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Fourier Analysis of WMT (Wal-Mart Stores, Inc. Common St)


WMT (Wal-Mart Stores, Inc. Common St) appears to have interesting cyclic behaviour every 211 weeks (2.3211*sine), 178 weeks (1.6913*sine), and 193 weeks (1.3119*sine).

WMT (Wal-Mart Stores, Inc. Common St) has an average price of 22.02 (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 8/25/1972 to 1/17/2017 for WMT (Wal-Mart Stores, Inc. Common St), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
022.01999   0 
19.26931 -25.48504 (1*2π)/23172,317 weeks
21.38788 -8.28484 (2*2π)/23171,159 weeks
34.89853 -8.83021 (3*2π)/2317772 weeks
4-1.48732 -9.12596 (4*2π)/2317579 weeks
5-.12406 -3.5828 (5*2π)/2317463 weeks
6-.63909 -5.8089 (6*2π)/2317386 weeks
7-1.31374 -2.47392 (7*2π)/2317331 weeks
8-.69604 -3.07924 (8*2π)/2317290 weeks
9-1.19311 -1.41126 (9*2π)/2317257 weeks
10.53011 -.88832 (10*2π)/2317232 weeks
11.30059 -2.32108 (11*2π)/2317211 weeks
12-.10494 -1.31189 (12*2π)/2317193 weeks
13.29517 -1.69134 (13*2π)/2317178 weeks
14-.22258 -1.30934 (14*2π)/2317166 weeks
15.29603 -1.24061 (15*2π)/2317154 weeks
16.00048 -1.35903 (16*2π)/2317145 weeks
17-.04046 -.87088 (17*2π)/2317136 weeks
18.39898 -1.0374 (18*2π)/2317129 weeks
19-.02439 -.98452 (19*2π)/2317122 weeks
20.50246 -.48682 (20*2π)/2317116 weeks
211.00065 -1.2463 (21*2π)/2317110 weeks
22.24371 -1.54631 (22*2π)/2317105 weeks
23.15638 -1.18963 (23*2π)/2317101 weeks
24.19421 -1.27934 (24*2π)/231797 weeks
25-.0614 -1.04851 (25*2π)/231793 weeks
26.37615 -.94047 (26*2π)/231789 weeks
27.23626 -1.46651 (27*2π)/231786 weeks
28-.28673 -1.28416 (28*2π)/231783 weeks
29-.14684 -.91474 (29*2π)/231780 weeks
30-.05593 -1.02306 (30*2π)/231777 weeks
31-.08033 -.98574 (31*2π)/231775 weeks
32-.20211 -1.17113 (32*2π)/231772 weeks
33-.38161 -1.02958 (33*2π)/231770 weeks
34-.66649 -.80781 (34*2π)/231768 weeks
35-.50564 -.48074 (35*2π)/231766 weeks
36-.21956 -.25497 (36*2π)/231764 weeks
37-.01456 -.65567 (37*2π)/231763 weeks
38-.40862 -.4947 (38*2π)/231761 weeks
39-.06657 -.38852 (39*2π)/231759 weeks
40-.23535 -.44567 (40*2π)/231758 weeks
41-.10247 -.28984 (41*2π)/231757 weeks
42.07567 -.43018 (42*2π)/231755 weeks
43-.17189 -.47002 (43*2π)/231754 weeks
44-.04839 -.28067 (44*2π)/231753 weeks
45.11634 -.4468 (45*2π)/231751 weeks
46-.1397 -.41824 (46*2π)/231750 weeks
47.04494 -.32801 (47*2π)/231749 weeks
48.04111 -.48296 (48*2π)/231748 weeks
49-.08907 -.2687 (49*2π)/231747 weeks
50.24078 -.43477 (50*2π)/231746 weeks
51-.02244 -.47551 (51*2π)/231745 weeks
52.14592 -.54147 (52*2π)/231745 weeks
53-.13229 -.62161 (53*2π)/231744 weeks
54-.19359 -.4576 (54*2π)/231743 weeks
55-.19781 -.38873 (55*2π)/231742 weeks
56-.16573 -.21544 (56*2π)/231741 weeks
57.0226 -.32051 (57*2π)/231741 weeks
58-.21086 -.2212 (58*2π)/231740 weeks
59.22901 -.08428 (59*2π)/231739 weeks
60.14234 -.57518 (60*2π)/231739 weeks
61-.16871 -.25178 (61*2π)/231738 weeks
62.26996 -.30984 (62*2π)/231737 weeks
63-.02685 -.58345 (63*2π)/231737 weeks
64-.12648 -.33232 (64*2π)/231736 weeks
65.04168 -.39391 (65*2π)/231736 weeks
66-.17297 -.3966 (66*2π)/231735 weeks
67-.07583 -.25288 (67*2π)/231735 weeks
68-.08645 -.24097 (68*2π)/231734 weeks
69.10157 -.1388 (69*2π)/231734 weeks
70.17787 -.45431 (70*2π)/231733 weeks
71-.08108 -.41709 (71*2π)/231733 weeks
72.07965 -.33655 (72*2π)/231732 weeks
73-.0831 -.59932 (73*2π)/231732 weeks
74-.26526 -.34533 (74*2π)/231731 weeks
75-.11901 -.30934 (75*2π)/231731 weeks
76-.33396 -.29763 (76*2π)/231730 weeks
77-.12179 -.01707 (77*2π)/231730 weeks
78.00871 -.21644 (78*2π)/231730 weeks
79-.1909 -.159 (79*2π)/231729 weeks
80.1083 -.04605 (80*2π)/231729 weeks
81.00678 -.3135 (81*2π)/231729 weeks
82-.11795 -.12253 (82*2π)/231728 weeks
83.17574 -.0849 (83*2π)/231728 weeks
84.03473 -.3516 (84*2π)/231728 weeks
85-.02208 -.12847 (85*2π)/231727 weeks
86.14097 -.23967 (86*2π)/231727 weeks
87.06921 -.28258 (87*2π)/231727 weeks
88.03845 -.31543 (88*2π)/231726 weeks
89-.04051 -.3497 (89*2π)/231726 weeks
90-.07303 -.16157 (90*2π)/231726 weeks
91.0822 -.26779 (91*2π)/231725 weeks
92-.0641 -.28301 (92*2π)/231725 weeks
93.01814 -.15712 (93*2π)/231725 weeks
94.03908 -.35936 (94*2π)/231725 weeks
95-.14203 -.17561 (95*2π)/231724 weeks
96.13307 -.11656 (96*2π)/231724 weeks
97.07943 -.40162 (97*2π)/231724 weeks
98-.10382 -.25953 (98*2π)/231724 weeks
99.01824 -.1968 (99*2π)/231723 weeks
100.03879 -.31184 (100*2π)/231723 weeks
101-.06137 -.30816 (101*2π)/231723 weeks
102-.11682 -.20559 (102*2π)/231723 weeks
103.06231 -.192 (103*2π)/231722 weeks
104-.02818 -.31972 (104*2π)/231722 weeks
105-.08204 -.25075 (105*2π)/231722 weeks
106-.07448 -.20947 (106*2π)/231722 weeks
107-.0024 -.20508 (107*2π)/231722 weeks
108-.04959 -.26114 (108*2π)/231721 weeks
109-.08876 -.22412 (109*2π)/231721 weeks
110-.05908 -.16936 (110*2π)/231721 weeks
111-.00489 -.15205 (111*2π)/231721 weeks
112.03128 -.2735 (112*2π)/231721 weeks
113-.08441 -.25131 (113*2π)/231721 weeks
114-.10371 -.21282 (114*2π)/231720 weeks
115-.05074 -.12174 (115*2π)/231720 weeks
116.03305 -.17266 (116*2π)/231720 weeks
117.01582 -.30209 (117*2π)/231720 weeks
118-.15429 -.24012 (118*2π)/231720 weeks
119-.03288 -.14467 (119*2π)/231719 weeks
120-.04032 -.25413 (120*2π)/231719 weeks
121-.16938 -.22185 (121*2π)/231719 weeks
122-.06748 -.10473 (122*2π)/231719 weeks
123-.16127 -.17382 (123*2π)/231719 weeks
124-.04391 .03866 (124*2π)/231719 weeks
125.09107 -.13946 (125*2π)/231719 weeks
126-.01036 -.13781 (126*2π)/231718 weeks
127.11995 -.15204 (127*2π)/231718 weeks
128-.00722 -.33721 (128*2π)/231718 weeks
129-.11102 -.13492 (129*2π)/231718 weeks
130.05227 -.19029 (130*2π)/231718 weeks
131-.06903 -.22045 (131*2π)/231718 weeks
132.03954 -.1982 (132*2π)/231718 weeks
133-.14076 -.30736 (133*2π)/231717 weeks
134-.09716 -.10078 (134*2π)/231717 weeks
135-.05314 -.20883 (135*2π)/231717 weeks
136-.14572 -.14504 (136*2π)/231717 weeks
137-.04172 -.03953 (137*2π)/231717 weeks
138.05913 -.20487 (138*2π)/231717 weeks
139-.13059 -.21705 (139*2π)/231717 weeks
140-.11507 -.10509 (140*2π)/231717 weeks
141-.06151 -.05079 (141*2π)/231716 weeks
142.01883 -.07953 (142*2π)/231716 weeks
143.0716 -.13848 (143*2π)/231716 weeks
144-.01989 -.27193 (144*2π)/231716 weeks
145-.13187 -.12735 (145*2π)/231716 weeks
146-.0151 -.10565 (146*2π)/231716 weeks
147-.02217 -.141 (147*2π)/231716 weeks
148-.019 -.12696 (148*2π)/231716 weeks
149.00067 -.20092 (149*2π)/231716 weeks
150-.12039 -.14793 (150*2π)/231715 weeks
151-.02007 -.09111 (151*2π)/231715 weeks
152-.03195 -.13569 (152*2π)/231715 weeks
153-.04779 -.10508 (153*2π)/231715 weeks
154.04785 -.08549 (154*2π)/231715 weeks
155.05008 -.20538 (155*2π)/231715 weeks
156-.06151 -.24915 (156*2π)/231715 weeks
157-.10351 -.12286 (157*2π)/231715 weeks
158-.00615 -.12913 (158*2π)/231715 weeks
159-.05796 -.22605 (159*2π)/231715 weeks
160-.1517 -.11149 (160*2π)/231714 weeks
161-.03235 -.06684 (161*2π)/231714 weeks
162-.07284 -.1376 (162*2π)/231714 weeks
163-.04626 -.00432 (163*2π)/231714 weeks
164.11179 -.13522 (164*2π)/231714 weeks
165-.07394 -.24136 (165*2π)/231714 weeks
166-.0948 -.04634 (166*2π)/231714 weeks
167.05042 -.13901 (167*2π)/231714 weeks
168-.08444 -.15445 (168*2π)/231714 weeks
169.00577 -.07245 (169*2π)/231714 weeks
170-.00695 -.21273 (170*2π)/231714 weeks
171-.10189 -.11817 (171*2π)/231714 weeks
172.00194 -.12627 (172*2π)/231713 weeks
173-.14422 -.17773 (173*2π)/231713 weeks
174-.04798 .04332 (174*2π)/231713 weeks
175.07371 -.14847 (175*2π)/231713 weeks
176-.0652 -.12682 (176*2π)/231713 weeks
177.02779 -.11482 (177*2π)/231713 weeks
178-.04331 -.16161 (178*2π)/231713 weeks
179-.03048 -.10963 (179*2π)/231713 weeks
180.01744 -.15733 (180*2π)/231713 weeks
181-.08627 -.19523 (181*2π)/231713 weeks
182-.06263 -.10657 (182*2π)/231713 weeks
183-.08985 -.17238 (183*2π)/231713 weeks
184-.13012 -.03861 (184*2π)/231713 weeks
185.02576 -.02453 (185*2π)/231713 weeks
186.01473 -.16591 (186*2π)/231712 weeks
187-.03852 -.11722 (187*2π)/231712 weeks
188-.039 -.1942 (188*2π)/231712 weeks
189-.1417 -.08756 (189*2π)/231712 weeks
190-.0114 -.06963 (190*2π)/231712 weeks
191-.06347 -.11519 (191*2π)/231712 weeks
192-.03019 -.0761 (192*2π)/231712 weeks
193-.00697 -.14787 (193*2π)/231712 weeks
194-.12966 -.13431 (194*2π)/231712 weeks
195-.04019 -.03707 (195*2π)/231712 weeks
196-.06547 -.1326 (196*2π)/231712 weeks
197-.06555 -.03107 (197*2π)/231712 weeks
198-.01749 -.11315 (198*2π)/231712 weeks
199-.11421 -.07633 (199*2π)/231712 weeks
200-.02032 .01459 (200*2π)/231712 weeks
201.02227 -.09778 (201*2π)/231712 weeks
202-.05867 -.07098 (202*2π)/231711 weeks
203.02961 -.01154 (203*2π)/231711 weeks
204.06739 -.15806 (204*2π)/231711 weeks
205-.08971 -.13488 (205*2π)/231711 weeks
206-.00576 -.03943 (206*2π)/231711 weeks
207.00838 -.15036 (207*2π)/231711 weeks
208-.07549 -.06422 (208*2π)/231711 weeks
209.05627 -.08151 (209*2π)/231711 weeks
210-.02334 -.18206 (210*2π)/231711 weeks
211-.08783 -.09469 (211*2π)/231711 weeks
212.00053 -.07575 (212*2π)/231711 weeks
213-.04273 -.13932 (213*2π)/231711 weeks
214-.04762 -.07115 (214*2π)/231711 weeks
215-.00252 -.11953 (215*2π)/231711 weeks
216