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Fourier Analysis of CYC (MORGAN STANLEY CYCLICAL INDEX)


CYC (MORGAN STANLEY CYCLICAL INDEX) appears to have interesting cyclic behaviour every 91 weeks (154.1006*sine), 97 weeks (151.0709*sine), and 106 weeks (119.2417*sine).

CYC (MORGAN STANLEY CYCLICAL INDEX) has an average price of 996.51 (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 3/20/2017 for CYC (MORGAN STANLEY CYCLICAL INDEX), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0996.512   0 
1551.7286 -515.2581 (1*2π)/12671,267 weeks
2390.8385 -508.5748 (2*2π)/1267634 weeks
3144.9489 -581.0847 (3*2π)/1267422 weeks
425.72553 -406.535 (4*2π)/1267317 weeks
5-72.36797 -352.8366 (5*2π)/1267253 weeks
6-165.1954 -203.9842 (6*2π)/1267211 weeks
7-95.38142 -39.05008 (7*2π)/1267181 weeks
8-1.51672 -68.73463 (8*2π)/1267158 weeks
9-8.07053 -19.3762 (9*2π)/1267141 weeks
1083.50697 -41.24512 (10*2π)/1267127 weeks
11101.6962 -95.19812 (11*2π)/1267115 weeks
1244.70612 -119.2417 (12*2π)/1267106 weeks
1340.15685 -151.0709 (13*2π)/126797 weeks
14-11.64357 -154.1006 (14*2π)/126791 weeks
15-42.48805 -104.8829 (15*2π)/126784 weeks
16-37.31843 -57.64593 (16*2π)/126779 weeks
17-28.64894 -58.39665 (17*2π)/126775 weeks
18-6.9115 -30.3982 (18*2π)/126770 weeks
1927.91635 -18.73022 (19*2π)/126767 weeks
2053.15099 -77.10244 (20*2π)/126763 weeks
218.7578 -96.29195 (21*2π)/126760 weeks
22-4.79873 -94.76054 (22*2π)/126758 weeks
23-32.24202 -86.36235 (23*2π)/126755 weeks
24-49.26104 -56.08014 (24*2π)/126753 weeks
25-56.48722 -47.25226 (25*2π)/126751 weeks
26-45.02182 -18.61722 (26*2π)/126749 weeks
27-23.68148 20.34778 (27*2π)/126747 weeks
2819.67185 6.85342 (28*2π)/126745 weeks
2932.90659 -22.31418 (29*2π)/126744 weeks
3023.59137 -47.34493 (30*2π)/126742 weeks
3110.26492 -60.347 (31*2π)/126741 weeks
32-16.89649 -55.94737 (32*2π)/126740 weeks
33-36.10686 -40.01342 (33*2π)/126738 weeks
34-37.6125 -24.16256 (34*2π)/126737 weeks
35-32.74623 -3.92842 (35*2π)/126736 weeks
36-13.2964 10.07702 (36*2π)/126735 weeks
3716.05436 24.10251 (37*2π)/126734 weeks
3834.5244 .90927 (38*2π)/126733 weeks
3937.18249 -24.24699 (39*2π)/126732 weeks
4026.65663 -46.3049 (40*2π)/126732 weeks
417.84782 -50.29738 (41*2π)/126731 weeks
42-4.52788 -40.72561 (42*2π)/126730 weeks
43-19.71323 -33.98054 (43*2π)/126729 weeks
44-20.31654 -18.69784 (44*2π)/126729 weeks
45-11.38644 -2.70692 (45*2π)/126728 weeks
464.75901 6.3349 (46*2π)/126728 weeks
4712.3776 .81992 (47*2π)/126727 weeks
4828.26053 -14.54784 (48*2π)/126726 weeks
4928.64163 -26.69797 (49*2π)/126726 weeks
508.16449 -41.95332 (50*2π)/126725 weeks
51-2.30592 -34.08266 (51*2π)/126725 weeks
52-9.08654 -28.28787 (52*2π)/126724 weeks
53-11.05313 -12.31844 (53*2π)/126724 weeks
542.48291 -6.45508 (54*2π)/126723 weeks
553.54588 -7.68491 (55*2π)/126723 weeks
5618.02326 -5.39021 (56*2π)/126723 weeks
5728.39906 -15.62217 (57*2π)/126722 weeks
5826.00719 -29.55359 (58*2π)/126722 weeks
5921.4512 -42.32522 (59*2π)/126721 weeks
604.38182 -52.00203 (60*2π)/126721 weeks
61-19.20887 -38.71579 (61*2π)/126721 weeks
62-12.2248 -20.33648 (62*2π)/126720 weeks
63-8.54343 -20.18417 (63*2π)/126720 weeks
64-6.84523 -11.21051 (64*2π)/126720 weeks
657.65254 -16.57647 (65*2π)/126719 weeks
665.9538 -14.69051 (66*2π)/126719 weeks
679.81975 -19.83054 (67*2π)/126719 weeks
6810.1855 -35.21926 (68*2π)/126719 weeks
69-3.71118 -42.25364 (69*2π)/126718 weeks
70-14.71825 -28.68622 (70*2π)/126718 weeks
71-16.525 -23.48261 (71*2π)/126718 weeks
72-21.01403 -18.72069 (72*2π)/126718 weeks
73-7.97117 -4.05826 (73*2π)/126717 weeks
74-3.48264 -13.99202 (74*2π)/126717 weeks
75-9.57375 -15.97923 (75*2π)/126717 weeks
76-.21037 -7.69392 (76*2π)/126717 weeks
77.49564 -22.57063 (77*2π)/126716 weeks
78-17.16436 -23.48561 (78*2π)/126716 weeks
79-14.26433 -11.35044 (79*2π)/126716 weeks
80-17.78244 -9.20933 (80*2π)/126716 weeks
81-19.61382 3.66349 (81*2π)/126716 weeks
82-2.72668 10.93096 (82*2π)/126715 weeks
834.43776 5.34312 (83*2π)/126715 weeks
849.84895 5.10256 (84*2π)/126715 weeks
8514.43064 -4.29595 (85*2π)/126715 weeks
8612.21639 -11.51092 (86*2π)/126715 weeks
8711.93339 -12.91206 (87*2π)/126715 weeks
884.05813 -17.24281 (88*2π)/126714 weeks
89-3.11147 -15.96929 (89*2π)/126714 weeks
90-.82889 -6.85209 (90*2π)/126714 weeks
911.22962 -4.21639 (91*2π)/126714 weeks
929.14223 .23949 (92*2π)/126714 weeks
9318.85078 -3.10693 (93*2π)/126714 weeks
9417.1171 -16.53449 (94*2π)/126713 weeks
9515.22947 -21.56416 (95*2π)/126713 weeks
9610.10209 -20.12827 (96*2π)/126713 weeks
976.09085 -23.96552 (97*2π)/126713 weeks
984.84547 -22.91259 (98*2π)/126713 weeks
99-.48148 -23.63995 (99*2π)/126713 weeks
100-5.24553 -13.80931 (100*2π)/126713 weeks
1014.13667 -7.63926 (101*2π)/126713 weeks
1029.58978 -14.41449 (102*2π)/126712 weeks
10310.89451 -22.65689 (103*2π)/126712 weeks
1047.0645 -22.73681 (104*2π)/126712 weeks
1052.72121 -27.30133 (105*2π)/126712 weeks
106-3.0797 -22.15995 (106*2π)/126712 weeks
1071.60387 -23.3558 (107*2π)/126712 weeks
108-6.21765 -23.26836 (108*2π)/126712 weeks
109-10.49158 -18.34941 (109*2π)/126712 weeks
110-3.48578 -13.01353 (110*2π)/126712 weeks
111-1.5527 -13.94014 (111*2π)/126711 weeks
1123.48197 -16.87228 (112*2π)/126711 weeks
1131.20755 -25.79357 (113*2π)/126711 weeks
114-8.71066 -23.3356 (114*2π)/126711 weeks
115-9.53359 -20.61687 (115*2π)/126711 weeks
116-11.85381 -16.62287 (116*2π)/126711 weeks
117-11.40559 -10.49126 (117*2π)/126711 weeks
118-5.44436 -10.28148 (118*2π)/126711 weeks
119-9.65242 -8.8624 (119*2π)/126711 weeks
120-2.05671 -7.37919 (120*2π)/126711 weeks
1212.13015 -11.14499 (121*2π)/126710 weeks
122.17986 -17.01548 (122*2π)/126710 weeks
123-3.63302 -19.55498 (123*2π)/126710 weeks
124-11.0949 -17.55608 (124*2π)/126710 weeks
125-14.15361 -11.51459 (125*2π)/126710 weeks
126-9.26701 -5.38602 (126*2π)/126710 weeks
127-2.78997 -5.49902 (127*2π)/126710 weeks
128-3.7027 -7.19071 (128*2π)/126710 weeks
129-3.33422 -7.32247 (129*2π)/126710 weeks
1302.49845 -7.00652 (130*2π)/126710 weeks
1317.30009 -11.25317 (131*2π)/126710 weeks
1323.81602 -21.17452 (132*2π)/126710 weeks
133-5.41275 -22.65006 (133*2π)/126710 weeks
134-12.463 -17.10315 (134*2π)/12679 weeks
135-11.70699 -10.85875 (135*2π)/12679 weeks
136-11.17664 -8.38952 (136*2π)/12679 weeks
137-5.28788 -6.12497 (137*2π)/12679 weeks
138-5.34013 -6.90693 (138*2π)/12679 weeks
139-4.47084 -5.69741 (139*2π)/12679 weeks
1401.35679 -8.2888 (140*2π)/12679 weeks
141.93724 -14.69895 (141*2π)/12679 weeks
142-5.33736 -14.22033 (142*2π)/12679 weeks
143-6.88514 -12.50364 (143*2π)/12679 weeks
144-10.73704 -11.95077 (144*2π)/12679 weeks
145-7.89981 -3.79182 (145*2π)/12679 weeks
146-3.45472 -4.51702 (146*2π)/12679 weeks
147-3.7876 -9.43996 (147*2π)/12679 weeks
148-1.75962 -5.4881 (148*2π)/12679 weeks
149-.2864 -7.94427 (149*2π)/12679 weeks
150-2.23759 -10.52181 (150*2π)/12678 weeks
151.05997 -10.42801 (151*2π)/12678 weeks
152-2.28701 -16.31105 (152*2π)/12678 weeks
153-9.2901 -10.84127 (153*2π)/12678 weeks
154-5.97511 -6.54332 (154*2π)/12678 weeks
155-3.65098 -5.59073 (155*2π)/12678 weeks
1562.23544 -5.82748 (156*2π)/12678 weeks
1575.31523 -12.46566 (157*2π)/12678 weeks
158-2.3214 -18.69496 (158*2π)/12678 weeks
159-6.4468 -16.38256 (159*2π)/12678 weeks
160-6.13627 -17.41223 (160*2π)/12678 weeks
161-12.13748 -14.64957 (161*2π)/12678 weeks
162-13.7272 -10.82873 (162*2π)/12678 weeks
163-16.51688 -8.47011 (163*2π)/12678 weeks
164-14.18204 4.11456 (164*2π)/12678 weeks
165.93048 1.77409 (165*2π)/12678 weeks
1661.64915 -6.01737 (166*2π)/12678 weeks
1671.32457 -8.69855 (167*2π)/12678 weeks
168.80634 -12.17894 (168*2π)/12678 weeks
169-4.49956 -13.90077 (169*2π)/12677 weeks
170-4.50009 -11.57864 (170*2π)/12677 weeks
171-5.1335 -17.02138 (171*2π)/12677 weeks
172-14.15478 -13.97711 (172*2π)/12677 weeks
173-14.11803 -4.67738 (173*2π)/12677 weeks
174-7.66353 -1.43117 (174*2π)/12677 weeks
175-4.28224 -6.33641 (175*2π)/12677 weeks
176-3.05966 -7.96651 (176*2π)/12677 weeks
177-6.59497 -11.60614 (177*2π)/12677 weeks
178-8.40935 -8.94881 (178*2π)/12677 weeks
179-6.0746 -8.60319 (179*2π)/12677 weeks
180-9.63948 -11.16684 (180*2π)/12677 weeks
181-12.78561 -6.84399 (181*2π)/12677 weeks
182-11.35728 -4.28531 (182*2π)/12677 weeks
183-11.49332 -2.99106 (183*2π)/12677 weeks
184-7.8602 2.61759 (184*2π)/12677 weeks
185-.27465 -1.65903 (185*2π)/12677 weeks
186-3.08409 -7.45755 (186*2π)/12677 weeks
187-4.74381 -6.13149 (187*2π)/12677 weeks
188-5.18663 -8.25772 (188*2π)/12677 weeks
189-8.64942 -6.52608 (189*2π)/12677 weeks
190-5.55755 -5.86988 (190*2π)/12677 weeks
191-8.58292 -8.06955 (191*2π)/12677 weeks
192-10.55265 -4.57938 (192*2π)/12677 weeks
193-6.0098 -1.54781 (193*2π)/12677 weeks
194-6.21892 -3.98899 (194*2π)/12677 weeks
195-5.72307 -4.73714 (195*2π)/12676 weeks
196-4.97182 -6.16053 (196*2π)/12676 weeks
197-10.76182 -8.22564 (197*2π)/12676 weeks
198-11.19946 -.91792 (198*2π)/12676 weeks
199-6.16484 -.04344 (199*2π)/12676 weeks
200-6.14964 -2.47541 (200*2π)/12676 weeks
201-5.50136 -1.60154 (201*2π)/12676 weeks
202-5.72043 -2.17246 (202*2π)/12676 weeks
203-6.86846 -2.18505 (203*2π)/12676 weeks
204-3.26473 -.82919 (204*2π)/12676 weeks
205-5.49577 -6.75087 (205*2π)/12676 weeks
206-9.40705 -5.62243 (206*2π)/12676 weeks
207-12.02626 -.30458 (207*2π)/12676 weeks
208-11.24008 4.29286 (208*2π)/12676 weeks
209-4.13565 8.05357 (209*2π)/12676 weeks
2102.0934 3.64218 (210*2π)/12676 weeks
211-.45638 1.01965 (211*2π)/12676 weeks
2122.38768 1.22998 (212*2π)/12676 weeks
2132.89814 -2.02738 (213*2π)/12676 weeks
2143.01799 -4.84146 (214*2π)/12676 weeks
2152.12651 -8.83171 (215*2π)/12676 weeks
216-6.42454 -10.85978 (216*2π)/12676 weeks
217-10.5094 -1.58382 (217*2π)/12676 weeks
218-2.6887 3.32409 (218*2π)/12676 weeks
219-.12852 -.34212 (219*2π)/12676 weeks
2201.63582 -2.19374 (220*2π)/12676 weeks
2212.75442 -5.06978 (221*2π)/12676 weeks
2221.00702 -5.98217 (222*2π)/12676 weeks
2231.27267 -7.56062 (223*2π)/12676 weeks
224.98457 -12.44103 (224*2π)/12676 weeks
225-6.22166 -13.89919 (225*2π)/12676 weeks
226-12.11257 -11.71393 (226*2π)/12676 weeks
227-13.38976 -4.71583 (227*2π)/12676 weeks
228-11.48464 .59216 (228*2π)/12676 weeks
229-6.48058 1.33908 (229*2π)/12676 weeks
230-5.30903 -.95835 (230*2π)/12676 weeks
231-5.91707 -.91351 (231*2π)/12675 weeks
232-2.6799 1.23433 (232*2π)/12675 weeks
233-2.25808 -1.81426 (233*2π)/12675 weeks
234-.98745 -3.67882 (234*2π)/12675 weeks
235-4.72754 -5.95915 (235*2π)/12675 weeks
236-9.37533 -5.4032 (236*2π)/12675 weeks
237-6.29693 2.63474 (237*2π)/12675 weeks
238-4.47954 .17576 (238*2π)/12675 weeks
239-3.00113 -.35317 (239*2π)/12675 weeks
240-1.30601 -2.39958 (240*2π)/12675 weeks
241-4.77501 -3.08771 (241*2π)/12675 weeks
242-5.10068 1.12362 (242*2π)/12675 weeks
243-1.58582 -1.27657 (243*2π)/12675 weeks
244-4.11152 -3.86951 (244*2π)/12675 weeks
245-3.94068 -.5191 (245*2π)/12675 weeks
246-4.24863 -.36081 (246*2π)/12675 weeks
247-2.7679 1.84366 (247*2π)/12675 weeks
2482.48312 1.98515 (248*2π)/12675 weeks
2492.24537 -5.95011 (249*2π)/12675 weeks
250-3.49943 -6.20482 (250*2π)/12675 weeks
251-3.88208 -3.28299 (251*2π)/12675 weeks
252-5.77351 -3.64261 (252*2π)/12675 weeks
253-4.13116 -.8128 (253*2π)/12675 weeks
254-1.53078 -1.55906 (254*2π)/12675 weeks
255-5.43328 -3.41479 (255*2π)/12675 weeks
256-6.35877 2.35025 (256*2π)/12675 weeks
2571.91691 3.7294 (257*2π)/12675 weeks
2582.11989 -2.49904 (258*2π)/12675 weeks
259.2747 -4.00661 (259*2π)/12675 weeks
260-1.16258 -6.52389 (260*2π)/12675 weeks
261-6.62746 -3.01595 (261*2π)/12675 weeks
262-1.57379 1.32459 (262*2π)/12675 weeks
263.53411 -3.83592 (263*2π)/12675 weeks
264-3.70279 -3.18838 (264*2π)/12675 weeks
265-1.43495 -1.46178 (265*2π)/12675 weeks
266-.76132 -1.79326 (266*2π)/12675 weeks
267-.00191 -1.61559 (267*2π)/12675 weeks
2683.06199 -5.68833 (268*2π)/12675 weeks
269-1.77743 -10.5309 (269*2π)/12675 weeks
270-6.93398 -6.146 (270*2π)/12675 weeks
271-6.92042 -4.23217 (271*2π)/12675 weeks
272-7.53053 -1.18745 (272*2π)/12675 weeks
273-2.7496 1.18603 (273*2π)/12675 weeks
274-1.38096 -3.98502 (274*2π)/12675 weeks
275-6.54306 -1.62634 (275*2π)/12675 weeks
276-2.22127 .8137 (276*2π)/12675 weeks
277-.94007 -2.94053 (277*2π)/12675 weeks
278-3.0136 -3.62268 (278*2π)/12675 weeks
279-5.05003 -3.41643 (279*2π)/12675 weeks
280-8.26622 -1.71285 (280*2π)/12675 weeks
281-7.4102 4.89431 (281*2π)/12675 weeks
282.00701 6.3028 (282*2π)/12674 weeks
2832.4843 1.77708 (283*2π)/12674 weeks
2842.22596 -.53395 (284*2π)/12674 weeks
2851.72271 -1.44311 (285*2π)/12674 weeks
2861.58614 -1.70102 (286*2π)/12674 weeks
2874.10007 -2.84748 (287*2π)/12674 weeks
2881.18174 -9.05829 (288*2π)/12674 weeks
289-5.10266 -7.3669 (289*2π)/12674 weeks
290-6.18952 -2.08572 (290*2π)/12674 weeks
291-5.3663 1.00115 (291*2π)/12674 weeks
292-.17932 2.76718 (292*2π)/12674 weeks
2934.79967 .44267 (293*2π)/12674 weeks
294.62098 -4.8072 (294*2π)/12674 weeks
295-.31383 -2.13923 (295*2π)/12674 weeks
2964.19064 -2.53803 (296*2π)/12674 weeks
2971.54009 -6.5061 (297*2π)/12674 weeks
298-.41057 -7.63006 (298*2π)/12674 weeks
299-3.45091 -7.09874 (299*2π)/12674 weeks
300-5.75383 -2.6699 (300*2π)/12674 weeks
301-.35539 .20384 (301*2π)/12674 weeks
3022.57115 -4.69809 (302*2π)/12674 weeks
303.8952 -6.92606 (303*2π)/12674 weeks
304-.04311 -7.29838 (304*2π)/12674 weeks
305-3.70577 -9.1407 (305*2π)/12674 weeks
306-5.07896 -4.6613 (306*2π)/12674 weeks
307-1.98972 -7.52375 (307*2π)/12674 weeks
308-8.26052 -9.561 (308*2π)/12674 weeks
309-11.19182 -1.18834 (309*2π)/12674 weeks
310-6.38608 .4002 (310*2π)/12674 weeks
311-3.89042 2.30317 (311*2π)/12674 weeks
3121.90386 .97449 (312*2π)/12674 weeks
313.2288 -6.83299 (313*2π)/12674 weeks
314-5.15316 -5.21619 (314*2π)/12674 weeks
315-3.04258 -1.13601 (315*2π)/12674 weeks
316-3.31142 -5.14179 (316*2π)/12674 weeks
317-5.02574 -4.04428 (317*2π)/12674 weeks
318-5.61773 -2.80439 (318*2π)/12674 weeks
319-7.92323 -1.08729 (319*2π)/12674 weeks
320-4.19682 3.51249 (320*2π)/12674 weeks
3211.56114 1.36068 (321*2π)/12674 weeks
322-.01473 -3.34787 (322*2π)/12674 weeks
323-1.43546 -4.27448 (323*2π)/12674 weeks
324-4.57585 -5.48912 (324*2π)/12674 weeks
325-6.16355 -1.27678 (325*2π)/12674 weeks
326-2.83517 -.33957 (326*2π)/12674 weeks
327-4.15078 -2.88679 (327*2π)/12674 weeks
328-6.19823 .5425 (328*2π)/12674 weeks
329-2.91021 3.94397 (329*2π)/12674 weeks
330.05796 2.58083 (330*2π)/12674 weeks
3313.07998 2.28407 (331*2π)/12674 weeks
3326.08053 -4.1776 (332*2π)/12674 weeks
333-.538 -9.00793 (333*2π)/12674 weeks
334-4.38749 -4.10671 (334*2π)/12674 weeks
335-3.3562 -3.02266 (335*2π)/12674 weeks
336-2.91112 -3.0393 (336*2π)/12674 weeks
337-2.81921 -3.00263 (337*2π)/12674 weeks
338-4.73692 -2.70497 (338*2π)/12674 weeks
339-5.86828 .88349 (339*2π)/12674 weeks
340-.21277 3.30205 (340*2π)/12674 weeks
3412.85731 -2.42482 (341*2π)/12674 weeks
342-.16723 -4.1671 (342*2π)/12674 weeks
343-2.37603 -4.25989 (343*2π)/12674 weeks
344-4.76586 -1.45136 (344*2π)/12674 weeks
345-2.18746 1.87308 (345*2π)/12674 weeks
3463.5615 -.34479 (346*2π)/12674 weeks
347.80888 -3.86877 (347*2π)/12674 weeks
348.48171 -3.15992 (348*2π)/12674 weeks
349.81193 -4.24528 (349*2π)/12674 weeks
3501.14623 -5.25191 (350*2π)/12674 weeks
3512.01603 -8.34971 (351*2π)/12674 weeks
352-3.55001 -12.06657 (352*2π)/12674 weeks
353-10.57494 -7.49369 (353*2π)/12674 weeks
354-8.52175 -.6732 (354*2π)/12674 weeks
355-5.92894 -.76125 (355*2π)/12674 weeks
356-4.42684 1.53232 (356*2π)/12674 weeks
357-.79903 -.88387 (357*2π)/12674 weeks
358-3.59721 -.67023 (358*2π)/12674 weeks
359-1.17929 1.36702 (359*2π)/12674 weeks
3603.12279 -1.91621 (360*2π)/12674 weeks
361.42596 -7.11339 (361*2π)/12674 weeks
362-2.90499 -5.90409 (362*2π)/12674 weeks
363-5.82472 -5.40784 (363*2π)/12673 weeks
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