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# Fourier Analysis of MITSY (Mitsui & Co.)

MITSY (Mitsui & Co.) appears to have interesting cyclic behaviour every 26 weeks (6.5629*cosine), 28 weeks (5.2305*cosine), and 26 weeks (3.9712*sine).

MITSY (Mitsui & Co.) has an average price of 288.26 (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 4/25/2011 to 5/21/2018 for MITSY (Mitsui & Co.), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0288.2642   0
124.50082 18.038 (1*2π)/370370 weeks
226.87824 -8.54622 (2*2π)/370185 weeks
3-3.86632 1.96221 (3*2π)/370123 weeks
46.00962 -.21617 (4*2π)/37093 weeks
58.27798 .25012 (5*2π)/37074 weeks
6.60887 -10.06994 (6*2π)/37062 weeks
72.56204 -.74092 (7*2π)/37053 weeks
82.56415 -5.34797 (8*2π)/37046 weeks
94.50691 5.83963 (9*2π)/37041 weeks
10-2.80381 .29296 (10*2π)/37037 weeks
11-.01915 1.82679 (11*2π)/37034 weeks
12-3.35426 .30456 (12*2π)/37031 weeks
13-5.23047 4.07837 (13*2π)/37028 weeks
14-6.56294 -3.97122 (14*2π)/37026 weeks
15-2.28545 -1.87061 (15*2π)/37025 weeks
16-.00753 2.10068 (16*2π)/37023 weeks
173.48112 -.79661 (17*2π)/37022 weeks
18.97459 .66913 (18*2π)/37021 weeks
19-1.24358 .76274 (19*2π)/37019 weeks
201.51028 -2.69342 (20*2π)/37019 weeks
21.38853 -.95892 (21*2π)/37018 weeks
22.60796 -1.93811 (22*2π)/37017 weeks
232.28887 -2.0637 (23*2π)/37016 weeks
241.18613 -2.16771 (24*2π)/37015 weeks
252.41643 -.46769 (25*2π)/37015 weeks
26.44947 -.58414 (26*2π)/37014 weeks
27-.93472 -1.85181 (27*2π)/37014 weeks
281.95423 -.23478 (28*2π)/37013 weeks
29-.13952 -1.76262 (29*2π)/37013 weeks
30.12912 -.09502 (30*2π)/37012 weeks
31.07201 .12193 (31*2π)/37012 weeks
32.07204 -.02476 (32*2π)/37012 weeks
33-.19995 -.69693 (33*2π)/37011 weeks
34.16488 -.87294 (34*2π)/37011 weeks
352.05568 -.30261 (35*2π)/37011 weeks
36-.25674 .36099 (36*2π)/37010 weeks
37.74848 -.0753 (37*2π)/37010 weeks
382.11244 1.00581 (38*2π)/37010 weeks
39-.29653 .9412 (39*2π)/3709 weeks
40-.58958 .20581 (40*2π)/3709 weeks
41-.2501 -.11375 (41*2π)/3709 weeks
42.06079 -.80406 (42*2π)/3709 weeks
43-1.20901 2.4513 (43*2π)/3709 weeks
44.00895 -.22392 (44*2π)/3708 weeks
45-1.20999 .01517 (45*2π)/3708 weeks
46-1.7766 .81512 (46*2π)/3708 weeks
47-1.06473 .58122 (47*2π)/3708 weeks
48-.19299 .18823 (48*2π)/3708 weeks
49-1.11054 -.85946 (49*2π)/3708 weeks
50-.29084 .28074 (50*2π)/3707 weeks
51-.75923 .50619 (51*2π)/3707 weeks
52-.27653 -1.06484 (52*2π)/3707 weeks
53-.19645 .03952 (53*2π)/3707 weeks
54-.36449 -1.20203 (54*2π)/3707 weeks
55.25751 -1.35587 (55*2π)/3707 weeks
56.9416 .3322 (56*2π)/3707 weeks
57.48661 .30971 (57*2π)/3706 weeks
581.10095 -.07213 (58*2π)/3706 weeks
59-.34143 .79671 (59*2π)/3706 weeks
601.5084 .06981 (60*2π)/3706 weeks
61.131 .53485 (61*2π)/3706 weeks
62-.19372 .0478 (62*2π)/3706 weeks
63.08407 .91116 (63*2π)/3706 weeks
64-.73888 -.57913 (64*2π)/3706 weeks
65-.08987 -.80046 (65*2π)/3706 weeks
66-.55138 .69903 (66*2π)/3706 weeks
67.47609 .60836 (67*2π)/3706 weeks
68.27451 -.51368 (68*2π)/3705 weeks
69-1.24154 -.15033 (69*2π)/3705 weeks
70-.11611 -.28426 (70*2π)/3705 weeks
711.13291 -.71859 (71*2π)/3705 weeks
72.12491 .7622 (72*2π)/3705 weeks
73.76601 .52295 (73*2π)/3705 weeks
74-.55201 -1.15475 (74*2π)/3705 weeks
75-.51077 .33435 (75*2π)/3705 weeks
76.18203 -.10353 (76*2π)/3705 weeks
77.75387 .2182 (77*2π)/3705 weeks
78-.60508 .74629 (78*2π)/3705 weeks
79.40161 -.34426 (79*2π)/3705 weeks
80-.23712 -.24835 (80*2π)/3705 weeks
81-.18914 -.35447 (81*2π)/3705 weeks
82-.02151 -.19215 (82*2π)/3705 weeks
83.4232 -.13794 (83*2π)/3704 weeks
84-.18081 .68032 (84*2π)/3704 weeks
85.31708 -.56057 (85*2π)/3704 weeks
861.10964 -.32046 (86*2π)/3704 weeks
87.87266 .1329 (87*2π)/3704 weeks
88-.40671 -.06457 (88*2π)/3704 weeks
89.11677 -.3794 (89*2π)/3704 weeks
90-.43108 -.00652 (90*2π)/3704 weeks
91.54346 -.22172 (91*2π)/3704 weeks
92.31955 -.49269 (92*2π)/3704 weeks
93.6797 .15682 (93*2π)/3704 weeks
94.48515 .13863 (94*2π)/3704 weeks
95-.27704 .76744 (95*2π)/3704 weeks
96-.03175 .15309 (96*2π)/3704 weeks
97.79865 .72905 (97*2π)/3704 weeks
98-.59204 .49797 (98*2π)/3704 weeks
99-.59825 .68445 (99*2π)/3704 weeks
100-.48762 -.00176 (100*2π)/3704 weeks
101-.38416 -.02767 (101*2π)/3704 weeks
102-.07631 .01648 (102*2π)/3704 weeks
103.11678 .03429 (103*2π)/3704 weeks
104-.55488 .00456 (104*2π)/3704 weeks
105.21246 1.04014 (105*2π)/3704 weeks
106.0347 -.59233 (106*2π)/3703 weeks
107.43832 .00107 (107*2π)/3703 weeks
108-.0828 .17228 (108*2π)/3703 weeks
109.11046 .55942 (109*2π)/3703 weeks
110-.321 .67409 (110*2π)/3703 weeks
111-.34935 -.65569 (111*2π)/3703 weeks
112.5575 -.62335 (112*2π)/3703 weeks
113-.04799 .43481 (113*2π)/3703 weeks
114.00288 -.50287 (114*2π)/3703 weeks
115-.12048 .00427 (115*2π)/3703 weeks
116.15168 -.75712 (116*2π)/3703 weeks
117-.21638 .16067 (117*2π)/3703 weeks
118-.24188 .30605 (118*2π)/3703 weeks
119.25768 -.64589 (119*2π)/3703 weeks
120.0877 .58533 (120*2π)/3703 weeks
121-.1892 .22599 (121*2π)/3703 weeks
122-.43281 .43717 (122*2π)/3703 weeks
123.04238 .42815 (123*2π)/3703 weeks
124.26307 .19205 (124*2π)/3703 weeks
125.15724 -.25032 (125*2π)/3703 weeks
126.06127 .12877 (126*2π)/3703 weeks
127.61446 .25806 (127*2π)/3703 weeks
128.3917 .60527 (128*2π)/3703 weeks
129.76334 -.44368 (129*2π)/3703 weeks
130.18819 .38695 (130*2π)/3703 weeks
131.44429 .50665 (131*2π)/3703 weeks
132-.38342 .23267 (132*2π)/3703 weeks
133-.09843 -.07856 (133*2π)/3703 weeks
134-.2584 .35837 (134*2π)/3703 weeks
135-.70469 -.08601 (135*2π)/3703 weeks
136-.88052 .0218 (136*2π)/3703 weeks
137-.11017 -1.20601 (137*2π)/3703 weeks
138.02035 -.48377 (138*2π)/3703 weeks
139.1064 -.04807 (139*2π)/3703 weeks
140.12764 -.28036 (140*2π)/3703 weeks
141.15782 -.48922 (141*2π)/3703 weeks
142.34063 .31529 (142*2π)/3703 weeks
143-.04476 .31762 (143*2π)/3703 weeks
144.23691 .18987 (144*2π)/3703 weeks
145.12513 .56909 (145*2π)/3703 weeks
146-.278 .62565 (146*2π)/3703 weeks
147-.20464 .3412 (147*2π)/3703 weeks
148.24499 .22843 (148*2π)/3703 weeks
149-.58686 -.10163 (149*2π)/3702 weeks
150-.13724 .56941 (150*2π)/3702 weeks
151-.62031 .06869 (151*2π)/3702 weeks
152-.04353 .08619 (152*2π)/3702 weeks
153.13108 -.25335 (153*2π)/3702 weeks
154.45749 .12033 (154*2π)/3702 weeks
155.32669 .09409 (155*2π)/3702 weeks
156.58676 .16331 (156*2π)/3702 weeks
157-.45877 .15885 (157*2π)/3702 weeks
158.23658 -.03037 (158*2π)/3702 weeks
159-.03118 -.17506 (159*2π)/3702 weeks
160-.66953 .47541 (160*2π)/3702 weeks
161-.31622 .24479 (161*2π)/3702 weeks
162-.42632 -.27521 (162*2π)/3702 weeks
163-.04471 .03396 (163*2π)/3702 weeks
164.7142 .29779 (164*2π)/3702 weeks
165.06127 -.52541 (165*2π)/3702 weeks
166-.11212 -.52991 (166*2π)/3702 weeks
167.618 .00254 (167*2π)/3702 weeks
168.65295 -.04619 (168*2π)/3702 weeks
169.44105 .09956 (169*2π)/3702 weeks
170.05012 -.20362 (170*2π)/3702 weeks
171.56019 .32106 (171*2π)/3702 weeks
172.33105 .25697 (172*2π)/3702 weeks
173-.31477 -.05417 (173*2π)/3702 weeks
174.44983 .07724 (174*2π)/3702 weeks
175-.07075 .22271 (175*2π)/3702 weeks
176-.49945 .36669 (176*2π)/3702 weeks
177.18236 .49344 (177*2π)/3702 weeks
178.18047 -.4346 (178*2π)/3702 weeks
179-.09928 .49646 (179*2π)/3702 weeks
180-.11285 -.82369 (180*2π)/3702 weeks
181-.35385 -.39068 (181*2π)/3702 weeks
182-.24572 .41765 (182*2π)/3702 weeks
183-.17858 -.42437 (183*2π)/3702 weeks
184-.09236 -.33923 (184*2π)/3702 weeks
185.30365   (185*2π)/3702 weeks
186-.09236 .33923 (186*2π)/3702 weeks
187-.17858 .42437 (187*2π)/3702 weeks
188-.24572 -.41765 (188*2π)/3702 weeks
189-.35385 .39068 (189*2π)/3702 weeks
190-.11285 .82369 (190*2π)/3702 weeks
191-.09928 -.49646 (191*2π)/3702 weeks
192.18047 .4346 (192*2π)/3702 weeks
193.18236 -.49344 (193*2π)/3702 weeks
194-.49945 -.36669 (194*2π)/3702 weeks
195-.07075 -.22271 (195*2π)/3702 weeks
196.44983 -.07724 (196*2π)/3702 weeks
197-.31477 .05417 (197*2π)/3702 weeks
198.33105 -.25697 (198*2π)/3702 weeks
199.56019 -.32106 (199*2π)/3702 weeks
200.05012 .20362 (200*2π)/3702 weeks
201.44105 -.09956 (201*2π)/3702 weeks
202.65295 .04619 (202*2π)/3702 weeks
203.618 -.00254 (203*2π)/3702 weeks
204-.11212 .52991 (204*2π)/3702 weeks
205.06127 .52541 (205*2π)/3702 weeks
206.7142 -.29779 (206*2π)/3702 weeks
207-.04471 -.03396 (207*2π)/3702 weeks
208-.42632 .27521 (208*2π)/3702 weeks
209-.31622 -.24479 (209*2π)/3702 weeks
210-.66953 -.47541 (210*2π)/3702 weeks
211-.03118 .17506 (211*2π)/3702 weeks
212.23658 .03037 (212*2π)/3702 weeks
213-.45877 -.15885 (213*2π)/3702 weeks
214.58676 -.16331 (214*2π)/3702 weeks
215.32669 -.09409 (215*2π)/3702 weeks
216.45749 -.12033 (216*2π)/3702 weeks
217.13108 .25335 (217*2π)/3702 weeks
218-.04353 -.08619 (218*2π)/3702 weeks
219-.62031 -.06869 (219*2π)/3702 weeks
220-.13724 -.56941 (220*2π)/3702 weeks
221-.58686 .10163 (221*2π)/3702 weeks
222.24499 -.22843 (222*2π)/3702 weeks
223-.20464 -.3412 (223*2π)/3702 weeks
224-.278 -.62565 (224*2π)/3702 weeks
225.12513 -.56909 (225*2π)/3702 weeks
226.23691 -.18987 (226*2π)/3702 weeks
227-.04476 -.31762 (227*2π)/3702 weeks
228.34063 -.31529 (228*2π)/3702 weeks
229.15782 .48922 (229*2π)/3702 weeks
230.12764 .28036 (230*2π)/3702 weeks
231.1064 .04807 (231*2π)/3702 weeks
232.02035 .48377 (232*2π)/3702 weeks
233-.11017 1.20601 (233*2π)/3702 weeks
234-.88052 -.0218 (234*2π)/3702 weeks
235-.70469 .08601 (235*2π)/3702 weeks
236-.2584 -.35837 (236*2π)/3702 weeks
237-.09843 .07856 (237*2π)/3702 weeks
238-.38342 -.23267 (238*2π)/3702 weeks
239.44429 -.50665 (239*2π)/3702 weeks
240.18819 -.38695 (240*2π)/3702 weeks
241.76334 .44368 (241*2π)/3702 weeks
242.3917 -.60527 (242*2π)/3702 weeks
243.61446 -.25806 (243*2π)/3702 weeks
244.06127 -.12877 (244*2π)/3702 weeks
245.15724 .25032 (245*2π)/3702 weeks
246.26307 -.19205 (246*2π)/3702 weeks
247.04238 -.42815 (247*2π)/3701 weeks
248-.43281 -.43717 (248*2π)/3701 weeks
249-.1892 -.22599 (249*2π)/3701 weeks
250.0877 -.58533 (250*2π)/3701 weeks
251.25768 .64589 (251*2π)/3701 weeks
252-.24188 -.30605 (252*2π)/3701 weeks
253-.21638 -.16067 (253*2π)/3701 weeks
254.15168 .75712 (254*2π)/3701 weeks
255-.12048 -.00427 (255*2π)/3701 weeks
256.00288 .50287 (256*2π)/3701 weeks
257-.04799 -.43481 (257*2π)/3701 weeks
258.5575 .62335 (258*2π)/3701 weeks
259-.34935 .65569 (259*2π)/3701 weeks
260-.321 -.67409 (260*2π)/3701 weeks
261.11046 -.55942 (261*2π)/3701 weeks
262-.0828 -.17228 (262*2π)/3701 weeks
263.43832 -.00107 (263*2π)/3701 weeks
264.0347 .59233 (264*2π)/3701 weeks
265.21246 -1.04014 (265*2π)/3701 weeks
266-.55488 -.00456 (266*2π)/3701 weeks
267.11678 -.03429 (267*2π)/3701 weeks
268-.07631 -.01648 (268*2π)/3701 weeks
269-.38416 .02767 (269*2π)/3701 weeks
270-.48762 .00176 (270*2π)/3701 weeks
271-.59825 -.68445 (271*2π)/3701 weeks
272-.59204 -.49797 (272*2π)/3701 weeks
273.79865 -.72905 (273*2π)/3701 weeks
274-.03175 -.15309 (274*2π)/3701 weeks
275-.27704 -.76744 (275*2π)/3701 weeks
276.48515 -.13863 (276*2π)/3701 weeks
277.6797 -.15682 (277*2π)/3701 weeks
278.31955 .49269 (278*2π)/3701 weeks
279.54346 .22172 (279*2π)/3701 weeks
280-.43108 .00652 (280*2π)/3701 weeks
281.11677 .3794 (281*2π)/3701 weeks
282-.40671 .06457 (282*2π)/3701 weeks
283.87266 -.1329 (283*2π)/3701 weeks
2841.10964 .32046 (284*2π)/3701 weeks
285.31708 .56057 (285*2π)/3701 weeks
286-.18081 -.68032 (286*2π)/3701 weeks
287.4232 .13794 (287*2π)/3701 weeks
288-.02151 .19215 (288*2π)/3701 weeks
289-.18914 .35447 (289*2π)/3701 weeks
290-.23712 .24835 (290*2π)/3701 weeks
291.40161 .34426 (291*2π)/3701 weeks
292-.60508 -.74629 (292*2π)/3701 weeks
293.75387 -.2182 (293*2π)/3701 weeks
294.18203 .10353 (294*2π)/3701 weeks
295-.51077 -.33435 (295*2π)/3701 weeks
296-.55201 1.15475 (296*2π)/3701 weeks
297.76601 -.52295 (297*2π)/3701 weeks
298.12491 -.7622 (298*2π)/3701 weeks
2991.13291 .71859 (299*2π)/3701 weeks
300-.11611 .28426 (300*2π)/3701 weeks
301-1.24154 .15033 (301*2π)/3701 weeks
302.27451 .51368 (302*2π)/3701 weeks
303.47609 -.60836 (303*2π)/3701 weeks
304-.55138 -.69903 (304*2π)/3701 weeks
305-.08987 .80046 (305*2π)/3701 weeks
306-.73888 .57913 (306*2π)/3701 weeks
307.08407 -.91116 (307*2π)/3701 weeks
308-.19372 -.0478 (308*2π)/3701 weeks
309.131 -.53485 (309*2π)/3701 weeks
3101.5084 -.06981 (310*2π)/3701 weeks
311-.34143 -.79671 (311*2π)/3701 weeks
3121.10095 .07213 (312*2π)/3701 weeks
313.48661 -.30971 (313*2π)/3701 weeks
314.9416 -.3322 (314*2π)/3701 weeks
315.25751 1.35587 (315*2π)/3701 weeks
316-.36449 1.20203 (316*2π)/3701 weeks
317-.19645 -.03952 (317*2π)/3701 weeks
318-.27653 1.06484 (318*2π)/3701 weeks
319-.75923 -.50619 (319*2π)/3701 weeks
320-.29084 -.28074 (320*2π)/3701 weeks
321-1.11054 .85946 (321*2π)/3701 weeks
322-.19299 -.18823 (322*2π)/3701 weeks
323-1.06473 -.58122 (323*2π)/3701 weeks
324-1.7766 -.81512 (324*2π)/3701 weeks
325-1.20999 -.01517 (325*2π)/3701 weeks
326.00895 .22392 (326*2π)/3701 weeks
327-1.20901 -2.4513 (327*2π)/3701 weeks
328.06079 .80406 (328*2π)/3701 weeks
329-.2501 .11375 (329*2π)/3701 weeks
330-.58958 -.20581 (330*2π)/3701 weeks
331-.29653 -.9412 (331*2π)/3701 weeks
3322.11244 -1.00581 (332*2π)/3701 weeks
333.74848 .0753 (333*2π)/3701 weeks
334-.25674 -.36099 (334*2π)/3701 weeks
3352.05568 .30261 (335*2π)/3701 weeks
336.16488 .87294 (336*2π)/3701 weeks
337-.19995 .69693 (337*2π)/3701 weeks
338.07204 .02476 (338*2π)/3701 weeks
339.07201 -.12193 (339*2π)/3701 weeks
340.12912 .09502 (340*2π)/3701 weeks
341-.13952 1.76262 (341*2π)/3701 weeks
3421.95423 .23478 (342*2π)/3701 weeks
343-.93472 1.85181 (343*2π)/3701 weeks
344.44947 .58414 (344*2π)/3701 weeks
3452.41643 .46769 (345*2π)/3701 weeks
3461.18613 2.16771 (346*2π)/3701 weeks
3472.28887 2.0637 (347*2π)/3701 weeks
348.60796 1.93811 (348*2π)/3701 weeks
349.38853 .95892 (349*2π)/3701 weeks
3501.51028 2.69342 (350*2π)/3701 weeks
351-1.24358 -.76274 (351*2π)/3701 weeks
352.97459 -.66913 (352*2π)/3701 weeks
3533.48112 .79661 (353*2π)/3701 weeks
354-.00753 -2.10068 (354*2π)/3701 weeks
355-2.28545 1.87061 (355*2π)/3701 weeks
356-6.56294 3.97122 (356*2π)/3701 weeks
357-5.23047 -4.07837 (357*2π)/3701 weeks
358-3.35426 -.30456 (358*2π)/3701 weeks
359-.01915 -1.82679 (359*2π)/3701 weeks
360-2.80381 -.29296 (360*2π)/3701 weeks
3614.50691 -5.83963 (361*2π)/3701 weeks
3622.56415 5.34797 (362*2π)/3701 weeks
3632.56204 .74092 (363*2π)/3701 weeks
364.60887 10.06994 (364*2π)/3701 weeks
3658.27798 -.25012 (365*2π)/3701 weeks
3666.00962 .21617 (366*2π)/3701 weeks
367-3.86632 -1.96221 (367*2π)/3701 weeks
36826.87824 8.54622 (368*2π)/3701 weeks