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Fourier Analysis of CYC (MORGAN STANLEY CYCLICAL INDEX)


CYC (MORGAN STANLEY CYCLICAL INDEX) appears to have interesting cyclic behaviour every 90 weeks (146.4232*sine), 84 weeks (124.4368*sine), and 97 weeks (116.3027*sine).

CYC (MORGAN STANLEY CYCLICAL INDEX) has an average price of 977.54 (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 12/14/1992 to 1/9/2017 for CYC (MORGAN STANLEY CYCLICAL INDEX), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0977.5398   0 
1525.7233 -491.0776 (1*2π)/12571,257 weeks
2387.5207 -471.7094 (2*2π)/1257629 weeks
3170.2482 -559.0029 (3*2π)/1257419 weeks
450.8363 -401.053 (4*2π)/1257314 weeks
5-40.65934 -365.598 (5*2π)/1257251 weeks
6-153.2106 -245.4419 (6*2π)/1257210 weeks
7-123.1999 -71.087 (7*2π)/1257180 weeks
8-26.57985 -75.94637 (8*2π)/1257157 weeks
9-46.44517 -25.61987 (9*2π)/1257140 weeks
1045.27229 -11.91992 (10*2π)/1257126 weeks
1191.73782 -48.19704 (11*2π)/1257114 weeks
1253.6156 -85.01387 (12*2π)/1257105 weeks
1368.18783 -116.3027 (13*2π)/125797 weeks
1433.75349 -146.4232 (14*2π)/125790 weeks
15-12.57973 -124.4368 (15*2π)/125784 weeks
16-31.07687 -79.5349 (16*2π)/125779 weeks
17-26.91108 -79.30785 (17*2π)/125774 weeks
18-27.05292 -45.03189 (18*2π)/125770 weeks
19-5.50107 -3.85626 (19*2π)/125766 weeks
2054.37094 -31.12375 (20*2π)/125763 weeks
2138.45396 -67.88714 (21*2π)/125760 weeks
2238.49213 -77.40916 (22*2π)/125757 weeks
2320.4133 -95.72217 (23*2π)/125755 weeks
24-11.01246 -88.01488 (24*2π)/125752 weeks
25-24.21806 -95.25687 (25*2π)/125750 weeks
26-39.30517 -80.46592 (26*2π)/125748 weeks
27-63.58913 -35.47242 (27*2π)/125747 weeks
28-33.36276 -4.864 (28*2π)/125745 weeks
29-4.72711 -2.87264 (29*2π)/125743 weeks
3014.35093 -14.67409 (30*2π)/125742 weeks
3130.75961 -31.06047 (31*2π)/125741 weeks
3220.64703 -52.2373 (32*2π)/125739 weeks
331.75714 -64.02634 (33*2π)/125738 weeks
34-10.60119 -69.96725 (34*2π)/125737 weeks
35-31.84316 -66.22163 (35*2π)/125736 weeks
36-41.1934 -49.88555 (36*2π)/125735 weeks
37-50.17922 -15.75661 (37*2π)/125734 weeks
38-35.814 3.21603 (38*2π)/125733 weeks
39-12.3411 9.84933 (39*2π)/125732 weeks
4010.45241 -1.1364 (40*2π)/125731 weeks
4117.91272 -14.7493 (41*2π)/125731 weeks
4218.17299 -21.97597 (42*2π)/125730 weeks
4311.5581 -41.59386 (43*2π)/125729 weeks
44-.19556 -46.99828 (44*2π)/125729 weeks
45-12.61587 -44.59346 (45*2π)/125728 weeks
46-26.99802 -30.85207 (46*2π)/125727 weeks
47-34.04031 -21.30734 (47*2π)/125727 weeks
48-21.49916 -6.08949 (48*2π)/125726 weeks
49-12.01176 6.95386 (49*2π)/125726 weeks
506.12282 -4.29729 (50*2π)/125725 weeks
518.98471 -14.7829 (51*2π)/125725 weeks
528.92859 -25.04796 (52*2π)/125724 weeks
53-2.33698 -32.75872 (53*2π)/125724 weeks
54-10.19876 -27.86066 (54*2π)/125723 weeks
55-17.30848 -31.31855 (55*2π)/125723 weeks
56-25.20862 -20.42711 (56*2π)/125722 weeks
57-27.09749 -6.71198 (57*2π)/125722 weeks
58-23.07874 4.28314 (58*2π)/125722 weeks
59-8.96159 15.08687 (59*2π)/125721 weeks
6011.73496 12.74502 (60*2π)/125721 weeks
6117.04751 -9.04934 (61*2π)/125721 weeks
628.25615 -14.4968 (62*2π)/125720 weeks
637.20424 -18.17555 (63*2π)/125720 weeks
64-3.33798 -23.92813 (64*2π)/125720 weeks
65-2.14329 -15.17127 (65*2π)/125719 weeks
66-11.63471 -14.75253 (66*2π)/125719 weeks
67-17.89012 -6.82289 (67*2π)/125719 weeks
68-10.04936 4.74089 (68*2π)/125718 weeks
696.00722 8.45577 (69*2π)/125718 weeks
709.88718 2.43783 (70*2π)/125718 weeks
7111.93992 -3.10346 (71*2π)/125718 weeks
7218.11437 -14.36536 (72*2π)/125717 weeks
733.97486 -15.56438 (73*2π)/125717 weeks
742.27579 -10.89196 (74*2π)/125717 weeks
758.5184 -14.70926 (75*2π)/125717 weeks
76-4.18215 -13.43427 (76*2π)/125717 weeks
77-2.88827 .95789 (77*2π)/125716 weeks
7812.72944 -1.97389 (78*2π)/125716 weeks
7913.74157 -3.86403 (79*2π)/125716 weeks
8020.45195 -5.95901 (80*2π)/125716 weeks
8125.55658 -20.42304 (81*2π)/125716 weeks
8216.12535 -27.71675 (82*2π)/125715 weeks
8310.81084 -28.11093 (83*2π)/125715 weeks
843.02031 -29.65059 (84*2π)/125715 weeks
85-2.7297 -27.5861 (85*2π)/125715 weeks
86-4.25344 -22.41914 (86*2π)/125715 weeks
87-7.14464 -15.14461 (87*2π)/125714 weeks
88-5.10404 -12.11844 (88*2π)/125714 weeks
894.18718 -10.08319 (89*2π)/125714 weeks
908.19092 -13.46534 (90*2π)/125714 weeks
9111.60308 -20.51761 (91*2π)/125714 weeks
928.48126 -26.51383 (92*2π)/125714 weeks
93-2.97508 -30.5493 (93*2π)/125714 weeks
94-7.86227 -28.48525 (94*2π)/125713 weeks
95-8.45203 -19.11947 (95*2π)/125713 weeks
96-10.1926 -20.13622 (96*2π)/125713 weeks
97-10.36582 -17.53602 (97*2π)/125713 weeks
98-10.99776 -12.05081 (98*2π)/125713 weeks
99-4.88148 -5.99635 (99*2π)/125713 weeks
1003.06319 -10.13938 (100*2π)/125713 weeks
1012.21592 -18.33214 (101*2π)/125712 weeks
102-2.79841 -25.47694 (102*2π)/125712 weeks
103-7.73309 -19.43179 (103*2π)/125712 weeks
104-10.31824 -19.07129 (104*2π)/125712 weeks
105-11.70889 -13.51771 (105*2π)/125712 weeks
106-8.47875 -14.90178 (106*2π)/125712 weeks
107-12.3495 -11.13005 (107*2π)/125712 weeks
108-13.41293 -7.2986 (108*2π)/125712 weeks
109-4.17011 -4.82763 (109*2π)/125712 weeks
110-1.7346 -9.08146 (110*2π)/125711 weeks
111-1.45597 -14.55678 (111*2π)/125711 weeks
112-6.59848 -18.62108 (112*2π)/125711 weeks
113-13.00758 -13.86737 (113*2π)/125711 weeks
114-13.79918 -10.78348 (114*2π)/125711 weeks
115-12.32365 -5.06703 (115*2π)/125711 weeks
116-9.35516 -2.56814 (116*2π)/125711 weeks
117-5.59782 -3.44015 (117*2π)/125711 weeks
118-7.32878 -.94144 (118*2π)/125711 weeks
119-.23319 -3.71805 (119*2π)/125711 weeks
1201.31837 -6.45961 (120*2π)/125710 weeks
121.5663 -11.86182 (121*2π)/125710 weeks
122-4.86217 -15.41224 (122*2π)/125710 weeks
123-12.26649 -10.50767 (123*2π)/125710 weeks
124-12.50156 -5.60378 (124*2π)/125710 weeks
125-9.43838 -1.10281 (125*2π)/125710 weeks
126-2.72151 .81696 (126*2π)/125710 weeks
127-2.24047 -2.63829 (127*2π)/125710 weeks
128-4.38099 -2.87532 (128*2π)/125710 weeks
1292.58584 .06809 (129*2π)/125710 weeks
1308.89871 -5.29555 (130*2π)/125710 weeks
1315.40565 -14.64967 (131*2π)/125710 weeks
132-.70806 -16.88281 (132*2π)/125710 weeks
133-8.72674 -15.89597 (133*2π)/12579 weeks
134-11.37666 -8.65089 (134*2π)/12579 weeks
135-9.81988 -5.97268 (135*2π)/12579 weeks
136-6.12722 -4.25684 (136*2π)/12579 weeks
137-7.03136 -2.60087 (137*2π)/12579 weeks
138-4.85367 -1.31875 (138*2π)/12579 weeks
139-.24007 -2.45191 (139*2π)/12579 weeks
1402.93928 -5.91763 (140*2π)/12579 weeks
141-.10389 -9.77679 (141*2π)/12579 weeks
142-4.13456 -10.18263 (142*2π)/12579 weeks
143-7.31279 -10.53815 (143*2π)/12579 weeks
144-8.41655 -4.56687 (144*2π)/12579 weeks
145-7.47782 -1.61438 (145*2π)/12579 weeks
146-3.82436 -4.28179 (146*2π)/12579 weeks
147-3.86744 -1.97253 (147*2π)/12579 weeks
148-3.34181 -.78701 (148*2π)/12578 weeks
149-1.21227 -2.71938 (149*2π)/12578 weeks
150.43896 -2.82727 (150*2π)/12578 weeks
1512.75776 -7.09229 (151*2π)/12578 weeks
152-2.98862 -9.1281 (152*2π)/12578 weeks
153-6.27938 -6.7238 (153*2π)/12578 weeks
154-7.65429 -1.9759 (154*2π)/12578 weeks
155-2.67569 2.88761 (155*2π)/12578 weeks
1563.16534 3.14168 (156*2π)/12578 weeks
1575.77721 -2.83331 (157*2π)/12578 weeks
1584.75752 -7.05249 (158*2π)/12578 weeks
1595.67015 -8.36162 (159*2π)/12578 weeks
1603.46135 -10.55517 (160*2π)/12578 weeks
1611.12013 -13.92045 (161*2π)/12578 weeks
162-4.22763 -18.28756 (162*2π)/12578 weeks
163-15.72929 -12.22763 (163*2π)/12578 weeks
164-11.76073 -1.87081 (164*2π)/12578 weeks
165-7.99988 .53584 (165*2π)/12578 weeks
166-3.1955 2.055 (166*2π)/12578 weeks
167-.0107 .77744 (167*2π)/12578 weeks
168.20624 -1.5512 (168*2π)/12577 weeks
169.95243 -.47845 (169*2π)/12577 weeks
1706.74234 -2.93748 (170*2π)/12577 weeks
1715.56996 -9.53632 (171*2π)/12577 weeks
172-.69679 -12.74781 (172*2π)/12577 weeks
173-8.04741 -8.27697 (173*2π)/12577 weeks
174-4.66731 -3.49575 (174*2π)/12577 weeks
175-1.96311 -1.95379 (175*2π)/12577 weeks
176-.26209 -4.17708 (176*2π)/12577 weeks
177.01813 -4.33234 (177*2π)/12577 weeks
178.69207 -3.2849 (178*2π)/12577 weeks
1792.92299 -4.53033 (179*2π)/12577 weeks
1803.24384 -7.51296 (180*2π)/12577 weeks
1811.09298 -10.34178 (181*2π)/12577 weeks
182-.6383 -11.70803 (182*2π)/12577 weeks
183-6.31674 -11.75174 (183*2π)/12577 weeks
184-8.51056 -5.54349 (184*2π)/12577 weeks
185-4.45554 -2.55986 (185*2π)/12577 weeks
186-3.05606 -3.35706 (186*2π)/12577 weeks
187-2.17016 -3.05315 (187*2π)/12577 weeks
188-1.97209 -4.38977 (188*2π)/12577 weeks
189-1.39281 -2.8974 (189*2π)/12577 weeks
190.15755 -4.13431 (190*2π)/12577 weeks
1911.37672 -6.67378 (191*2π)/12577 weeks
192-1.99951 -6.79405 (192*2π)/12577 weeks
193-4.08316 -5.75187 (193*2π)/12577 weeks
194-2.43195 -3.69271 (194*2π)/12576 weeks
195-2.36479 -1.75074 (195*2π)/12576 weeks
1962.93524 -2.69859 (196*2π)/12576 weeks
1972.91017 -7.50963 (197*2π)/12576 weeks
198-1.62937 -8.1918 (198*2π)/12576 weeks
199-1.54435 -5.62573 (199*2π)/12576 weeks
200-.34618 -5.52191 (200*2π)/12576 weeks
201-2.23278 -6.31453 (201*2π)/12576 weeks
202-1.13179 -6.22466 (202*2π)/12576 weeks
203-4.61817 -5.389 (203*2π)/12576 weeks
204-3.25511 -2.19192 (204*2π)/12576 weeks
2052.6351 1.0741 (205*2π)/12576 weeks
2066.71383 -4.17449 (206*2π)/12576 weeks
2076.42188 -10.57533 (207*2π)/12576 weeks
2082.57493 -13.66018 (208*2π)/12576 weeks
209-1.34521 -12.11972 (209*2π)/12576 weeks
210-2.24995 -12.20451 (210*2π)/12576 weeks
211-3.6252 -11.43763 (211*2π)/12576 weeks
212-6.23834 -12.89841 (212*2π)/12576 weeks
213-10.13958 -9.4628 (213*2π)/12576 weeks
214-10.27629 -2.41043 (214*2π)/12576 weeks
215-3.28842 .94914 (215*2π)/12576 weeks
2162.73231 -3.73667 (216*2π)/12576 weeks
217.56106 -9.10937 (217*2π)/12576 weeks
218-2.8462 -11.50526 (218*2π)/12576 weeks
219-4.52893 -10.22531 (219*2π)/12576 weeks
220-4.93884 -9.92717 (220*2π)/12576 weeks
221-8.24063 -10.60524 (221*2π)/12576 weeks
222-10.30184 -9.77376 (222*2π)/12576 weeks
223-13.81851 -6.15369 (223*2π)/12576 weeks
224-15.51926 -.07641 (224*2π)/12576 weeks
225-7.77501 5.53283 (225*2π)/12576 weeks
226-2.96843 3.37252 (226*2π)/12576 weeks
227-1.49466 .70352 (227*2π)/12576 weeks
228-.785 -1.61578 (228*2π)/12576 weeks
229-2.45419 -3.25463 (229*2π)/12575 weeks
230-.2666 -1.44376 (230*2π)/12575 weeks
231-.22066 -4.82774 (231*2π)/12575 weeks
232-2.41935 -7.7476 (232*2π)/12575 weeks
233-6.92052 -4.77525 (233*2π)/12575 weeks
234-7.54793 -3.09991 (234*2π)/12575 weeks
235-3.0466 1.42297 (235*2π)/12575 weeks
236-2.09362 -.42385 (236*2π)/12575 weeks
237-.11441 -3.51416 (237*2π)/12575 weeks
238-2.07092 -5.44356 (238*2π)/12575 weeks
239-4.03638 -2.84275 (239*2π)/12575 weeks
240-2.51358 -1.27295 (240*2π)/12575 weeks
241-2.07369 -3.71303 (241*2π)/12575 weeks
242-3.17994 -4.3432 (242*2π)/12575 weeks
243-2.75046 -3.18141 (243*2π)/12575 weeks
244-4.40648 -1.27096 (244*2π)/12575 weeks
245-.27333 .43877 (245*2π)/12575 weeks
2463.1042 -2.23071 (246*2π)/12575 weeks
247.88548 -7.59682 (247*2π)/12575 weeks
248-2.71799 -7.78356 (248*2π)/12575 weeks
249-4.7462 -5.84576 (249*2π)/12575 weeks
250-6.2098 -3.88534 (250*2π)/12575 weeks
251-2.92504 -2.83174 (251*2π)/12575 weeks
252-2.67241 -3.79527 (252*2π)/12575 weeks
253-5.35068 -3.89304 (253*2π)/12575 weeks
254-6.09249 -.41615 (254*2π)/12575 weeks
255-.3684 2.63465 (255*2π)/12575 weeks
2562.50822 -1.89585 (256*2π)/12575 weeks
257.94589 -5.84329 (257*2π)/12575 weeks
258-1.54584 -7.23105 (258*2π)/12575 weeks
259-5.51072 -4.6953 (259*2π)/12575 weeks
260-2.97457 -1.21657 (260*2π)/12575 weeks
261-.5013 -3.30635 (261*2π)/12575 weeks
262-2.42074 -4.44483 (262*2π)/12575 weeks
263-2.78231 -3.64833 (263*2π)/12575 weeks
264-2.21862 -1.12134 (264*2π)/12575 weeks
265.18508 -1.44458 (265*2π)/12575 weeks
2662.95795 -4.10256 (266*2π)/12575 weeks
2672.57935 -8.66546 (267*2π)/12575 weeks
268-2.26012 -9.85666 (268*2π)/12575 weeks
269-5.79902 -8.72074 (269*2π)/12575 weeks
270-6.96957 -5.24209 (270*2π)/12575 weeks
271-4.43294 -2.65549 (271*2π)/12575 weeks
272-2.07112 -4.76945 (272*2π)/12575 weeks
273-5.45901 -5.21219 (273*2π)/12575 weeks
274-4.71519 -2.96343 (274*2π)/12575 weeks
275-2.65255 -2.69137 (275*2π)/12575 weeks
276-.59015 -4.49337 (276*2π)/12575 weeks
277-2.95945 -8.08434 (277*2π)/12575 weeks
278-7.03997 -8.44122 (278*2π)/12575 weeks
279-10.59622 -5.56356 (279*2π)/12575 weeks
280-10.72591 .11076 (280*2π)/12574 weeks
281-6.34331 2.79372 (281*2π)/12574 weeks
282-3.0015 .37803 (282*2π)/12574 weeks
283-4.72959 -.30092 (283*2π)/12574 weeks
284-3.70673 1.81535 (284*2π)/12574 weeks
285-.43459 2.68621 (285*2π)/12574 weeks
2862.56566 -1.29348 (286*2π)/12574 weeks
2872.16991 -5.55004 (287*2π)/12574 weeks
288-2.45884 -8.30794 (288*2π)/12574 weeks
289-8.20585 -6.63692 (289*2π)/12574 weeks
290-7.43421 -1.65836 (290*2π)/12574 weeks
291-5.42187 2.05946 (291*2π)/12574 weeks
292-3.38869 -.34062 (292*2π)/12574 weeks
293-3.90363 -1.44758 (293*2π)/12574 weeks
294-4.3007 2.22838 (294*2π)/12574 weeks
295-1.6937 2.97475 (295*2π)/12574 weeks
2962.28025 .23047 (296*2π)/12574 weeks
297.90694 -3.62495 (297*2π)/12574 weeks
298-2.89298 -4.93251 (298*2π)/12574 weeks
299-5.69743 -2.37853 (299*2π)/12574 weeks
300-4.70759 1.08527 (300*2π)/12574 weeks
301-.87523 2.77148 (301*2π)/12574 weeks
302.62352 1.67442 (302*2π)/12574 weeks
3031.74516 -.37925 (303*2π)/12574 weeks
304-.2774 -.83674 (304*2π)/12574 weeks
3052.27605 1.00458 (305*2π)/12574 weeks
3066.37788 -2.39407 (306*2π)/12574 weeks
3072.97257 -7.99226 (307*2π)/12574 weeks
308-.462 -9.34765 (308*2π)/12574 weeks
309-5.1677 -7.15961 (309*2π)/12574 weeks
310-6.27181 -1.42704 (310*2π)/12574 weeks
311-1.64155 -.03979 (311*2π)/12574 weeks
312.60116 -2.09512 (312*2π)/12574 weeks
313-2.07266 -2.5187 (313*2π)/12574 weeks
314-1.21484 -1.90729 (314*2π)/12574 weeks
3151.04981 -.82333 (315*2π)/12574 weeks
3162.58643 -3.25698 (316*2π)/12574 weeks
3171.53964 -7.377 (317*2π)/12574 weeks
318-1.87774 -8.06028 (318*2π)/12574 weeks
319-5.53274 -5.38871 (319*2π)/12574 weeks
320-5.44281 -1.83248 (320*2π)/12574 weeks
321-2.23064 .48427 (321*2π)/12574 weeks
3221.13929 -2.06983 (322*2π)/12574 weeks
323-.40896 -3.81276 (323*2π)/12574 weeks
324-.65348 -2.77561 (324*2π)/12574 weeks
3251.087 -3.26828 (325*2π)/12574 weeks
3262.34572 -4.96223 (326*2π)/12574 weeks
327.83099 -8.66133 (327*2π)/12574 weeks
328-2.93305 -10.0617 (328*2π)/12574 weeks
329-7.6123 -8.41901 (329*2π)/12574 weeks
330-9.04668 -2.85761 (330*2π)/12574 weeks
331-4.92777 .86603 (331*2π)/12574 weeks
332-2.04726 -.26511 (332*2π)/12574 weeks
333-1.71046 -3.31601 (333*2π)/12574 weeks
334-3.5318 -2.11828 (334*2π)/12574 weeks
335-1.35697 .15419 (335*2π)/12574 weeks
336.84014 -1.59038 (336*2π)/12574 weeks
3371.86899 -4.82465 (337*2π)/12574 weeks
338-1.17582 -8.30352 (338*2π)/12574 weeks
339-4.95754 -6.12018 (339*2π)/12574 weeks
340-5.22848 -1.77923 (340*2π)/12574 weeks
341-1.04788 -.40234 (341*2π)/12574 weeks
342.51306 -3.66848 (342*2π)/12574 weeks
343.50075 -6.86165 (343*2π)/12574 weeks
344-3.05829 -7.03825 (344*2π)/12574 weeks
345-4.46115 -6.06663 (345*2π)/12574 weeks
346-3.88072 -4.86411 (346*2π)/12574 weeks
347-3.70821 -7.37642 (347*2π)/12574 weeks
348-7.63437 -7.98543 (348*2π)/12574 weeks
349-10.89058 -3.60459 (349*2π)/12574 weeks
350-10.15198 1.8789 (350*2π)/12574 weeks
351-4.64351 4.8655 (351*2π)/12574 weeks
352-.83489 1.9793 (352*2π)/12574 weeks
353.02734 -.08938 (353*2π)/12574 weeks
354-.40755 -2.22338 (354*2π)/12574 weeks
355-.68092 -.76585 (355*2π)/12574 weeks
356.51554 -2.58523 (356*2π)/12574 weeks
3571.12778 -5.22613 (357*2π)/12574 weeks
358-2.39654 -8.3823 (358*2π)/12574 weeks
359-6.3773 -5.45413 (359*2π)/12574 weeks
360-6.95931 -1.45834 (360*2π)/12573 weeks
361-2.51002 .24465 (361*2π)/12573 weeks
362-.87434 -1.85835 (362*2π)/12573 weeks
363-2.66508 -4.57604 (363*2π)/12573 weeks
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