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Fourier Analysis of CMR (MORGAN STANLEY CONSUMER INDEX)


CMR (MORGAN STANLEY CONSUMER INDEX) appears to have interesting cyclic behaviour every 127 weeks (28.3618*cosine), 97 weeks (27.1483*sine), and 115 weeks (23.1407*cosine).

CMR (MORGAN STANLEY CONSUMER INDEX) has an average price of 368.46 (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 3/13/2017 for CMR (MORGAN STANLEY CONSUMER INDEX), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0368.4638   0 
1-182.7944 -189.4251 (1*2π)/12661,266 weeks
2-97.49438 -64.74858 (2*2π)/1266633 weeks
3-82.90706 34.92205 (3*2π)/1266422 weeks
4-52.49279 82.91325 (4*2π)/1266317 weeks
533.82792 43.65067 (5*2π)/1266253 weeks
640.07134 43.44641 (6*2π)/1266211 weeks
737.46581 10.33241 (7*2π)/1266181 weeks
843.64514 -52.37666 (8*2π)/1266158 weeks
9-6.37654 -23.64514 (9*2π)/1266141 weeks
10-28.36181 -13.74221 (10*2π)/1266127 weeks
11-23.14071 -5.73011 (11*2π)/1266115 weeks
12-15.31222 22.69767 (12*2π)/1266106 weeks
13-2.46452 27.14834 (13*2π)/126697 weeks
148.23434 11.96415 (14*2π)/126690 weeks
1522.83105 6.25137 (15*2π)/126684 weeks
1616.88606 4.57527 (16*2π)/126679 weeks
177.04325 -20.64314 (17*2π)/126674 weeks
182.56756 -15.93853 (18*2π)/126670 weeks
19-12.0737 .47877 (19*2π)/126667 weeks
20-12.86484 -3.40399 (20*2π)/126663 weeks
21-4.89763 4.98703 (21*2π)/126660 weeks
22-4.11871 18.97261 (22*2π)/126658 weeks
236.83609 8.2775 (23*2π)/126655 weeks
2416.27784 4.51175 (24*2π)/126653 weeks
2511.11212 .67594 (25*2π)/126651 weeks
265.88154 -13.93982 (26*2π)/126649 weeks
27-2.6649 -10.62893 (27*2π)/126647 weeks
28-2.61605 -.87899 (28*2π)/126645 weeks
29-12.43785 -2.63276 (29*2π)/126644 weeks
30-7.5163 7.71141 (30*2π)/126642 weeks
315.22943 12.31268 (31*2π)/126641 weeks
326.90029 6.49004 (32*2π)/126640 weeks
338.18966 -.57091 (33*2π)/126638 weeks
3410.25945 -2.58718 (34*2π)/126637 weeks
35-.2844 -6.21525 (35*2π)/126636 weeks
36-1.31122 -9.35661 (36*2π)/126635 weeks
37-1.03872 .52306 (37*2π)/126634 weeks
38-7.07553 -.96454 (38*2π)/126633 weeks
39-3.78779 1.20783 (39*2π)/126632 weeks
40-.60893 8.76665 (40*2π)/126632 weeks
413.89592 8.37475 (41*2π)/126631 weeks
4212.26201 -.06103 (42*2π)/126630 weeks
436.57416 -6.61443 (43*2π)/126629 weeks
441.34017 -4.28843 (44*2π)/126629 weeks
45-2.05806 -6.5157 (45*2π)/126628 weeks
46-2.53359 -3.3645 (46*2π)/126628 weeks
47-5.76831 3.06704 (47*2π)/126627 weeks
48-3.36674 1.44832 (48*2π)/126626 weeks
493.76683 6.85128 (49*2π)/126626 weeks
503.76787 4.75567 (50*2π)/126625 weeks
515.04002 -.1732 (51*2π)/126625 weeks
529.04844 -5.41223 (52*2π)/126624 weeks
53.28758 -5.92446 (53*2π)/126624 weeks
54-3.06258 -2.87642 (54*2π)/126623 weeks
55-1.82305 -4.037 (55*2π)/126623 weeks
56-4.49384 1.84826 (56*2π)/126623 weeks
57-1.47148 4.73788 (57*2π)/126622 weeks
581.11815 1.59072 (58*2π)/126622 weeks
594.8385 5.23791 (59*2π)/126621 weeks
606.01888 -1.23279 (60*2π)/126621 weeks
612.69282 -4.16505 (61*2π)/126621 weeks
624.35663 -4.64762 (62*2π)/126620 weeks
63-3.23667 -5.73599 (63*2π)/126620 weeks
64-6.53021 -1.18494 (64*2π)/126620 weeks
65.39772 1.84798 (65*2π)/126619 weeks
66-1.23786 3.55059 (66*2π)/126619 weeks
67.09055 2.87632 (67*2π)/126619 weeks
685.78534 1.03052 (68*2π)/126619 weeks
693.66655 -2.53928 (69*2π)/126618 weeks
701.42753 -.65489 (70*2π)/126618 weeks
715.10548 -3.42716 (71*2π)/126618 weeks
72-2.70957 -8.08408 (72*2π)/126618 weeks
73-7.59899 .98504 (73*2π)/126617 weeks
741.20116 .64272 (74*2π)/126617 weeks
75-1.97543 1.935 (75*2π)/126617 weeks
76.9422 5.60275 (76*2π)/126617 weeks
776.5568 -2.44415 (77*2π)/126616 weeks
78.90766 -1.31837 (78*2π)/126616 weeks
792.55501 -.32061 (79*2π)/126616 weeks
801.5224 -6.4177 (80*2π)/126616 weeks
81-1.31915 -1.94825 (81*2π)/126616 weeks
82-2.56635 -3.21727 (82*2π)/126615 weeks
83-4.93042 -.64111 (83*2π)/126615 weeks
84-.22758 5.99874 (84*2π)/126615 weeks
852.68271 2.47565 (85*2π)/126615 weeks
862.79078 -1.49219 (86*2π)/126615 weeks
874.9458 -.39426 (87*2π)/126615 weeks
881.56785 -4.00251 (88*2π)/126614 weeks
89-2.24107 -5.45416 (89*2π)/126614 weeks
90-.56937 .16681 (90*2π)/126614 weeks
91-1.85 -2.28332 (91*2π)/126614 weeks
92-4.26757 -1.10072 (92*2π)/126614 weeks
93.05543 5.19473 (93*2π)/126614 weeks
942.00423 1.96315 (94*2π)/126613 weeks
953.27612 -.8934 (95*2π)/126613 weeks
963.66019 -2.73986 (96*2π)/126613 weeks
97-.82061 -3.69848 (97*2π)/126613 weeks
98.05051 -1.25356 (98*2π)/126613 weeks
99-.75603 -4.61145 (99*2π)/126613 weeks
100-4.03498 1.20638 (100*2π)/126613 weeks
101.12346 1.23616 (101*2π)/126613 weeks
102-1.28027 -1.43047 (102*2π)/126612 weeks
103-.38686 3.50055 (103*2π)/126612 weeks
1043.53636 1.84059 (104*2π)/126612 weeks
1053.27966 -3.73281 (105*2π)/126612 weeks
1061.54831 -2.50641 (106*2π)/126612 weeks
107-1.28442 -3.17245 (107*2π)/126612 weeks
108-2.58932 -3.1852 (108*2π)/126612 weeks
109-3.16513 .13861 (109*2π)/126612 weeks
110-1.23118 2.50676 (110*2π)/126612 weeks
111-.21921 .17215 (111*2π)/126611 weeks
1121.22159 1.00395 (112*2π)/126611 weeks
1132.02987 1.01282 (113*2π)/126611 weeks
1141.47358 -.92615 (114*2π)/126611 weeks
1153.61686 -4.4086 (115*2π)/126611 weeks
116-2.20573 -3.99388 (116*2π)/126611 weeks
117-4.89861 -1.2492 (117*2π)/126611 weeks
118-.43493 .72037 (118*2π)/126611 weeks
119-3.10429 2.0068 (119*2π)/126611 weeks
1201.54621 2.20742 (120*2π)/126611 weeks
1212.4737 -1.285 (121*2π)/126610 weeks
122-.4569 -.53738 (122*2π)/126610 weeks
123.96856 -.35578 (123*2π)/126610 weeks
1241.42195 -1.54968 (124*2π)/126610 weeks
125.51512 -3.19382 (125*2π)/126610 weeks
126-4.10413 -3.70804 (126*2π)/126610 weeks
127-3.33013 1.68945 (127*2π)/126610 weeks
128.36378 1.47139 (128*2π)/126610 weeks
129-2.35049 1.5378 (129*2π)/126610 weeks
1302.70183 1.43343 (130*2π)/126610 weeks
1312.72654 -1.20923 (131*2π)/126610 weeks
132-.69865 -2.26682 (132*2π)/126610 weeks
133.32333 -1.70838 (133*2π)/126610 weeks
134-.62527 -1.41018 (134*2π)/12669 weeks
135-1.42231 -1.52053 (135*2π)/12669 weeks
136-4.13487 -2.14584 (136*2π)/12669 weeks
137-1.51944 3.03873 (137*2π)/12669 weeks
138.39163 2.64829 (138*2π)/12669 weeks
139.48686 .54795 (139*2π)/12669 weeks
1403.67568 -.15299 (140*2π)/12669 weeks
1411.61087 -3.17681 (141*2π)/12669 weeks
142-3.55248 -3.32655 (142*2π)/12669 weeks
143-1.22134 .54572 (143*2π)/12669 weeks
144-.38306 -.06209 (144*2π)/12669 weeks
145-2.23849 -1.77816 (145*2π)/12669 weeks
146-2.55036 1.74624 (146*2π)/12669 weeks
147.51386 1.83501 (147*2π)/12669 weeks
148.43426 1.38556 (148*2π)/12669 weeks
1493.01253 .24986 (149*2π)/12668 weeks
150.87068 -3.45519 (150*2π)/12668 weeks
151-2.52336 -1.36613 (151*2π)/12668 weeks
152-.53321 -1.77636 (152*2π)/12668 weeks
153-3.27925 -.13429 (153*2π)/12668 weeks
154-.14449 2.67454 (154*2π)/12668 weeks
155-.56849 -2.91195 (155*2π)/12668 weeks
156-3.36689 2.52482 (156*2π)/12668 weeks
1572.44183 4.16199 (157*2π)/12668 weeks
1582.48272 -2.55847 (158*2π)/12668 weeks
159.01858 -1.05369 (159*2π)/12668 weeks
160.69602 -2.30784 (160*2π)/12668 weeks
161-3.33197 -3.21454 (161*2π)/12668 weeks
162-2.98902 1.5166 (162*2π)/12668 weeks
163-.90016 1.83979 (163*2π)/12668 weeks
164-.94534 1.38227 (164*2π)/12668 weeks
1651.34788 .37196 (165*2π)/12668 weeks
166.06881 .31177 (166*2π)/12668 weeks
167-.08709 .37432 (167*2π)/12668 weeks
1682.40652 -.60532 (168*2π)/12668 weeks
169-.4281 -3.37488 (169*2π)/12667 weeks
170-3.65065 -.14586 (170*2π)/12667 weeks
171.10751 -.29923 (171*2π)/12667 weeks
172-3.49545 -.32217 (172*2π)/12667 weeks
173-1.74442 4.88223 (173*2π)/12667 weeks
1744.47125 .83255 (174*2π)/12667 weeks
175-.69786 -2.48493 (175*2π)/12667 weeks
176-.40142 2.11036 (176*2π)/12667 weeks
1771.1575 -2.51799 (177*2π)/12667 weeks
178-1.18852 -.04593 (178*2π)/12667 weeks
179.345 -.02059 (179*2π)/12667 weeks
180-2.44368 -3.04415 (180*2π)/12667 weeks
181-2.95747 2.38875 (181*2π)/12667 weeks
182-.44975 2.99703 (182*2π)/12667 weeks
183.48103 1.35225 (183*2π)/12667 weeks
1843.26506 .83113 (184*2π)/12667 weeks
185.45972 -2.22085 (185*2π)/12667 weeks
186-2.14162 -.81254 (186*2π)/12667 weeks
187.64423 .62585 (187*2π)/12667 weeks
188-.07911 -1.08233 (188*2π)/12667 weeks
189-3.28957 -.8271 (189*2π)/12667 weeks
190-1.28328 1.60702 (190*2π)/12667 weeks
191-.47005 1.80359 (191*2π)/12667 weeks
192-1.04393 2.13097 (192*2π)/12667 weeks
1934.11698 1.90717 (193*2π)/12667 weeks
1942.0232 -2.60848 (194*2π)/12667 weeks
195-2.43721 -2.13464 (195*2π)/12666 weeks
196-1.10043 .00458 (196*2π)/12666 weeks
197-1.16969 1.19645 (197*2π)/12666 weeks
198-.40191 .34635 (198*2π)/12666 weeks
199-1.29859 -.60628 (199*2π)/12666 weeks
200-.69319 2.97271 (200*2π)/12666 weeks
201.91738 1.18928 (201*2π)/12666 weeks
202-.01083 .66768 (202*2π)/12666 weeks
2033.09575 .78196 (203*2π)/12666 weeks
204.56191 -2.75304 (204*2π)/12666 weeks
205-2.78014 -2.02021 (205*2π)/12666 weeks
206-1.30041 1.32399 (206*2π)/12666 weeks
207-1.0708 2.40352 (207*2π)/12666 weeks
208.38108 .19886 (208*2π)/12666 weeks
209-.60026 .43132 (209*2π)/12666 weeks
210.32686 2.52882 (210*2π)/12666 weeks
211.97403 -.30473 (211*2π)/12666 weeks
2121.0593 .47078 (212*2π)/12666 weeks
2131.49876 -.15811 (213*2π)/12666 weeks
214-.83915 -2.94135 (214*2π)/12666 weeks
215-2.19469 -.05835 (215*2π)/12666 weeks
216-1.90085 1.9568 (216*2π)/12666 weeks
217-.12393 2.37507 (217*2π)/12666 weeks
2181.68797 .79144 (218*2π)/12666 weeks
219-.07587 .83507 (219*2π)/12666 weeks
220.92065 .79615 (220*2π)/12666 weeks
2211.07743 -.85902 (221*2π)/12666 weeks
222.64033 .25437 (222*2π)/12666 weeks
223-.53921 -1.2533 (223*2π)/12666 weeks
224-1.13022 -.969 (224*2π)/12666 weeks
225-1.93261 .83142 (225*2π)/12666 weeks
226-2.18022 2.71699 (226*2π)/12666 weeks
2273.24159 3.46832 (227*2π)/12666 weeks
2282.06555 -2.16772 (228*2π)/12666 weeks
229-1.11829 .70427 (229*2π)/12666 weeks
2301.83093 .24531 (230*2π)/12666 weeks
231-.41375 -1.95576 (231*2π)/12665 weeks
232-.42903 1.81952 (232*2π)/12665 weeks
233.299 -1.59898 (233*2π)/12665 weeks
234-1.74033 .0191 (234*2π)/12665 weeks
235-1.18208 2.95142 (235*2π)/12665 weeks
236.18082 1.42174 (236*2π)/12665 weeks
2373.37605 2.53863 (237*2π)/12665 weeks
2382.05878 -2.29059 (238*2π)/12665 weeks
239-1.81764 -1.26857 (239*2π)/12665 weeks
240.5734 1.12098 (240*2π)/12665 weeks
241.47738 -.90764 (241*2π)/12665 weeks
242-1.71515 .4756 (242*2π)/12665 weeks
243.27131 1.14052 (243*2π)/12665 weeks
244.21404 -.20117 (244*2π)/12665 weeks
245-1.84912 1.78148 (245*2π)/12665 weeks
2462.09255 3.23599 (246*2π)/12665 weeks
2473.97405 -1.24919 (247*2π)/12665 weeks
248-.76629 -1.98554 (248*2π)/12665 weeks
249.15003 -.16618 (249*2π)/12665 weeks
250-1.01654 -1.03572 (250*2π)/12665 weeks
251-1.28488 2.18078 (251*2π)/12665 weeks
2521.35487 -.17024 (252*2π)/12665 weeks
253-1.20537 .52391 (253*2π)/12665 weeks
2541.39452 2.76321 (254*2π)/12665 weeks
255.85628 -1.10562 (255*2π)/12665 weeks
256.17005 2.13953 (256*2π)/12665 weeks
2574.65705 -.44169 (257*2π)/12665 weeks
258-1.35676 -4.66372 (258*2π)/12665 weeks
259-3.0205 1.49169 (259*2π)/12665 weeks
2601.09695 1.46429 (260*2π)/12665 weeks
261-1.13933 -.10689 (261*2π)/12665 weeks
2621.08976 2.47347 (262*2π)/12665 weeks
2632.0641 .36274 (263*2π)/12665 weeks
264-.31746 -1.01889 (264*2π)/12665 weeks
265.7963 1.16056 (265*2π)/12665 weeks
2662.46588 .25565 (266*2π)/12665 weeks
267.3499 -2.32958 (267*2π)/12665 weeks
268-1.22095 -1.10938 (268*2π)/12665 weeks
269-1.25393 .39413 (269*2π)/12665 weeks
270-1.11324 3.01161 (270*2π)/12665 weeks
2712.96729 .94433 (271*2π)/12665 weeks
272.64114 -1.11933 (272*2π)/12665 weeks
273.14369 1.77111 (273*2π)/12665 weeks
2742.56291 -1.94855 (274*2π)/12665 weeks
275-1.48561 .06129 (275*2π)/12665 weeks
2761.87138 1.7079 (276*2π)/12665 weeks
2771.17202 -3.85537 (277*2π)/12665 weeks
278-2.61628 -.12287 (278*2π)/12665 weeks
279-.88701 2.35512 (279*2π)/12665 weeks
280.63678 1.48841 (280*2π)/12665 weeks
2812.61767 1.08843 (281*2π)/12665 weeks
2821.36023 -.72863 (282*2π)/12664 weeks
283.68307 -.83218 (283*2π)/12664 weeks
2841.10106 -1.29515 (284*2π)/12664 weeks
285-1.26565 -.17685 (285*2π)/12664 weeks
286.65017 .39384 (286*2π)/12664 weeks
287.55209 -1.40724 (287*2π)/12664 weeks
288-1.73142 .6522 (288*2π)/12664 weeks
289-.60496 1.91808 (289*2π)/12664 weeks
2903.23821 2.09057 (290*2π)/12664 weeks
2912.64878 -1.56018 (291*2π)/12664 weeks
292-.41325 -1.6761 (292*2π)/12664 weeks
293.88198 -.31642 (293*2π)/12664 weeks
294-.49741 -1.30353 (294*2π)/12664 weeks
295-1.43287 .90178 (295*2π)/12664 weeks
2961.72723 .40515 (296*2π)/12664 weeks
297.07821 -.46703 (297*2π)/12664 weeks
298-.60841 .07809 (298*2π)/12664 weeks
299.13237 1.63806 (299*2π)/12664 weeks
3003.17909 1.24672 (300*2π)/12664 weeks
3011.78674 -2.60289 (301*2π)/12664 weeks
302-.88971 -1.3934 (302*2π)/12664 weeks
303.68125 -.7763 (303*2π)/12664 weeks
304-1.82378 -.46781 (304*2π)/12664 weeks
305.18805 1.59094 (305*2π)/12664 weeks
3061.15295 -.14795 (306*2π)/12664 weeks
307.14087 .34278 (307*2π)/12664 weeks
308.95926 -.39198 (308*2π)/12664 weeks
309-.1162 .78118 (309*2π)/12664 weeks
3103.41404 .7436 (310*2π)/12664 weeks
3111.00333 -4.14491 (311*2π)/12664 weeks
312-2.31643 -.82083 (312*2π)/12664 weeks
313.26458 .81226 (313*2π)/12664 weeks
314-1.32016 -.70356 (314*2π)/12664 weeks
315.1478 2.37884 (315*2π)/12664 weeks
3163.16078 .26855 (316*2π)/12664 weeks
317.32433 -2.05832 (317*2π)/12664 weeks
318-.56267 .00555 (318*2π)/12664 weeks
3191.54346 .96938 (319*2π)/12664 weeks
3201.64448 -1.71718 (320*2π)/12664 weeks
321-.35059 -1.97592 (321*2π)/12664 weeks
322-.9117 -.80366 (322*2π)/12664 weeks
323-1.72942 .71285 (323*2π)/12664 weeks
324.53604 1.54563 (324*2π)/12664 weeks
3252.04459 -.0121 (325*2π)/12664 weeks
326.73659 .54175 (326*2π)/12664 weeks
3272.35917 -1.86247 (327*2π)/12664 weeks
328-1.2847 -2.51487 (328*2π)/12664 weeks
329-.56848 3.02591 (329*2π)/12664 weeks
3303.6078 -2.84241 (330*2π)/12664 weeks
331-3.05297 -2.76129 (331*2π)/12664 weeks
332-1.28045 3.16943 (332*2π)/12664 weeks
3331.53123 -.86326 (333*2π)/12664 weeks
334-.39102 1.32181 (334*2π)/12664 weeks
3352.87657 .75494 (335*2π)/12664 weeks
3361.19281 -2.93151 (336*2π)/12664 weeks
337-.56073 -1.04877 (337*2π)/12664 weeks
338-.32415 -.55481 (338*2π)/12664 weeks
339-.50392 .13916 (339*2π)/12664 weeks
3401.1075 -.32215 (340*2π)/12664 weeks
341-.27882 -1.74894 (341*2π)/12664 weeks
342-2.16295 .66576 (342*2π)/12664 weeks
3431.46081 2.06104 (343*2π)/12664 weeks
3442.34719 -.64327 (344*2π)/12664 weeks
345.04599 -1.24383 (345*2π)/12664 weeks
3461.81162 -.59759 (346*2π)/12664 weeks
347-.3742 -3.55559 (347*2π)/12664 weeks
348-3.21973 1.04643 (348*2π)/12664 weeks
3492.02001 1.33235 (349*2π)/12664 weeks
350.07876 -2.55751 (350*2π)/12664 weeks
351-1.30084 1.47044 (351*2π)/12664 weeks
3521.09369 .0242 (352*2π)/12664 weeks
353.28601 .14433 (353*2π)/12664 weeks
3542.43056 .45074 (354*2π)/12664 weeks
355.62933 -3.53012 (355*2π)/12664 weeks
356-1.20896 -.84293 (356*2π)/12664 weeks
357-.01396 -.99266 (357*2π)/12664 weeks
358-2.72377 .25951 (358*2π)/12664 weeks
3591.26295 2.34096 (359*2π)/12664 weeks
3602.0988 -1.29409 (360*2π)/12664 weeks
361-1.3221 -1.24073 (361*2π)/12664 weeks
362.22367 .9768 (362*2π)/12663 weeks
3631.89164 -.30765 (363*2π)/12663 weeks
364.36572 -1.69126 (364*2π)/12663 weeks
365-.50865 -.91574 (365*2π)/12663 weeks
366.33058 -1.53875 (366*2π)/12663 weeks
367-2.56034 -.92724 (367*2π)/12663 weeks
368-.90497 2.41298 (368*2π)/12663 weeks
3692.62452 .70454 (369*2π)/12663 weeks
370.58842 -1.11382 (370*2π)/12663 weeks
371-.04137 -1.52336 (371*2π)/12663 weeks
372-.3365 .09305 (372*2π)/12663 weeks
373.95936 .4259 (373*2π)/12663 weeks
374.65704 -2.96091 (374*2π)/12663 weeks
375-1.55784 -.66609 (375*2π)/12663 weeks
376-.17623 .33943 (376*2π)/12663 weeks
377-1.73253 -.77912 (377*2π)/12663 weeks
378.15782 2.26769 (378*2π)/12663 weeks
3792.50971 .69346 (379*2π)/12663 weeks
380.82011 -2.29996 (380*2π)/12663 weeks
381-.07221 -1.80642 (381*2π)/12663 weeks
382-1.47176 .52517 (382*2π)/12663 weeks
3831.04231 -.56433 (383*2π)/12663 weeks
384-.38832 -2.13675 (384*2π)/12663 weeks
385-1.79901 1.00345 (385*2π)/12663 weeks
386.65102 -.33059 (386*2π)/12663 weeks
387-1.1625 .01848 (387*2π)/12663 weeks
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