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# Fourier Analysis of LOCO (El Pollo Loco Holdings)

LOCO (El Pollo Loco Holdings) appears to have interesting cyclic behaviour every 12 weeks (.9554*sine), 12 weeks (.651*sine), and 16 weeks (.6081*sine).

LOCO (El Pollo Loco Holdings) has an average price of 16.28 (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 7/25/2014 to 4/16/2018 for LOCO (El Pollo Loco Holdings), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
016.28362   0
14.93658 4.73244 (1*2π)/196196 weeks
2.83001 5.25304 (2*2π)/19698 weeks
3-.42192 2.67588 (3*2π)/19665 weeks
41.20226 1.69937 (4*2π)/19649 weeks
51.32892 2.3076 (5*2π)/19639 weeks
6-.21358 2.3899 (6*2π)/19633 weeks
7-.50467 1.6268 (7*2π)/19628 weeks
8-.5759 1.36702 (8*2π)/19625 weeks
9-.21995 .6125 (9*2π)/19622 weeks
10-.58594 .26636 (10*2π)/19620 weeks
11.26325 .40388 (11*2π)/19618 weeks
12.07418 .6081 (12*2π)/19616 weeks
13.35489 .35539 (13*2π)/19615 weeks
14.32678 .35452 (14*2π)/19614 weeks
15.49751 .41857 (15*2π)/19613 weeks
16.32107 .95543 (16*2π)/19612 weeks
17-.31596 .65099 (17*2π)/19612 weeks
18-.22833 .54965 (18*2π)/19611 weeks
19.07614 .3273 (19*2π)/19610 weeks
20-.06375 .28073 (20*2π)/19610 weeks
21.15292 .18046 (21*2π)/1969 weeks
22.17541 .27418 (22*2π)/1969 weeks
23.21732 .17773 (23*2π)/1969 weeks
24.30922 .41772 (24*2π)/1968 weeks
25.24033 .43689 (25*2π)/1968 weeks
26.21998 .53327 (26*2π)/1968 weeks
27.06554 .38818 (27*2π)/1967 weeks
28.28831 .29783 (28*2π)/1967 weeks
29.20865 .33099 (29*2π)/1967 weeks
30.3125 .43165 (30*2π)/1967 weeks
31.00492 .63232 (31*2π)/1966 weeks
32-.0146 .23011 (32*2π)/1966 weeks
33.028 .38628 (33*2π)/1966 weeks
34-.05234 .38685 (34*2π)/1966 weeks
35.03894 .34631 (35*2π)/1966 weeks
36-.00513 .13326 (36*2π)/1965 weeks
37.13528 .37034 (37*2π)/1965 weeks
38.02263 .39319 (38*2π)/1965 weeks
39.01113 .25224 (39*2π)/1965 weeks
40.04205 .25306 (40*2π)/1965 weeks
41-.01335 .41076 (41*2π)/1965 weeks
42-.05757 .38931 (42*2π)/1965 weeks
43-.12877 .29835 (43*2π)/1965 weeks
44-.13668 .33469 (44*2π)/1964 weeks
45-.15499 .21516 (45*2π)/1964 weeks
46-.20469 .14178 (46*2π)/1964 weeks
47.0138 .14125 (47*2π)/1964 weeks
48-.12335 .16893 (48*2π)/1964 weeks
49-.16026 .1527 (49*2π)/1964 weeks
50-.02763 .04625 (50*2π)/1964 weeks
51.04143 .03557 (51*2π)/1964 weeks
52.07562 .13037 (52*2π)/1964 weeks
53.02274 .11241 (53*2π)/1964 weeks
54-.00825 .2031 (54*2π)/1964 weeks
55-.01706 .08857 (55*2π)/1964 weeks
56-.03346 .16623 (56*2π)/1964 weeks
57-.04349 .15439 (57*2π)/1963 weeks
58.08124 .07567 (58*2π)/1963 weeks
59.04857 .23103 (59*2π)/1963 weeks
60-.00215 .12573 (60*2π)/1963 weeks
61-.00926 .0476 (61*2π)/1963 weeks
62.10679 .06323 (62*2π)/1963 weeks
63-.03174 .1611 (63*2π)/1963 weeks
64.00169 .05221 (64*2π)/1963 weeks
65.06179 .15336 (65*2π)/1963 weeks
66.01194 .21319 (66*2π)/1963 weeks
67-.08149 .15589 (67*2π)/1963 weeks
68-.08424 .07089 (68*2π)/1963 weeks
69-.02988 .06413 (69*2π)/1963 weeks
70-.12835 .06604 (70*2π)/1963 weeks
71-.0633 .01234 (71*2π)/1963 weeks
72-.02817 .10342 (72*2π)/1963 weeks
73-.04254 .05789 (73*2π)/1963 weeks
74.00683 .07404 (74*2π)/1963 weeks
75.03877 .02395 (75*2π)/1963 weeks
76.01832 .06437 (76*2π)/1963 weeks
77-.06775 .09774 (77*2π)/1963 weeks
78-.05433 .06349 (78*2π)/1963 weeks
79-.04977 .05754 (79*2π)/1962 weeks
80-.0503 .099 (80*2π)/1962 weeks
81-.02151 -.00038 (81*2π)/1962 weeks
82  .03992 (82*2π)/1962 weeks
83-.03004 .0169 (83*2π)/1962 weeks
84-.01098 .06935 (84*2π)/1962 weeks
85.04551 .06987 (85*2π)/1962 weeks
86-.05172 -.02532 (86*2π)/1962 weeks
87.00458 .05932 (87*2π)/1962 weeks
88-.02251 .01838 (88*2π)/1962 weeks
89.00862 .00638 (89*2π)/1962 weeks
90.04063 .0432 (90*2π)/1962 weeks
91.02612 .08527 (91*2π)/1962 weeks
92-.09551 .13875 (92*2π)/1962 weeks
93-.11911 -.01355 (93*2π)/1962 weeks
94-.12438 .06459 (94*2π)/1962 weeks
95-.07616 -.04864 (95*2π)/1962 weeks
96.03537 -.02937 (96*2π)/1962 weeks
97-.03429 .04028 (97*2π)/1962 weeks
98-.01531   (98*2π)/1962 weeks
99-.03429 -.04028 (99*2π)/1962 weeks
100.03537 .02937 (100*2π)/1962 weeks
101-.07616 .04864 (101*2π)/1962 weeks
102-.12438 -.06459 (102*2π)/1962 weeks
103-.11911 .01355 (103*2π)/1962 weeks
104-.09551 -.13875 (104*2π)/1962 weeks
105.02612 -.08527 (105*2π)/1962 weeks
106.04063 -.0432 (106*2π)/1962 weeks
107.00862 -.00638 (107*2π)/1962 weeks
108-.02251 -.01838 (108*2π)/1962 weeks
109.00458 -.05932 (109*2π)/1962 weeks
110-.05172 .02532 (110*2π)/1962 weeks
111.04551 -.06987 (111*2π)/1962 weeks
112-.01098 -.06935 (112*2π)/1962 weeks
113-.03004 -.0169 (113*2π)/1962 weeks
114  -.03992 (114*2π)/1962 weeks
115-.02151 .00038 (115*2π)/1962 weeks
116-.0503 -.099 (116*2π)/1962 weeks
117-.04977 -.05754 (117*2π)/1962 weeks
118-.05433 -.06349 (118*2π)/1962 weeks
119-.06775 -.09774 (119*2π)/1962 weeks
120.01832 -.06437 (120*2π)/1962 weeks
121.03877 -.02395 (121*2π)/1962 weeks
122.00683 -.07404 (122*2π)/1962 weeks
123-.04254 -.05789 (123*2π)/1962 weeks
124-.02817 -.10342 (124*2π)/1962 weeks
125-.0633 -.01234 (125*2π)/1962 weeks
126-.12835 -.06604 (126*2π)/1962 weeks
127-.02988 -.06413 (127*2π)/1962 weeks
128-.08424 -.07089 (128*2π)/1962 weeks
129-.08149 -.15589 (129*2π)/1962 weeks
130.01194 -.21319 (130*2π)/1962 weeks
131.06179 -.15336 (131*2π)/1961 weeks
132.00169 -.05221 (132*2π)/1961 weeks
133-.03174 -.1611 (133*2π)/1961 weeks
134.10679 -.06323 (134*2π)/1961 weeks
135-.00926 -.0476 (135*2π)/1961 weeks
136-.00215 -.12573 (136*2π)/1961 weeks
137.04857 -.23103 (137*2π)/1961 weeks
138.08124 -.07567 (138*2π)/1961 weeks
139-.04349 -.15439 (139*2π)/1961 weeks
140-.03346 -.16623 (140*2π)/1961 weeks
141-.01706 -.08857 (141*2π)/1961 weeks
142-.00825 -.2031 (142*2π)/1961 weeks
143.02274 -.11241 (143*2π)/1961 weeks
144.07562 -.13037 (144*2π)/1961 weeks
145.04143 -.03557 (145*2π)/1961 weeks
146-.02763 -.04625 (146*2π)/1961 weeks
147-.16026 -.1527 (147*2π)/1961 weeks
148-.12335 -.16893 (148*2π)/1961 weeks
149.0138 -.14125 (149*2π)/1961 weeks
150-.20469 -.14178 (150*2π)/1961 weeks
151-.15499 -.21516 (151*2π)/1961 weeks
152-.13668 -.33469 (152*2π)/1961 weeks
153-.12877 -.29835 (153*2π)/1961 weeks
154-.05757 -.38931 (154*2π)/1961 weeks
155-.01335 -.41076 (155*2π)/1961 weeks
156.04205 -.25306 (156*2π)/1961 weeks
157.01113 -.25224 (157*2π)/1961 weeks
158.02263 -.39319 (158*2π)/1961 weeks
159.13528 -.37034 (159*2π)/1961 weeks
160-.00513 -.13326 (160*2π)/1961 weeks
161.03894 -.34631 (161*2π)/1961 weeks
162-.05234 -.38685 (162*2π)/1961 weeks
163.028 -.38628 (163*2π)/1961 weeks
164-.0146 -.23011 (164*2π)/1961 weeks
165.00492 -.63232 (165*2π)/1961 weeks
166.3125 -.43165 (166*2π)/1961 weeks
167.20865 -.33099 (167*2π)/1961 weeks
168.28831 -.29783 (168*2π)/1961 weeks
169.06554 -.38818 (169*2π)/1961 weeks
170.21998 -.53327 (170*2π)/1961 weeks
171.24033 -.43689 (171*2π)/1961 weeks
172.30922 -.41772 (172*2π)/1961 weeks
173.21732 -.17773 (173*2π)/1961 weeks
174.17541 -.27418 (174*2π)/1961 weeks
175.15292 -.18046 (175*2π)/1961 weeks
176-.06375 -.28073 (176*2π)/1961 weeks
177.07614 -.3273 (177*2π)/1961 weeks
178-.22833 -.54965 (178*2π)/1961 weeks
179-.31596 -.65099 (179*2π)/1961 weeks
180.32107 -.95543 (180*2π)/1961 weeks
181.49751 -.41857 (181*2π)/1961 weeks
182.32678 -.35452 (182*2π)/1961 weeks
183.35489 -.35539 (183*2π)/1961 weeks
184.07418 -.6081 (184*2π)/1961 weeks
185.26325 -.40388 (185*2π)/1961 weeks
186-.58594 -.26636 (186*2π)/1961 weeks
187-.21995 -.6125 (187*2π)/1961 weeks
188-.5759 -1.36702 (188*2π)/1961 weeks
189-.50467 -1.6268 (189*2π)/1961 weeks
190-.21358 -2.3899 (190*2π)/1961 weeks
1911.32892 -2.3076 (191*2π)/1961 weeks
1921.20226 -1.69937 (192*2π)/1961 weeks
193-.42192 -2.67588 (193*2π)/1961 weeks
194.83001 -5.25304 (194*2π)/1961 weeks