-.48299 -1.0975 (42*2π)/211850 weeks
43.12629 -.93133 (43*2π)/211849 weeks
44-.42137 -1.24494 (44*2π)/211848 weeks
45-.595 -.69135 (45*2π)/211847 weeks
46-.05903 -.42381 (46*2π)/211846 weeks
47-.07257 -.75301 (47*2π)/211845 weeks
48.02163 -.95842 (48*2π)/211844 weeks
49-.49372 -1.04597 (49*2π)/211843 weeks
50-.65667 -.56324 (50*2π)/211842 weeks
51-.02728 -.54028 (51*2π)/211842 weeks
52-.13577 -.97476 (52*2π)/211841 weeks
53-.77968 -.43761 (53*2π)/211840 weeks
54-.51383 -.16684 (54*2π)/211839 weeks
55-.38293 -.22887 (55*2π)/211839 weeks
56.02254 .12521 (56*2π)/211838 weeks
57.09682 -.48409 (57*2π)/211837 weeks
58-.11607 -.79186 (58*2π)/211837 weeks
59.26819 -.0566 (59*2π)/211836 weeks
60.35694 -.72531 (60*2π)/211835 weeks
61-.26073 -.32393 (61*2π)/211835 weeks
62.15048 -.274 (62*2π)/211834 weeks
63.01545 -.50211 (63*2π)/211834 weeks
64.17232 -.65777 (64*2π)/211833 weeks
65-.02277 -.93366 (65*2π)/211833 weeks
66.05904 -.72746 (66*2π)/211832 weeks
67.34004 -.73087 (67*2π)/211832 weeks
68-.16374 -.71808 (68*2π)/211831 weeks
69-.306 -.33896 (69*2π)/211831 weeks
70-.11688 -.20806 (70*2π)/211830 weeks
71.2267 -.40015 (71*2π)/211830 weeks
72-.03503 -.83547 (72*2π)/211829 weeks
73-.02374 -.71541 (73*2π)/211829 weeks
74.14943 -.69908 (74*2π)/211829 weeks
75-.04778 -.66685 (75*2π)/211828 weeks
76-.07031 -.32275 (76*2π)/211828 weeks
77-.17224 -.3017 (77*2π)/211828 weeks
78-.06098 -.32226 (78*2π)/211827 weeks
79-.20821 -.48482 (79*2π)/211827 weeks
80.12993 -.58562 (80*2π)/211826 weeks
81-.24141 -.77398 (81*2π)/211826 weeks
82-.05986 -.52602 (82*2π)/211826 weeks
83-.32196 -.29379 (83*2π)/211826 weeks
84-.05625 -.0566 (84*2π)/211825 weeks
85-.13346 -.15425 (85*2π)/211825 weeks
86-.01663 -.10682 (86*2π)/211825 weeks
87-.07408 -.57908 (87*2π)/211824 weeks
88.16044 -.35415 (88*2π)/211824 weeks
89.11125 -.49465 (89*2π)/211824 weeks
90.05649 -.54768 (90*2π)/211824 weeks
91-.03353 -.29003 (91*2π)/211823 weeks
92.04153 -.33122 (92*2π)/211823 weeks
93-.30065 -.36401 (93*2π)/211823 weeks
94-.1179 -.54976 (94*2π)/211823 weeks
95-.1472 -.37772 (95*2π)/211822 weeks
96.08058 -.31651 (96*2π)/211822 weeks
97-.00022 -.73412 (97*2π)/211822 weeks
98-.12533 -.13925 (98*2π)/211822 weeks
99-.08693 -.35507 (99*2π)/211821 weeks
100-.11021 -.33384 (100*2π)/211821 weeks
101-.23174 -.42398 (101*2π)/211821 weeks
102-.36125 -.41078 (102*2π)/211821 weeks
103-.33282 .06407 (103*2π)/211821 weeks
104.24428 -.38359 (104*2π)/211820 weeks
105-.01095 -.22873 (105*2π)/211820 weeks
106.24809 -.24748 (106*2π)/211820 weeks
107-.25757 -.41226 (107*2π)/211820 weeks
108-.00094 -.26523 (108*2π)/211820 weeks
109-.21983 -.62747 (109*2π)/211819 weeks
110-.69969 .09704 (110*2π)/211819 weeks
111-.10724 -.10011 (111*2π)/211819 weeks
112-.08286 .1316 (112*2π)/211819 weeks
113.06273 -.23296 (113*2π)/211819 weeks
114-.2343 -.1476 (114*2π)/211819 weeks
115-.05139 -.25539 (115*2π)/211818 weeks
116-.25144 -.11755 (116*2π)/211818 weeks
117.02346 -.01375 (117*2π)/211818 weeks
118.15229 -.07477 (118*2π)/211818 weeks
119.09293 -.1347 (119*2π)/211818 weeks
120.08377 -.34435 (120*2π)/211818 weeks
121-.19631 -.14647 (121*2π)/211818 weeks
122.06752 -.00253 (122*2π)/211817 weeks
123.03323 -.30463 (123*2π)/211817 weeks
124.07667 -.33363 (124*2π)/211817 weeks
125-.14198 -.5077 (125*2π)/211817 weeks
126-.14232 -.07622 (126*2π)/211817 weeks
127.052 -.09418 (127*2π)/211817 weeks
128-.03839 -.26626 (128*2π)/211817 weeks
129.27063 -.27903 (129*2π)/211816 weeks
130-.19206 -.55658 (130*2π)/211816 weeks
131-.35993 -.29526 (131*2π)/211816 weeks
132-.03134 .05748 (132*2π)/211816 weeks
133.21489 .06335 (133*2π)/211816 weeks
134.34434 -.25947 (134*2π)/211816 weeks
135-.12784 -.5573 (135*2π)/211816 weeks
136-.3714 -.19339 (136*2π)/211816 weeks
137-.0296 -.0147 (137*2π)/211815 weeks
138-.03763 -.26538 (138*2π)/211815 weeks
139.10267 -.27886 (139*2π)/211815 weeks
140-.1233 -.14816 (140*2π)/211815 weeks
141.15734 -.02235 (141*2π)/211815 weeks
142.07797 -.23997 (142*2π)/211815 weeks
143-.13226 -.0847 (143*2π)/211815 weeks
144.16811 -.20241 (144*2π)/211815 weeks
145-.17 -.45814 (145*2π)/211815 weeks
146.14383 -.25747 (146*2π)/211815 weeks
147.03218 -.42994 (147*2π)/211814 weeks
148.02226 -.24461 (148*2π)/211814 weeks
149-.07841 -.32445 (149*2π)/211814 weeks
150-.1216 -.09428 (150*2π)/211814 weeks
151-.10551 -.11887 (151*2π)/211814 weeks
152-.1598 -.24584 (152*2π)/211814 weeks
153.08661 -.25241 (153*2π)/211814 weeks
154-.04808 -.42204 (154*2π)/211814 weeks
155-.20188 -.03136 (155*2π)/211814 weeks
156.24663 -.11988 (156*2π)/211814 weeks
157-.06165 -.34931 (157*2π)/211813 weeks
158-.09891 -.00103 (158*2π)/211813 weeks
159-.04137 -.2731 (159*2π)/211813 weeks
160-.11306 -.23035 (160*2π)/211813 weeks
161-.01333 -.31 (161*2π)/211813 weeks
162-.16739 -.09488 (162*2π)/211813 weeks
163.12758 -.26566 (163*2π)/211813 weeks
164-.19425 -.08434 (164*2π)/211813 weeks
165.16966 -.11223 (165*2π)/211813 weeks
166-.01945 -.27271 (166*2π)/211813 weeks
167-.07085 -.20485 (167*2π)/211813 weeks
168-.0301 -.32396 (168*2π)/211813 weeks
169.0032 -.21462 (169*2π)/211813 weeks
170-.0057 -.22968 (170*2π)/211812 weeks
171-.15274 -.18959 (171*2π)/211812 weeks
172-.04361 -.26798 (172*2π)/211812 weeks
173-.2723 -.04105 (173*2π)/211812 weeks
174.06288 -.005 (174*2π)/211812 weeks
175.02507 -.31306 (175*2π)/211812 weeks
176-.03448 -.33169 (176*2π)/211812 weeks
177-.0883 -.11151 (177*2π)/211812 weeks
178.01528 -.03426 (178*2π)/211812 weeks
179.11266 -.19711 (179*2π)/211812 weeks
180-.09371 -.48775 (180*2π)/211812 weeks
181-.26651 -.29386 (181*2π)/211812 weeks
182-.23758 -.27983 (182*2π)/211812 weeks
183-.22393 -.04774 (183*2π)/211812 weeks
184.00139 -.16312 (184*2π)/211812 weeks
185-.11289 .06882 (185*2π)/211811 weeks
186.08211 .01269 (186*2π)/211811 weeks
187.03093 -.12727 (187*2π)/211811 weeks
188-.05205 -.21685 (188*2π)/211811 weeks
189-.14212 -.18531 (189*2π)/211811 weeks
190.00282 -.12073 (190*2π)/211811 weeks
191.03131 -.1799 (191*2π)/211811 weeks
192.08018 -.23789 (192*2π)/211811 weeks
193-.01245 -.11443 (193*2π)/211811 weeks
194.13464 -.10746 (194*2π)/211811 weeks
195-.14016 -.18647 (195*2π)/211811 weeks
196.01018 -.2096 (196*2π)/211811 weeks
197-.06822 -.11364 (197*2π)/211811 weeks
198.18273 -.19739 (198*2π)/211811 weeks
199-.06754 -.30499 (199*2π)/211811 weeks
200.09433 -.24718 (200*2π)/211811 weeks
201-.08898 -.33039 (201*2π)/211811 weeks
202-.22152 -.15098 (202*2π)/211810 weeks
203-.17969 -.20823 (203*2π)/211810 weeks
204-.08003 -.15232 (204*2π)/211810 weeks
205-.09628 -.11741 (205*2π)/211810 weeks
206-.05165 -.19756 (206*2π)/211810 weeks
207-.0972 -.15871 (207*2π)/211810 weeks
208.05689 -.01731 (208*2π)/211810 weeks
209-.00304 -.28436 (209*2π)/211810 weeks
210-.07455 -.25917 (210*2π)/211810 weeks
211-.21741 -.26156 (211*2π)/211810 weeks
212-.17886 .05721 (212*2π)/211810 weeks
213.11671 -.09006 (213*2π)/211810 weeks
214.06975 -.28039 (214*2π)/211810 weeks
215-.12528 -.26133 (215*2π)/211810 weeks
216-.23572 -.13375 (216*2π)/211810 weeks
217-.16222 -.07774 (217*2π)/211810 weeks
218.00325 .05263 (218*2π)/211810 weeks
219.14903 -.16678 (219*2π)/211810 weeks
220-.0858 -.24024 (220*2π)/211810 weeks
221-.04203 -.11583 (221*2π)/211810 weeks
222.00216 -.13723 (222*2π)/211810 weeks
223.019 -.19172 (223*2π)/21189 weeks
224-.13037 -.26521 (224*2π)/21189 weeks
225-.07458 -.12866 (225*2π)/21189 weeks
226-.03053 -.15755 (226*2π)/21189 weeks
227-.07364 -.20639 (227*2π)/21189 weeks
228-.07458 -.03804 (228*2π)/21189 weeks
229.00207 -.08926 (229*2π)/21189 weeks
230-.08331 -.10291 (230*2π)/21189 weeks
231-.07969 -.22898 (231*2π)/21189 weeks
232-.13689 -.12399 (232*2π)/21189 weeks
233-.09453 -.17611 (233*2π)/21189 weeks
234-.12608 -.11923 (234*2π)/21189 weeks
235-.01399 -.02771 (235*2π)/21189 weeks
236-.09945 -.10824 (236*2π)/21189 weeks
237-.09962 .06632 (237*2π)/21189 weeks
238-.05203 -.09237 (238*2π)/21189 weeks
239-.11565 -.02442 (239*2π)/21189 weeks
240.04086 -.11735 (240*2π)/21189 weeks
241.01591 -.13773 (241*2π)/21189 weeks
242.08496 -.0883 (242*2π)/21189 weeks
243.01641 -.2518 (243*2π)/21189 weeks
244-.02459 .02492 (244*2π)/21189 weeks
245.02087 -.06059 (245*2π)/21189 weeks
246-.08892 -.17522 (246*2π)/21189 weeks
247-.18512 -.09761 (247*2π)/21189 weeks
248.0158 -.00115 (248*2π)/21189 weeks
249.05815 -.13626 (249*2π)/21189 weeks
250-.04848 -.19871 (250*2π)/21188 weeks
251-.05495 -.09679 (251*2π)/21188 weeks
252-.00309 -.08008 (252*2π)/21188 weeks
253-.1053 -.03865 (253*2π)/21188 weeks
254.03545 -.12477 (254*2π)/21188 weeks
255-.06176 -.19071 (255*2π)/21188 weeks
256.01943 -.07614 (256*2π)/21188 weeks
257.00412 -.22233 (257*2π)/21188 weeks
258-.16352 -.19421 (258*2π)/21188 weeks
259-.04034 -.00386 (259*2π)/21188 weeks
260-.01554 -.01903 (260*2π)/21188 weeks
261.03792 -.14461 (261*2π)/21188 weeks
262-.03833 -.19006 (262*2π)/21188 weeks
263-.10568 -.13044 (263*2π)/21188 weeks
264-.0585 -.05977 (264*2π)/21188 weeks
265-.00728 -.11338 (265*2π)/21188 weeks
266-.0036 -.10638 (266*2π)/21188 weeks
267-.06015 -.17313 (267*2π)/21188 weeks
268-.09252 -.1647 (268*2π)/21188 weeks
269-.06307 -.06279 (269*2π)/21188 weeks
270-.03169 -.10244 (270*2π)/21188 weeks
271.06662 -.10699 (271*2π)/21188 weeks
272-.01575 -.17462 (272*2π)/21188 weeks
273-.08425 -.13933 (273*2π)/21188 weeks
274-.11546 -.03363 (274*2π)/21188 weeks
275.09367 -.01671 (275*2π)/21188 weeks
276.01739 -.25042 (276*2π)/21188 weeks
277-.05316 -.19344 (277*2π)/21188 weeks
278-.06143 -.17863 (278*2π)/21188 weeks
279-.07775 -.02287 (279*2π)/21188 weeks
280.00815 -.17345 (280*2π)/21188 weeks
281-.01857 -.07756 (281*2π)/21188 weeks
282-.05728 -.23828 (282*2π)/21188 weeks
283-.2123 -.23528 (283*2π)/21187 weeks
284-.11284 -.02446 (284*2π)/21187 weeks
285.06273 -.0674 (285*2π)/21187 weeks
286.06624 -.13377 (286*2π)/21187 weeks
287-.05956 -.21191 (287*2π)/21187 weeks
288-.15479 -.09717 (288*2π)/21187 weeks
289-.01064 .0383 (289*2π)/21187 weeks
290-.05256 -.17392 (290*2π)/21187 weeks
291-.08952 -.10514 (291*2π)/21187 weeks
292-.00077 -.25014 (292*2π)/21187 weeks
293-.17349 -.06801 (293*2π)/21187 weeks
294-.01161 -.05696 (294*2π)/21187 weeks
295-.10137 -.17856 (295*2π)/21187 weeks
296-.09062 .0189 (296*2π)/21187 weeks
297-.14394