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Fourier Analysis of ENFR (Alerian Energy Infrastructure E)


ENFR (Alerian Energy Infrastructure E) appears to have interesting cyclic behaviour every 11 weeks (.1992*cosine), 12 weeks (.1982*cosine), and 10 weeks (.19*cosine).

ENFR (Alerian Energy Infrastructure E) has an average price of 23.29 (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 11/1/2013 to 1/9/2017 for ENFR (Alerian Energy Infrastructure E), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
023.28804   0 
1.00936 4.62218 (1*2π)/168168 weeks
2.56216 -1.25572 (2*2π)/16884 weeks
3-1.03406 -.74896 (3*2π)/16856 weeks
4.44786 .25688 (4*2π)/16842 weeks
5.16905 .23704 (5*2π)/16834 weeks
6.02365 -.29569 (6*2π)/16828 weeks
7-.12643 .20954 (7*2π)/16824 weeks
8.24189 -.14734 (8*2π)/16821 weeks
9-.00062 -.07799 (9*2π)/16819 weeks
10.05244 -.08303 (10*2π)/16817 weeks
11.13012 -.13792 (11*2π)/16815 weeks
12-.03725 -.06293 (12*2π)/16814 weeks
13.09462 -.06323 (13*2π)/16813 weeks
14-.19823 -.14245 (14*2π)/16812 weeks
15.19924 -.03427 (15*2π)/16811 weeks
16-.04778 .03075 (16*2π)/16811 weeks
17-.18999 -.01209 (17*2π)/16810 weeks
18.01762 .00457 (18*2π)/1689 weeks
19.12513 -.11952 (19*2π)/1689 weeks
20-.04307 .13718 (20*2π)/1688 weeks
21-.09718 -.01644 (21*2π)/1688 weeks
22.09813 .00982 (22*2π)/1688 weeks
23.0679 .02366 (23*2π)/1687 weeks
24-.10233 -.06697 (24*2π)/1687 weeks
25.07632 .08253 (25*2π)/1687 weeks
26-.0807 -.02012 (26*2π)/1686 weeks
27-.01961 -.08905 (27*2π)/1686 weeks
28-.02165 -.03031 (28*2π)/1686 weeks
29-.14856 .05024 (29*2π)/1686 weeks
30.07103 .01941 (30*2π)/1686 weeks
31.01086 -.10562 (31*2π)/1685 weeks
32-.15859 -.01636 (32*2π)/1685 weeks
33.06901 .03756 (33*2π)/1685 weeks
34-.07376 -.05687 (34*2π)/1685 weeks
35-.07572 -.03042 (35*2π)/1685 weeks
36.10438 .03857 (36*2π)/1685 weeks
37.00278 .01758 (37*2π)/1685 weeks
38-.1261 -.02874 (38*2π)/1684 weeks
39.14066 -.02684 (39*2π)/1684 weeks
40.02955 .01206 (40*2π)/1684 weeks
41-.08168 -.08537 (41*2π)/1684 weeks
42.03865 .07152 (42*2π)/1684 weeks
43.01868 -.07422 (43*2π)/1684 weeks
44-.04072 -.08243 (44*2π)/1684 weeks
45.04709 .01622 (45*2π)/1684 weeks
46-.01423 -.02353 (46*2π)/1684 weeks
47-.07668 -.01249 (47*2π)/1684 weeks
48-.02079 -.00047 (48*2π)/1684 weeks
49-.02985 -.01459 (49*2π)/1683 weeks
50.03573 .07373 (50*2π)/1683 weeks
51-.04037 .02829 (51*2π)/1683 weeks
52-.02915 .00329 (52*2π)/1683 weeks
53.10857 -.04433 (53*2π)/1683 weeks
54-.06148 -.02966 (54*2π)/1683 weeks
55-.02742 .005 (55*2π)/1683 weeks
56-.00995 .01667 (56*2π)/1683 weeks
57-.05003 -.00948 (57*2π)/1683 weeks
58.01715 -.03477 (58*2π)/1683 weeks
59-.0526 .01575 (59*2π)/1683 weeks
60-.01964 .02684 (60*2π)/1683 weeks
61.02279 -.01026 (61*2π)/1683 weeks
62.00411 -.01549 (62*2π)/1683 weeks
63.05837 .01378 (63*2π)/1683 weeks
64-.06951 -.017 (64*2π)/1683 weeks
65.05163 -.02242 (65*2π)/1683 weeks
66-.00586 -.00753 (66*2π)/1683 weeks
67-.01972 .05326 (67*2π)/1683 weeks
68-.0164 -.0224 (68*2π)/1682 weeks
69-.01384 .03831 (69*2π)/1682 weeks
70.06582 -.04737 (70*2π)/1682 weeks
71-.01684 .04907 (71*2π)/1682 weeks
72.00733 -.00226 (72*2π)/1682 weeks
73-.0278 -.02656 (73*2π)/1682 weeks
74.04899 .02572 (74*2π)/1682 weeks
75-.07454 .01315 (75*2π)/1682 weeks
76.06052 -.01628 (76*2π)/1682 weeks
77.05592 .03122 (77*2π)/1682 weeks
78-.05185 .0384 (78*2π)/1682 weeks
79-.02066 -.05997 (79*2π)/1682 weeks
80.0224 .11017 (80*2π)/1682 weeks
81.03688 -.04932 (81*2π)/1682 weeks
82-.03103 -.0204 (82*2π)/1682 weeks
83.02027 .02089 (83*2π)/1682 weeks
84-.00603   (84*2π)/1682 weeks
85.02027 -.02089 (85*2π)/1682 weeks
86-.03103 .0204 (86*2π)/1682 weeks
87.03688 .04932 (87*2π)/1682 weeks
88.0224 -.11017 (88*2π)/1682 weeks
89-.02066 .05997 (89*2π)/1682 weeks
90-.05185 -.0384 (90*2π)/1682 weeks
91.05592 -.03122 (91*2π)/1682 weeks
92.06052 .01628 (92*2π)/1682 weeks
93-.07454 -.01315 (93*2π)/1682 weeks
94.04899 -.02572 (94*2π)/1682 weeks
95-.0278 .02656 (95*2π)/1682 weeks
96.00733 .00226 (96*2π)/1682 weeks
97-.01684 -.04907 (97*2π)/1682 weeks
98.06582 .04737 (98*2π)/1682 weeks
99-.01384 -.03831 (99*2π)/1682 weeks
100-.0164 .0224 (100*2π)/1682 weeks
101-.01972 -.05326 (101*2π)/1682 weeks
102-.00586 .00753 (102*2π)/1682 weeks
103.05163 .02242 (103*2π)/1682 weeks
104-.06951 .017 (104*2π)/1682 weeks
105.05837 -.01378 (105*2π)/1682 weeks
106.00411 .01549 (106*2π)/1682 weeks
107.02279 .01026 (107*2π)/1682 weeks
108-.01964 -.02684 (108*2π)/1682 weeks
109-.0526 -.01575 (109*2π)/1682 weeks
110.01715 .03477 (110*2π)/1682 weeks
111-.05003 .00948 (111*2π)/1682 weeks
112-.00995 -.01667 (112*2π)/1682 weeks
113-.02742 -.005 (113*2π)/1681 weeks
114-.06148 .02966 (114*2π)/1681 weeks
115.10857 .04433 (115*2π)/1681 weeks
116-.02915 -.00329 (116*2π)/1681 weeks
117-.04037 -.02829 (117*2π)/1681 weeks
118.03573 -.07373 (118*2π)/1681 weeks
119-.02985 .01459 (119*2π)/1681 weeks
120-.02079 .00047 (120*2π)/1681 weeks
121-.07668 .01249 (121*2π)/1681 weeks
122-.01423 .02353 (122*2π)/1681 weeks
123.04709 -.01622 (123*2π)/1681 weeks
124-.04072 .08243 (124*2π)/1681 weeks
125.01868 .07422 (125*2π)/1681 weeks
126.03865 -.07152 (126*2π)/1681 weeks
127-.08168 .08537 (127*2π)/1681 weeks
128.02955 -.01206 (128*2π)/1681 weeks
129.14066 .02684 (129*2π)/1681 weeks
130-.1261 .02874 (130*2π)/1681 weeks
131.00278 -.01758 (131*2π)/1681 weeks
132.10438 -.03857 (132*2π)/1681 weeks
133-.07572 .03042 (133*2π)/1681 weeks
134-.07376 .05687 (134*2π)/1681 weeks
135.06901 -.03756 (135*2π)/1681 weeks
136-.15859 .01636 (136*2π)/1681 weeks
137.01086 .10562 (137*2π)/1681 weeks
138.07103 -.01941 (138*2π)/1681 weeks
139-.14856 -.05024 (139*2π)/1681 weeks
140-.02165 .03031 (140*2π)/1681 weeks
141-.01961 .08905 (141*2π)/1681 weeks
142-.0807 .02012 (142*2π)/1681 weeks
143.07632 -.08253 (143*2π)/1681 weeks
144-.10233 .06697 (144*2π)/1681 weeks
145.0679 -.02366 (145*2π)/1681 weeks
146.09813 -.00982 (146*2π)/1681 weeks
147-.09718 .01644 (147*2π)/1681 weeks
148-.04307 -.13718 (148*2π)/1681 weeks
149.12513 .11952 (149*2π)/1681 weeks
150.01762 -.00457 (150*2π)/1681 weeks
151-.18999 .01209 (151*2π)/1681 weeks
152-.04778 -.03075 (152*2π)/1681 weeks
153.19924 .03427 (153*2π)/1681 weeks
154-.19823 .14245 (154*2π)/1681 weeks
155.09462 .06323 (155*2π)/1681 weeks
156-.03725 .06293 (156*2π)/1681 weeks
157.13012 .13792 (157*2π)/1681 weeks
158.05244 .08303 (158*2π)/1681 weeks
159-.00062 .07799 (159*2π)/1681 weeks
160.24189 .14734 (160*2π)/1681 weeks
161-.12643 -.20954 (161*2π)/1681 weeks
162.02365 .29569 (162*2π)/1681 weeks
163.16905 -.23704 (163*2π)/1681 weeks
164.44786 -.25688 (164*2π)/1681 weeks
165-1.03406 .74896 (165*2π)/1681 weeks
166.56216 1.25572 (166*2π)/1681 weeks

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