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# Fourier Analysis of FPL (First Trust New Opportunities MLP & Energy Fund)

FPL (First Trust New Opportunities MLP & Energy Fund) appears to have interesting cyclic behaviour every 20 weeks (.2035*cosine), 10 weeks (.1804*sine), and 20 weeks (.1525*sine).

FPL (First Trust New Opportunities MLP & Energy Fund) has an average price of 11.44 (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.

## Fourier Analysis

Using data from 3/27/2014 to 6/4/2018 for FPL (First Trust New Opportunities MLP & Energy Fund), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
011.43988   0
11.19366 .2493 (1*2π)/220220 weeks
2-.61771 1.02169 (2*2π)/220110 weeks
3.04479 -.19384 (3*2π)/22073 weeks
4.22668 .57246 (4*2π)/22055 weeks
5-.27305 .02986 (5*2π)/22044 weeks
6.06377 .47138 (6*2π)/22037 weeks
7-.13575 .12407 (7*2π)/22031 weeks
8.08538 .16444 (8*2π)/22028 weeks
9.05193 .29271 (9*2π)/22024 weeks
10.10989 -.03775 (10*2π)/22022 weeks
11.20346 .15249 (11*2π)/22020 weeks
12.06417 .02834 (12*2π)/22018 weeks
13.08279 .01411 (13*2π)/22017 weeks
14-.01539 .02385 (14*2π)/22016 weeks
15.03924 .02875 (15*2π)/22015 weeks
16-.07714 .05593 (16*2π)/22014 weeks
17-.0916 .15167 (17*2π)/22013 weeks
18.02245 -.00434 (18*2π)/22012 weeks
19.09752 .07686 (19*2π)/22012 weeks
20-.0275 .07231 (20*2π)/22011 weeks
21-.08225 .02029 (21*2π)/22010 weeks
22.0131 .18036 (22*2π)/22010 weeks
23-.07063 .00984 (23*2π)/22010 weeks
24.04468 .07792 (24*2π)/2209 weeks
25-.05198 .05856 (25*2π)/2209 weeks
26.01311 -.01044 (26*2π)/2208 weeks
27-.00274 .0866 (27*2π)/2208 weeks
28.04496 .06295 (28*2π)/2208 weeks
29.02237 .04576 (29*2π)/2208 weeks
30.0597 .06637 (30*2π)/2207 weeks
31.02123 .06312 (31*2π)/2207 weeks
32.05587 .02453 (32*2π)/2207 weeks
33.09065 -.01082 (33*2π)/2207 weeks
34.00646 .0132 (34*2π)/2206 weeks
35-.02338 .02095 (35*2π)/2206 weeks
36.01909 -.03206 (36*2π)/2206 weeks
37-.04772 .04432 (37*2π)/2206 weeks
38-.00631 -.03998 (38*2π)/2206 weeks
39.06268 .06326 (39*2π)/2206 weeks
40-.00653 -.03547 (40*2π)/2206 weeks
41.07135 .08608 (41*2π)/2205 weeks
42-.01599 .02959 (42*2π)/2205 weeks
43.07947 .02417 (43*2π)/2205 weeks
44.0315 .02301 (44*2π)/2205 weeks
45.0048 -.00019 (45*2π)/2205 weeks
46.01944 .04785 (46*2π)/2205 weeks
47-.0425 .04273 (47*2π)/2205 weeks
48.05307 .01208 (48*2π)/2205 weeks
49.01689 .01826 (49*2π)/2204 weeks
50.05507 -.0522 (50*2π)/2204 weeks
51.01868 .08695 (51*2π)/2204 weeks
52.00209 -.00561 (52*2π)/2204 weeks
53.0199 .07169 (53*2π)/2204 weeks
54-.01372 -.01752 (54*2π)/2204 weeks
55.03223 .00863 (55*2π)/2204 weeks
56.01902 .03324 (56*2π)/2204 weeks
57.04782 -.01922 (57*2π)/2204 weeks
58.01222 .02302 (58*2π)/2204 weeks
59.0212 .00517 (59*2π)/2204 weeks
60.00211 .00232 (60*2π)/2204 weeks
61-.00778 .02727 (61*2π)/2204 weeks
62.00198 -.0101 (62*2π)/2204 weeks
63.01456 -.00449 (63*2π)/2203 weeks
64-.00032 .05256 (64*2π)/2203 weeks
65.01429 -.02798 (65*2π)/2203 weeks
66.02526 .03338 (66*2π)/2203 weeks
67.04356 .0168 (67*2π)/2203 weeks
68.03778 -.0214 (68*2π)/2203 weeks
69.03451 .02807 (69*2π)/2203 weeks
70-.0444 -.04255 (70*2π)/2203 weeks
71.0222 -.00896 (71*2π)/2203 weeks
72-.0311 -.04761 (72*2π)/2203 weeks
73.00879 -.00236 (73*2π)/2203 weeks
74.01712 .03943 (74*2π)/2203 weeks
75-.00513 .00325 (75*2π)/2203 weeks
76.01001 .02023 (76*2π)/2203 weeks
77.03507 .02472 (77*2π)/2203 weeks
78.02517 .02534 (78*2π)/2203 weeks
79.02016 -.00761 (79*2π)/2203 weeks
80.01266 .0096 (80*2π)/2203 weeks
81-.02244 -.00058 (81*2π)/2203 weeks
82.02968 .01281 (82*2π)/2203 weeks
83.00517 .04146 (83*2π)/2203 weeks
84-.02704 -.00783 (84*2π)/2203 weeks
85.03921 -.00182 (85*2π)/2203 weeks
86.02327 .03331 (86*2π)/2203 weeks
87.02152 .00771 (87*2π)/2203 weeks
88.03594 .01855 (88*2π)/2203 weeks
89.04099 .00815 (89*2π)/2202 weeks
90-.00583 .03556 (90*2π)/2202 weeks
91.02779 -.01075 (91*2π)/2202 weeks
92.01781 .03608 (92*2π)/2202 weeks
93-.00132 .0122 (93*2π)/2202 weeks
94-.00084 -.001 (94*2π)/2202 weeks
95.01081 .00607 (95*2π)/2202 weeks
96-.00231 -.01022 (96*2π)/2202 weeks
97.03745 -.0214 (97*2π)/2202 weeks
98.055 .02794 (98*2π)/2202 weeks
99-.01278 .02583 (99*2π)/2202 weeks
100.03222 .03095 (100*2π)/2202 weeks
101.00241 .00634 (101*2π)/2202 weeks
102.01823 -.01299 (102*2π)/2202 weeks
103.01155 -.03147 (103*2π)/2202 weeks
104.05213 -.02598 (104*2π)/2202 weeks
105-.01119 .04295 (105*2π)/2202 weeks
106.01505 -.03603 (106*2π)/2202 weeks
107.01507 .01487 (107*2π)/2202 weeks
108.006 .00447 (108*2π)/2202 weeks
109.03633 -.02952 (109*2π)/2202 weeks
110.01071   (110*2π)/2202 weeks
111.03633 .02952 (111*2π)/2202 weeks
112.006 -.00447 (112*2π)/2202 weeks
113.01507 -.01487 (113*2π)/2202 weeks
114.01505 .03603 (114*2π)/2202 weeks
115-.01119 -.04295 (115*2π)/2202 weeks
116.05213 .02598 (116*2π)/2202 weeks
117.01155 .03147 (117*2π)/2202 weeks
118.01823 .01299 (118*2π)/2202 weeks
119.00241 -.00634 (119*2π)/2202 weeks
120.03222 -.03095 (120*2π)/2202 weeks
121-.01278 -.02583 (121*2π)/2202 weeks
122.055 -.02794 (122*2π)/2202 weeks
123.03745 .0214 (123*2π)/2202 weeks
124-.00231 .01022 (124*2π)/2202 weeks
125.01081 -.00607 (125*2π)/2202 weeks
126-.00084 .001 (126*2π)/2202 weeks
127-.00132 -.0122 (127*2π)/2202 weeks
128.01781 -.03608 (128*2π)/2202 weeks
129.02779 .01075 (129*2π)/2202 weeks
130-.00583 -.03556 (130*2π)/2202 weeks
131.04099 -.00815 (131*2π)/2202 weeks
132.03594 -.01855 (132*2π)/2202 weeks
133.02152 -.00771 (133*2π)/2202 weeks
134.02327 -.03331 (134*2π)/2202 weeks
135.03921 .00182 (135*2π)/2202 weeks
136-.02704 .00783 (136*2π)/2202 weeks
137.00517 -.04146 (137*2π)/2202 weeks
138.02968 -.01281 (138*2π)/2202 weeks
139-.02244 .00058 (139*2π)/2202 weeks
140.01266 -.0096 (140*2π)/2202 weeks
141.02016 .00761 (141*2π)/2202 weeks
142.02517 -.02534 (142*2π)/2202 weeks
143.03507 -.02472 (143*2π)/2202 weeks
144.01001 -.02023 (144*2π)/2202 weeks
145-.00513 -.00325 (145*2π)/2202 weeks
146.01712 -.03943 (146*2π)/2202 weeks
147.00879 .00236 (147*2π)/2201 weeks
148-.0311 .04761 (148*2π)/2201 weeks
149.0222 .00896 (149*2π)/2201 weeks
150-.0444 .04255 (150*2π)/2201 weeks
151.03451 -.02807 (151*2π)/2201 weeks
152.03778 .0214 (152*2π)/2201 weeks
153.04356 -.0168 (153*2π)/2201 weeks
154.02526 -.03338 (154*2π)/2201 weeks
155.01429 .02798 (155*2π)/2201 weeks
156-.00032 -.05256 (156*2π)/2201 weeks
157.01456 .00449 (157*2π)/2201 weeks
158.00198 .0101 (158*2π)/2201 weeks
159-.00778 -.02727 (159*2π)/2201 weeks
160.00211 -.00232 (160*2π)/2201 weeks
161.0212 -.00517 (161*2π)/2201 weeks
162.01222 -.02302 (162*2π)/2201 weeks
163.04782 .01922 (163*2π)/2201 weeks
164.01902 -.03324 (164*2π)/2201 weeks
165.03223 -.00863 (165*2π)/2201 weeks
166-.01372 .01752 (166*2π)/2201 weeks
167.0199 -.07169 (167*2π)/2201 weeks
168.00209 .00561 (168*2π)/2201 weeks
169.01868 -.08695 (169*2π)/2201 weeks
170.05507 .0522 (170*2π)/2201 weeks
171.01689 -.01826 (171*2π)/2201 weeks
172.05307 -.01208 (172*2π)/2201 weeks
173-.0425 -.04273 (173*2π)/2201 weeks
174.01944 -.04785 (174*2π)/2201 weeks
175.0048 .00019 (175*2π)/2201 weeks
176.0315 -.02301 (176*2π)/2201 weeks
177.07947 -.02417 (177*2π)/2201 weeks
178-.01599 -.02959 (178*2π)/2201 weeks
179.07135 -.08608 (179*2π)/2201 weeks
180-.00653 .03547 (180*2π)/2201 weeks
181.06268 -.06326 (181*2π)/2201 weeks
182-.00631 .03998 (182*2π)/2201 weeks
183-.04772 -.04432 (183*2π)/2201 weeks
184.01909 .03206 (184*2π)/2201 weeks
185-.02338 -.02095 (185*2π)/2201 weeks
186.00646 -.0132 (186*2π)/2201 weeks
187.09065 .01082 (187*2π)/2201 weeks
188.05587 -.02453 (188*2π)/2201 weeks
189.02123 -.06312 (189*2π)/2201 weeks
190.0597 -.06637 (190*2π)/2201 weeks
191.02237 -.04576 (191*2π)/2201 weeks
192.04496 -.06295 (192*2π)/2201 weeks
193-.00274 -.0866 (193*2π)/2201 weeks
194.01311 .01044 (194*2π)/2201 weeks
195-.05198 -.05856 (195*2π)/2201 weeks
196.04468 -.07792 (196*2π)/2201 weeks
197-.07063 -.00984 (197*2π)/2201 weeks
198.0131 -.18036 (198*2π)/2201 weeks
199-.08225 -.02029 (199*2π)/2201 weeks
200-.0275 -.07231 (200*2π)/2201 weeks
201.09752 -.07686 (201*2π)/2201 weeks
202.02245 .00434 (202*2π)/2201 weeks
203-.0916 -.15167 (203*2π)/2201 weeks
204-.07714 -.05593 (204*2π)/2201 weeks
205.03924 -.02875 (205*2π)/2201 weeks
206-.01539 -.02385 (206*2π)/2201 weeks
207.08279 -.01411 (207*2π)/2201 weeks
208.06417 -.02834 (208*2π)/2201 weeks
209.20346 -.15249 (209*2π)/2201 weeks
210.10989 .03775 (210*2π)/2201 weeks
211.05193 -.29271 (211*2π)/2201 weeks
212.08538 -.16444 (212*2π)/2201 weeks
213-.13575 -.12407 (213*2π)/2201 weeks
214.06377 -.47138 (214*2π)/2201 weeks
215-.27305 -.02986 (215*2π)/2201 weeks
216.22668 -.57246 (216*2π)/2201 weeks
217.04479 .19384 (217*2π)/2201 weeks
218-.61771 -1.02169 (218*2π)/2201 weeks