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Fourier Analysis of CMR (MORGAN STANLEY CONSUMER INDEX)


CMR (MORGAN STANLEY CONSUMER INDEX) appears to have interesting cyclic behaviour every 126 weeks (27.0569*sine), 105 weeks (23.9498*cosine), and 57 weeks (19.4246*cosine).

CMR (MORGAN STANLEY CONSUMER INDEX) has an average price of 442.4 (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 CMR (MORGAN STANLEY CONSUMER INDEX), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0442.4042   0 
1-179.4667 -233.0425 (1*2π)/12571,257 weeks
2-89.24048 -98.53516 (2*2π)/1257629 weeks
3-87.17117 10.47611 (3*2π)/1257419 weeks
4-68.93159 68.78777 (4*2π)/1257314 weeks
526.66053 38.65658 (5*2π)/1257251 weeks
631.72287 47.32296 (6*2π)/1257210 weeks
734.2322 17.95746 (7*2π)/1257180 weeks
859.66817 -49.94441 (8*2π)/1257157 weeks
93.39648 -30.17776 (9*2π)/1257140 weeks
10-23.46832 -27.05686 (10*2π)/1257126 weeks
11-21.3953 -21.67646 (11*2π)/1257114 weeks
12-23.94982 10.34483 (12*2π)/1257105 weeks
13-15.15831 21.80032 (13*2π)/125797 weeks
14-1.18221 10.66673 (14*2π)/125790 weeks
1517.22899 11.93291 (15*2π)/125784 weeks
1613.351 12.71817 (16*2π)/125779 weeks
1715.52992 -17.8483 (17*2π)/125774 weeks
1812.67292 -18.37159 (18*2π)/125770 weeks
19-9.80028 -8.86619 (19*2π)/125766 weeks
20-11.21092 -15.82893 (20*2π)/125763 weeks
21-8.60047 -6.67532 (21*2π)/125760 weeks
22-19.42462 9.55201 (22*2π)/125757 weeks
23-6.48042 7.99508 (23*2π)/125755 weeks
246.28099 12.92545 (24*2π)/125752 weeks
255.37162 11.07956 (25*2π)/125750 weeks
2612.7859 -5.19553 (26*2π)/125748 weeks
276.55817 -11.28745 (27*2π)/125747 weeks
281.6362 -3.38972 (28*2π)/125745 weeks
29-6.72151 -14.48564 (29*2π)/125743 weeks
30-13.09679 -6.7657 (30*2π)/125742 weeks
31-9.19465 7.80011 (31*2π)/125741 weeks
32-5.8187 8.50706 (32*2π)/125739 weeks
33.59299 5.90072 (33*2π)/125738 weeks
346.73953 8.88998 (34*2π)/125737 weeks
352.87995 -.97114 (35*2π)/125736 weeks
367.07672 -7.54431 (36*2π)/125735 weeks
371.41417 -.62381 (37*2π)/125734 weeks
38-2.91572 -8.11728 (38*2π)/125733 weeks
39-2.92376 -7.8588 (39*2π)/125732 weeks
40-9.59741 -1.28398 (40*2π)/125731 weeks
41-12.35926 3.80952 (41*2π)/125731 weeks
42-1.16947 10.95981 (42*2π)/125730 weeks
435.47021 5.89727 (43*2π)/125729 weeks
443.14908 3.3627 (44*2π)/125729 weeks
455.05773 -2.5232 (45*2π)/125728 weeks
465.16607 -3.33427 (46*2π)/125727 weeks
47-3.36361 -5.14607 (47*2π)/125727 weeks
48-2.80661 -8.10587 (48*2π)/125726 weeks
49-6.45662 1.32904 (49*2π)/125726 weeks
50-8.18518 3.25178 (50*2π)/125725 weeks
51-5.99396 3.43194 (51*2π)/125725 weeks
522.86779 9.73245 (52*2π)/125724 weeks
534.58293 4.08478 (53*2π)/125724 weeks
541.91212 .1286 (54*2π)/125723 weeks
556.26199 -.9561 (55*2π)/125723 weeks
561.14745 -4.44226 (56*2π)/125722 weeks
57-3.83336 -3.24783 (57*2π)/125722 weeks
58-1.52268 -3.74337 (58*2π)/125722 weeks
59-7.73662 1.86125 (59*2π)/125721 weeks
60-3.72752 5.40067 (60*2π)/125721 weeks
61-.76143 2.75037 (61*2π)/125721 weeks
621.75041 8.17855 (62*2π)/125720 weeks
635.80294 2.77002 (63*2π)/125720 weeks
643.95362 -5.55912 (64*2π)/125720 weeks
652.17265 -.90681 (65*2π)/125719 weeks
66-1.43609 -2.66572 (66*2π)/125719 weeks
67-3.60689 -4.84076 (67*2π)/125719 weeks
68-4.53859 1.52099 (68*2π)/125718 weeks
69-1.00507 2.86398 (69*2π)/125718 weeks
70-3.45493 .48541 (70*2π)/125718 weeks
71-3.1347 8.36346 (71*2π)/125718 weeks
727.14183 5.72145 (72*2π)/125717 weeks
732.65224 -5.22352 (73*2π)/125717 weeks
742.50337 .87941 (74*2π)/125717 weeks
752.81981 -3.27189 (75*2π)/125717 weeks
76-5.98898 -5.84408 (76*2π)/125717 weeks
77-2.06163 3.36121 (77*2π)/125716 weeks
78-1.17912 .1915 (78*2π)/125716 weeks
79-5.88779 1.45363 (79*2π)/125716 weeks
801.28162 5.11433 (80*2π)/125716 weeks
81-.12612 3.49405 (81*2π)/125716 weeks
823.01934 3.68918 (82*2π)/125715 weeks
837.71146 -1.26321 (83*2π)/125715 weeks
84.38956 -4.00974 (84*2π)/125715 weeks
85-2.94657 -3.1871 (85*2π)/125715 weeks
86-.63955 -2.34975 (86*2π)/125715 weeks
87-5.16599 1.48339 (87*2π)/125714 weeks
88-4.24054 3.73823 (88*2π)/125714 weeks
892.81066 3.10229 (89*2π)/125714 weeks
90-1.15756 2.68825 (90*2π)/125714 weeks
91.99523 3.89928 (91*2π)/125714 weeks
927.32009 .64816 (92*2π)/125714 weeks
931.33668 -2.67118 (93*2π)/125714 weeks
94-.76908 -3.49428 (94*2π)/125713 weeks
95-1.81968 -2.66058 (95*2π)/125713 weeks
96-3.97288 1.7455 (96*2π)/125713 weeks
97-.10127 1.635 (97*2π)/125713 weeks
98-2.99284 .52298 (98*2π)/125713 weeks
991.0256 6.29282 (99*2π)/125713 weeks
1002.80885 .83314 (100*2π)/125713 weeks
101-.40456 .5764 (101*2π)/125712 weeks
1024.26125 2.43913 (102*2π)/125712 weeks
1033.31931 -2.5269 (103*2π)/125712 weeks
104-1.76322 -4.41441 (104*2π)/125712 weeks
105-1.23591 -.54078 (105*2π)/125712 weeks
106-3.49249 1.0531 (106*2π)/125712 weeks
107-3.00964 1.92293 (107*2π)/125712 weeks
108-.05816 4.24643 (108*2π)/125712 weeks
1092.54807 3.42612 (109*2π)/125712 weeks
1101.16691 .44993 (110*2π)/125711 weeks
1112.97851 .45295 (111*2π)/125711 weeks
1122.6768 -.24958 (112*2π)/125711 weeks
113.30349 -1.40964 (113*2π)/125711 weeks
114.2924 -4.58441 (114*2π)/125711 weeks
115-4.25829 .39265 (115*2π)/125711 weeks
116-3.68044 3.72176 (116*2π)/125711 weeks
1172.06478 2.35554 (117*2π)/125711 weeks
118-.29862 4.24506 (118*2π)/125711 weeks
1193.9578 1.20933 (119*2π)/125711 weeks
1202.16948 -2.02451 (120*2π)/125710 weeks
121-.22507 .70635 (121*2π)/125710 weeks
1221.47734 -.09523 (122*2π)/125710 weeks
1231.01474 -1.23095 (123*2π)/125710 weeks
124-.4776 -1.97414 (124*2π)/125710 weeks
125-4.74767 -.58997 (125*2π)/125710 weeks
126-1.31997 4.41184 (126*2π)/125710 weeks
1272.27792 2.38111 (127*2π)/125710 weeks
128-.84924 2.99131 (128*2π)/125710 weeks
1294.4615 1.22654 (129*2π)/125710 weeks
1303.21207 -1.25019 (130*2π)/125710 weeks
131-.55148 -1.31095 (131*2π)/125710 weeks
132.9543 -1.01394 (132*2π)/125710 weeks
133-.22067 -.37623 (133*2π)/12579 weeks
134-.83265 -.25086 (134*2π)/12579 weeks
135-3.59132 -.91905 (135*2π)/12579 weeks
136-.15251 4.37084 (136*2π)/12579 weeks
1371.65686 3.68024 (137*2π)/12579 weeks
1381.55583 1.28962 (138*2π)/12579 weeks
1395.06901 .52549 (139*2π)/12579 weeks
1402.76156 -2.58944 (140*2π)/12579 weeks
141-2.7591 -2.92759 (141*2π)/12579 weeks
142-.17442 1.25055 (142*2π)/12579 weeks
143.6574 .62035 (143*2π)/12579 weeks
144-1.15127 -1.55182 (144*2π)/12579 weeks
145-1.95786 2.06005 (145*2π)/12579 weeks
1461.11173 2.49531 (146*2π)/12579 weeks
147.78474 2.34904 (147*2π)/12579 weeks
1484.17182 2.02989 (148*2π)/12578 weeks
1493.01752 -2.66921 (149*2π)/12578 weeks
150-1.30257 -1.26049 (150*2π)/12578 weeks
1511.40313 -1.36266 (151*2π)/12578 weeks
152-2.19258 -1.03498 (152*2π)/12578 weeks
153-.25684 3.42059 (153*2π)/12578 weeks
1541.6677 -2.80834 (154*2π)/12578 weeks
155-3.65452 1.24973 (155*2π)/12578 weeks
1561.02642 6.1339 (156*2π)/12578 weeks
1574.3953 -.21048 (157*2π)/12578 weeks
1581.77842 .16866 (158*2π)/12578 weeks
1593.58799 -.83272 (159*2π)/12578 weeks
160.31965 -4.58725 (160*2π)/12578 weeks
161-2.11428 -.38207 (161*2π)/12578 weeks
162-.76606 1.05751 (162*2π)/12578 weeks
163-1.33826 .78769 (163*2π)/12578 weeks
1641.58604 1.64725 (164*2π)/12578 weeks
165.94565 .94432 (165*2π)/12578 weeks
166.21574 .70907 (166*2π)/12578 weeks
1673.32121 2.29997 (167*2π)/12578 weeks
1684.12172 -2.04109 (168*2π)/12577 weeks
169-1.15753 -2.65177 (169*2π)/12577 weeks
1702.06641 -.2562 (170*2π)/12577 weeks
171-.51552 -3.81988 (171*2π)/12577 weeks
172-5.06932 1.04956 (172*2π)/12577 weeks
1732.29685 4.52531 (173*2π)/12577 weeks
1742.31903 -1.6535 (174*2π)/12577 weeks
175-1.4416 1.90519 (175*2π)/12577 weeks
1763.75763 -.19358 (176*2π)/12577 weeks
177.5238 -.51733 (177*2π)/12577 weeks
1781.59555 1.6716 (178*2π)/12577 weeks
1793.72189 -3.87498 (179*2π)/12577 weeks
180-1.52241 -2.50402 (180*2π)/12577 weeks
181-2.18676 .14333 (181*2π)/12577 weeks
182-1.2843 -.10561 (182*2π)/12577 weeks
183.51087 3.67971 (183*2π)/12577 weeks
1842.88059 .92649 (184*2π)/12577 weeks
1851.00402 -2.04338 (185*2π)/12577 weeks
186.72777 .99357 (186*2π)/12577 weeks
1872.42294 .76808 (187*2π)/12577 weeks
1881.54103 -3.30265 (188*2π)/12577 weeks
189.00405 -1.84525 (189*2π)/12577 weeks
190-.56165 -.99403 (190*2π)/12577 weeks
191-2.59075 -2.53864 (191*2π)/12577 weeks
192-1.91825 3.88972 (192*2π)/12577 weeks
1932.55885 3.27566 (193*2π)/12577 weeks
1942.46848 -1.38783 (194*2π)/12576 weeks
1951.90676 -.72164 (195*2π)/12576 weeks
196.1249 -.99222 (196*2π)/12576 weeks
197.39131 -.27057 (197*2π)/12576 weeks
1982.55449 -1.9764 (198*2π)/12576 weeks
199-1.37053 -1.60753 (199*2π)/12576 weeks
200-.79753 -.10124 (200*2π)/12576 weeks
201-.95279 -1.66295 (201*2π)/12576 weeks
202-1.77205 2.94032 (202*2π)/12576 weeks
2031.91648 2.55622 (203*2π)/12576 weeks
2043.57769 -1.4202 (204*2π)/12576 weeks
2051.80616 -1.04125 (205*2π)/12576 weeks
206-.96679 -1.85275 (206*2π)/12576 weeks
207.37761 -.46874 (207*2π)/12576 weeks
2081.28381 -1.46001 (208*2π)/12576 weeks
209-2.03286 -1.20599 (209*2π)/12576 weeks
210-.12394 -.54312 (210*2π)/12576 weeks
211-.9512 .06327 (211*2π)/12576 weeks
212-1.76663 2.19947 (212*2π)/12576 weeks
2132.66787 1.59926 (213*2π)/12576 weeks
2142.74347 -.10482 (214*2π)/12576 weeks
2151.5719 -1.92378 (215*2π)/12576 weeks
216-.29775 -2.57547 (216*2π)/12576 weeks
217-.36053 .06065 (217*2π)/12576 weeks
218-.34966 -1.11745 (218*2π)/12576 weeks
219-1.38105 -.76224 (219*2π)/12576 weeks
220.11653 .42097 (220*2π)/12576 weeks
221-1.40023 1.10373 (221*2π)/12576 weeks
222.35448 1.17672 (222*2π)/12576 weeks
2232.07349 1.26951 (223*2π)/12576 weeks
2242.63367 .29779 (224*2π)/12576 weeks
2252.89472 -4.39053 (225*2π)/12576 weeks
226-3.37893 -2.46818 (226*2π)/12576 weeks
227.08583 1.68402 (227*2π)/12576 weeks
228.17921 -2.03343 (228*2π)/12576 weeks
229-2.15275 .26993 (229*2π)/12575 weeks
2301.86064 1.17958 (230*2π)/12575 weeks
231-1.624 -1.16775 (231*2π)/12575 weeks
232.42368 1.92277 (232*2π)/12575 weeks
2332.90624 1.101 (233*2π)/12575 weeks
234.93722 -1.72847 (234*2π)/12575 weeks
2352.65008 -2.84913 (235*2π)/12575 weeks
236-2.96088 -2.86504 (236*2π)/12575 weeks
237-2.42639 1.46398 (237*2π)/12575 weeks
2381.43914 -.08427 (238*2π)/12575 weeks
239-.97409 -.90881 (239*2π)/12575 weeks
240-.68292 1.70389 (240*2π)/12575 weeks
2411.09316 -.16237 (241*2π)/12575 weeks
242-.22064 -.53206 (242*2π)/12575 weeks
243.39062 2.00735 (243*2π)/12575 weeks
2443.52207 -1.09728 (244*2π)/12575 weeks
245.09855 -4.53207 (245*2π)/12575 weeks
246-3.15617 -.19722 (246*2π)/12575 weeks
247-.14622 .01527 (247*2π)/12575 weeks
248-1.69838 .17036 (248*2π)/12575 weeks
249.80287 2.43517 (249*2π)/12575 weeks
250.90042 -1.94457 (250*2π)/12575 weeks
251-.93664 .96511 (251*2π)/12575 weeks
2522.77305 .74032 (252*2π)/12575 weeks
253-.70795 -2.42131 (253*2π)/12575 weeks
254.74169 1.20055 (254*2π)/12575 weeks
2552.60821 -3.66403 (255*2π)/12575 weeks
256-5.18823 -2.89043 (256*2π)/12575 weeks
257-1.84107 3.65422 (257*2π)/12575 weeks
2581.82662 .45514 (258*2π)/12575 weeks
259-1.37049 .18275 (259*2π)/12575 weeks
2602.27107 1.36925 (260*2π)/12575 weeks
2611.43778 -1.34058 (261*2π)/12575 weeks
262-1.49045 -1.1822 (262*2π)/12575 weeks
263.97409 .50222 (263*2π)/12575 weeks
2641.73802 -1.25017 (264*2π)/12575 weeks
265-1.5887 -2.56403 (265*2π)/12575 weeks
266-2.08919 -.44694 (266*2π)/12575 weeks
267-1.40187 .79251 (267*2π)/12575 weeks
268-.61533 3.26992 (268*2π)/12575 weeks
2693.12603 -.28178 (269*2π)/12575 weeks
270-.24182 -1.7808 (270*2π)/12575 weeks
271-.14795 1.657 (271*2π)/12575 weeks
2721.85917 -2.87266 (272*2π)/12575 weeks
273-2.24056 .20402 (273*2π)/12575 weeks
2741.73183 1.36577 (274*2π)/12575 weeks
275.15427 -4.57265 (275*2π)/12575 weeks
276-3.36895 .19022 (276*2π)/12575 weeks
277-1.18654 2.41187 (277*2π)/12575 weeks
278.13087 1.32929 (278*2π)/12575 weeks
2792.40404 1.1238 (279*2π)/12575 weeks
2801.07458 -.97339 (280*2π)/12574 weeks
281.24639 -1.08105 (281*2π)/12574 weeks
282.94121 -1.48295 (282*2π)/12574 weeks
283-1.749 -.59719 (283*2π)/12574 weeks
284.16266 .16359 (284*2π)/12574 weeks
285.35304 -1.77079 (285*2π)/12574 weeks
286-2.40785 .03131 (286*2π)/12574 weeks
287-1.81441 1.36345 (287*2π)/12574 weeks
2882.09335 2.81397 (288*2π)/12574 weeks
2892.69413 -.90794 (289*2π)/12574 weeks
290-.43209 -2.09742 (290*2π)/12574 weeks
291.55528 -.29821 (291*2π)/12574 weeks
292-.48838 -1.8039 (292*2π)/12574 weeks
293-2.45619 .03325 (293*2π)/12574 weeks
294.93949 .72008 (294*2π)/12574 weeks
295-.33615 -.58997 (295*2π)/12574 weeks
296-1.18656 -.53868 (296*2π)/12574 weeks
297-1.59474 1.14872 (297*2π)/12574 weeks
2981.40482 2.9692 (298*2π)/12574 weeks
2992.59175 -1.09825 (299*2π)/12574 weeks
300-.3115 -1.79967 (300*2π)/12574 weeks
3011.02227 -.65294 (301*2π)/12574 weeks
302-1.74446 -2.0127 (302*2π)/12574 weeks
303-1.41159 1.02573 (303*2π)/12574 weeks
304.42388 .12165 (304*2π)/12574 weeks
305-.97055 .21719 (305*2π)/12574 weeks
306.54758 .07247 (306*2π)/12574 weeks
307-1.59463 .02831 (307*2π)/12574 weeks
3081.07999 3.5256 (308*2π)/12574 weeks
3093.75694 -1.87572 (309*2π)/12574 weeks
310-.84466 -2.74292 (310*2π)/12574 weeks
311-.4619 .29757 (311*2π)/12574 weeks
312-.83242 -2.49258 (312*2π)/12574 weeks
313-2.89084 .77013 (313*2π)/12574 weeks
314.76649 2.71785 (314*2π)/12574 weeks
3151.29604 -.90881 (315*2π)/12574 weeks
316-.83784 -.91502 (316*2π)/12574 weeks
317-.80893 1.76989 (317*2π)/12574 weeks
3181.62382 .8778 (318*2π)/12574 weeks
3191.50418 -.93529 (319*2π)/12574 weeks
320.96546 -1.38998 (320*2π)/12574 weeks
321-1.48477 -2.36526 (321*2π)/12574 weeks
322-2.19826 -.06441 (322*2π)/12574 weeks
323.13905 1.15276 (323*2π)/12574 weeks
324-1.71832 .76483 (324*2π)/12574 weeks
3251.66487 2.13888 (325*2π)/12574 weeks
3262.46888 -2.30018 (326*2π)/12574 weeks
327-4.27494 .10242 (327*2π)/12574 weeks
3283.12981 3.31762 (328*2π)/12574 weeks
3292.82819 -3.64293 (329*2π)/12574 weeks
330-3.43016 -1.18979 (330*2π)/12574 weeks
3311.02459 .05595 (331*2π)/12574 weeks
332-2.20335 -1.32935 (332*2π)/12574 weeks
333-1.99256 2.83199 (333*2π)/12574 weeks
3342.06469 1.18696 (334*2π)/12574 weeks
335.77823 -.18907 (335*2π)/12574 weeks
336.70445 -.14734 (336*2π)/12574 weeks
337-.33544 -1.01415 (337*2π)/12574 weeks
338-.26407 .88679 (338*2π)/12574 weeks
3392.04671 .16109 (339*2π)/12574 weeks
340.10281 -3.24724 (340*2π)/12574 weeks
341-2.61224 -.52282 (341*2π)/12574 weeks
342-.94825 1.83919 (342*2π)/12574 weeks
343-.12576 -.27474 (343*2π)/12574 weeks
344-1.13246 2.4677 (344*2π)/12574 weeks
3453.83318 1.6602 (345*2π)/12574 weeks
346.3876 -3.4941 (346*2π)/12574 weeks
347-1.96342 1.068 (347*2π)/12574 weeks
3482.86012 .42315 (348*2π)/12574 weeks
349-.82018 -2.03498 (349*2π)/12574 weeks
350-.20064 -.0884 (350*2π)/12574 weeks
351-.41528 -1.60563 (351*2π)/12574 weeks
352-3.33945 1.35349 (352*2π)/12574 weeks
3531.46334 2.21904 (353*2π)/12574 weeks
354.80575 -.07398 (354*2π)/12574 weeks
3551.39978 1.79916 (355*2π)/12574 weeks
3562.28786 -2.67927 (356*2π)/12574 weeks
357-2.01099 -1.63132 (357*2π)/12574 weeks
358-.7166 1.82962 (358*2π)/12574 weeks
3591.52601 -.70871 (359*2π)/12574 weeks
360-.52113 -1.55829 (360*2π)/12573 weeks
361-1.53081 .54817 (361*2π)/12573 weeks
362-.22138 1.02691 (362*2π)/12573 weeks
363-.28125 .05202 (363*2π)/12573 weeks
364.30916 2.46599 (364*2π)/12573 weeks
3653.33768 -.07904 (365*2π)/12573 weeks
366.71481 -3.19875 (366*2π)/12573 weeks
367-1.61174 -.16641 (367*2π)/12573 weeks
368-.96264 -.0489 (368*2π)/12573 weeks
369.57495 .61779 (369*2π)/12573 weeks
370.62658 -.60508 (370*2π)/12573 weeks
371-2.3149 -1.13482 (371*2π)/12573 weeks
372-.01285 2.18943 (372*2π)/12573 weeks
3731.28091 .52992 (373*2π)/12573 weeks
374-.45595 .91211 (374*2π)/12573 weeks
3753.11775 .09366 (375*2π)/12573 weeks
3761.14883 -2.43668 (376*2π)/12573 weeks
377-2.22394 -1.38841 (377*2π)/12573 weeks
378-.97358 .07606 (378*2π)/12573 weeks
379.16325 2.06109 (379*2π)/12573 weeks
380.60688 -1.19248 (380*2π)/12573 weeks
381-1.31785 -.27078 (381*2π)/12573 weeks
382.70913 2.4788 (382*2π)/12573 weeks
3831.01765 -1.04378 (383*2π)/12573 weeks
384.07491 .88899 (384*2π)/12573 weeks
3852.9156 .08335 (385*2π)/12573 weeks
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