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# Fourier Analysis of NTG (Tortoise MLP Fund)

NTG (Tortoise MLP Fund) appears to have interesting cyclic behaviour every 41 weeks (.3273*sine), 24 weeks (.3067*cosine), and 17 weeks (.1498*cosine).

NTG (Tortoise MLP Fund) has an average price of 16.64 (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 7/29/2010 to 4/23/2018 for NTG (Tortoise MLP Fund), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
016.63643   0
1-1.53058 -.11489 (1*2π)/405405 weeks
21.14247 -1.29313 (2*2π)/405203 weeks
3-.89988 -.91231 (3*2π)/405135 weeks
4-.32515 .52332 (4*2π)/405101 weeks
5.41824 -.39881 (5*2π)/40581 weeks
6.02025 -.10256 (6*2π)/40568 weeks
7-.34331 -.27858 (7*2π)/40558 weeks
8.34757 -.19311 (8*2π)/40551 weeks
9.09781 -.44645 (9*2π)/40545 weeks
10-.08132 -.32725 (10*2π)/40541 weeks
11.02439 -.04889 (11*2π)/40537 weeks
12-.0062 .06989 (12*2π)/40534 weeks
13-.14738 -.18963 (13*2π)/40531 weeks
14-.10064 -.12987 (14*2π)/40529 weeks
15-.01345 -.12349 (15*2π)/40527 weeks
16-.10953 -.05455 (16*2π)/40525 weeks
17-.30669 -.01423 (17*2π)/40524 weeks
18.02834 .09405 (18*2π)/40523 weeks
19-.06073 -.03083 (19*2π)/40521 weeks
20-.0672 .05676 (20*2π)/40520 weeks
21-.02809 -.0058 (21*2π)/40519 weeks
22-.03045 .03949 (22*2π)/40518 weeks
23.0451 .11677 (23*2π)/40518 weeks
24.14978 .01995 (24*2π)/40517 weeks
25-.00673 .04799 (25*2π)/40516 weeks
26.09149 .05138 (26*2π)/40516 weeks
27.03799 -.01835 (27*2π)/40515 weeks
28.07977 -.02651 (28*2π)/40514 weeks
29.08245 .02304 (29*2π)/40514 weeks
30.035 -.13845 (30*2π)/40514 weeks
31.12361 .00657 (31*2π)/40513 weeks
32.04963 -.06456 (32*2π)/40513 weeks
33.01337 -.10006 (33*2π)/40512 weeks
34.03268 -.1097 (34*2π)/40512 weeks
35-.11193 -.0053 (35*2π)/40512 weeks
36.05459 .04355 (36*2π)/40511 weeks
37-.03605 -.04911 (37*2π)/40511 weeks
38.01952 -.02288 (38*2π)/40511 weeks
39.01545 -.04262 (39*2π)/40510 weeks
40.03953 -.065 (40*2π)/40510 weeks
41-.04642 -.11486 (41*2π)/40510 weeks
42-.04285 .00757 (42*2π)/40510 weeks
43.03045 -.01295 (43*2π)/4059 weeks
44.02443 -.0375 (44*2π)/4059 weeks
45-.07383 -.04443 (45*2π)/4059 weeks
46-.03519 .09952 (46*2π)/4059 weeks
47.01282 -.08748 (47*2π)/4059 weeks
48-.05131 -.01866 (48*2π)/4058 weeks
49.06613 .0088 (49*2π)/4058 weeks
50.0663 .01046 (50*2π)/4058 weeks
51.02251 -.05995 (51*2π)/4058 weeks
52-.04741 -.06347 (52*2π)/4058 weeks
53-.00153 -.01017 (53*2π)/4058 weeks
54-.02498 -.08323 (54*2π)/4058 weeks
55-.0401 -.02379 (55*2π)/4057 weeks
56.06321 -.01055 (56*2π)/4057 weeks
57-.01967 -.02647 (57*2π)/4057 weeks
58.04744 -.02136 (58*2π)/4057 weeks
59-.01929 -.03235 (59*2π)/4057 weeks
60-.0588 -.04151 (60*2π)/4057 weeks
61-.01897 -.06864 (61*2π)/4057 weeks
62-.05649 -.0411 (62*2π)/4057 weeks
63.02829 .00683 (63*2π)/4056 weeks
64-.02003 -.00354 (64*2π)/4056 weeks
65.01879 -.05461 (65*2π)/4056 weeks
66-.00154 -.08385 (66*2π)/4056 weeks
67-.03851 -.01691 (67*2π)/4056 weeks
68-.02548 .00764 (68*2π)/4056 weeks
69.02315 -.00259 (69*2π)/4056 weeks
70.04536 -.06223 (70*2π)/4056 weeks
71-.06522 -.03457 (71*2π)/4056 weeks
72.00533 .00449 (72*2π)/4056 weeks
73.0134 -.00013 (73*2π)/4056 weeks
74-.04646 -.08522 (74*2π)/4055 weeks
75-.03768 -.00747 (75*2π)/4055 weeks
76.01713 .02288 (76*2π)/4055 weeks
77-.01008 -.05493 (77*2π)/4055 weeks
78-.06319 .01129 (78*2π)/4055 weeks
79.02541 .02651 (79*2π)/4055 weeks
80.0146 -.04253 (80*2π)/4055 weeks
81-.02364 -.00065 (81*2π)/4055 weeks
82.01808 -.01058 (82*2π)/4055 weeks
83.03059 -.02658 (83*2π)/4055 weeks
84-.00441 -.05125 (84*2π)/4055 weeks
85-.0522 .03373 (85*2π)/4055 weeks
86.04958 -.03855 (86*2π)/4055 weeks
87-.06993 -.03372 (87*2π)/4055 weeks
88-.00705 -.01324 (88*2π)/4055 weeks
89-.02087 .00796 (89*2π)/4055 weeks
90.01308 -.02711 (90*2π)/4055 weeks
91-.03645 -.00099 (91*2π)/4054 weeks
92.00008 .06365 (92*2π)/4054 weeks
93.08177 -.05504 (93*2π)/4054 weeks
94-.07089 -.01238 (94*2π)/4054 weeks
95-.01872 -.02977 (95*2π)/4054 weeks
96.01588 .00637 (96*2π)/4054 weeks
97.01288 -.05816 (97*2π)/4054 weeks
98-.08515 -.00193 (98*2π)/4054 weeks
99-.03269 .03748 (99*2π)/4054 weeks
100.01352 -.03955 (100*2π)/4054 weeks
101-.0288 -.04264 (101*2π)/4054 weeks
102-.02438 -.00741 (102*2π)/4054 weeks
103.03351 -.01287 (103*2π)/4054 weeks
104-.05355 -.01167 (104*2π)/4054 weeks
105-.03294 .03565 (105*2π)/4054 weeks
106.01747 .01295 (106*2π)/4054 weeks
107-.02812 -.02676 (107*2π)/4054 weeks
108-.01604 -.00786 (108*2π)/4054 weeks
109-.02986 .00278 (109*2π)/4054 weeks
110-.00955 -.01887 (110*2π)/4054 weeks
111-.003 -.00122 (111*2π)/4054 weeks
112.01075 .01587 (112*2π)/4054 weeks
113.02659 -.05711 (113*2π)/4054 weeks
114-.03363 .01969 (114*2π)/4054 weeks
115-.00601 .00079 (115*2π)/4054 weeks
116.00348 -.02162 (116*2π)/4053 weeks
117-.00499 -.00162 (117*2π)/4053 weeks
118-.01073 -.00284 (118*2π)/4053 weeks
119.0191 -.03571 (119*2π)/4053 weeks
120-.0414 -.01889 (120*2π)/4053 weeks
121.02581 .02198 (121*2π)/4053 weeks
122.00175 -.02859 (122*2π)/4053 weeks
123.01088 -.02713 (123*2π)/4053 weeks
124-.03686 -.03901 (124*2π)/4053 weeks
125-.02527 -.02548 (125*2π)/4053 weeks
126-.00675 -.01325 (126*2π)/4053 weeks
127.0369 -.02077 (127*2π)/4053 weeks
128-.01568 -.04994 (128*2π)/4053 weeks
129-.04266 -.00057 (129*2π)/4053 weeks
130-.027 .00028 (130*2π)/4053 weeks
131-.03204 -.02114 (131*2π)/4053 weeks
132-.0314 -.06021 (132*2π)/4053 weeks
133-.04083 -.01541 (133*2π)/4053 weeks
134-.01874 .00701 (134*2π)/4053 weeks
135-.03943 .00556 (135*2π)/4053 weeks
136-.01816 .01571 (136*2π)/4053 weeks
137-.00778 .02255 (137*2π)/4053 weeks
138-.00963 .01044 (138*2π)/4053 weeks
139-.0366 .00384 (139*2π)/4053 weeks
140-.0209 -.01136 (140*2π)/4053 weeks
141-.03255 .02865 (141*2π)/4053 weeks
142.00454 .023 (142*2π)/4053 weeks
143.00231 -.00527 (143*2π)/4053 weeks
144-.00727 .0208 (144*2π)/4053 weeks
145-.00923 .0291 (145*2π)/4053 weeks
146.01052 -.00898 (146*2π)/4053 weeks
147-.01718 .00751 (147*2π)/4053 weeks
148.00108 -.00469 (148*2π)/4053 weeks
149.04582 -.02687 (149*2π)/4053 weeks
150-.03776 -.01051 (150*2π)/4053 weeks
151-.01436 .01116 (151*2π)/4053 weeks
152.00972 -.01138 (152*2π)/4053 weeks
153-.04037 .01565 (153*2π)/4053 weeks
154.02613 -.00246 (154*2π)/4053 weeks
155-.01548 -.05198 (155*2π)/4053 weeks
156-.01433 -.02441 (156*2π)/4053 weeks
157-.0172 .02192 (157*2π)/4053 weeks
158-.01849 -.00961 (158*2π)/4053 weeks
159-.03556 .01666 (159*2π)/4053 weeks
160-.01244 .01438 (160*2π)/4053 weeks
161-.02594 -.01689 (161*2π)/4053 weeks
162-.00102 .00292 (162*2π)/4053 weeks
163-.01935 -.00017 (163*2π)/4052 weeks
164-.02117 .0106 (164*2π)/4052 weeks
165.02775 .01403 (165*2π)/4052 weeks
166-.00483 -.01767 (166*2π)/4052 weeks
167-.02578 -.01666 (167*2π)/4052 weeks
168-.01413 .02255 (168*2π)/4052 weeks
169.01065 -.01533 (169*2π)/4052 weeks
170-.02048 .00991 (170*2π)/4052 weeks
171.01472 .00754 (171*2π)/4052 weeks
172-.0255 -.00106 (172*2π)/4052 weeks
173.00804 -.00491 (173*2π)/4052 weeks
174.00267 -.00089 (174*2π)/4052 weeks
175.00588 .00477 (175*2π)/4052 weeks
176-.02727 .00171 (176*2π)/4052 weeks
177-.00072 .01465 (177*2π)/4052 weeks
178-.00666 -.03927 (178*2π)/4052 weeks
179.01082 .02898 (179*2π)/4052 weeks
180.01461 -.02893 (180*2π)/4052 weeks
181-.04905 .00462 (181*2π)/4052 weeks
182-.00353 .0232 (182*2π)/4052 weeks
183-.02509 -.0238 (183*2π)/4052 weeks
184.00191 -.0206 (184*2π)/4052 weeks
185-.00609 -.01541 (185*2π)/4052 weeks
186.01535 .00155 (186*2π)/4052 weeks
187-.02264 -.01673 (187*2π)/4052 weeks
188-.01605 -.0061 (188*2π)/4052 weeks
189-.02641 -.00662 (189*2π)/4052 weeks
190-.05889 .01447 (190*2π)/4052 weeks
191.00458 .0149 (191*2π)/4052 weeks
192-.02993 .00091 (192*2π)/4052 weeks
193-.00804 .03301 (193*2π)/4052 weeks
194-.00268 -.03112 (194*2π)/4052 weeks
195-.00154 -.00653 (195*2π)/4052 weeks
196-.02782 .02982 (196*2π)/4052 weeks
197.0079 .01928 (197*2π)/4052 weeks
198-.0066 .00947 (198*2π)/4052 weeks
199-.00803 .01526 (199*2π)/4052 weeks
200.02722 .00437 (200*2π)/4052 weeks
201.0038 -.00782 (201*2π)/4052 weeks
202-.01219 -.01716 (202*2π)/4052 weeks
203-.01219 .01716 (203*2π)/4052 weeks
204.0038 .00782 (204*2π)/4052 weeks
205.02722 -.00437 (205*2π)/4052 weeks
206-.00803 -.01526 (206*2π)/4052 weeks
207-.0066 -.00947 (207*2π)/4052 weeks
208.0079 -.01928 (208*2π)/4052 weeks
209-.02782 -.02982 (209*2π)/4052 weeks
210-.00154 .00653 (210*2π)/4052 weeks
211-.00268 .03112 (211*2π)/4052 weeks
212-.00804 -.03301 (212*2π)/4052 weeks
213-.02993 -.00091 (213*2π)/4052 weeks
214.00458 -.0149 (214*2π)/4052 weeks
215-.05889 -.01447 (215*2π)/4052 weeks
216-.02641 .00662 (216*2π)/4052 weeks
217-.01605 .0061 (217*2π)/4052 weeks
218-.02264 .01673 (218*2π)/4052 weeks
219.01535 -.00155 (219*2π)/4052 weeks
220-.00609 .01541 (220*2π)/4052 weeks
221.00191 .0206 (221*2π)/4052 weeks
222-.02509 .0238 (222*2π)/4052 weeks
223-.00353 -.0232 (223*2π)/4052 weeks
224-.04905 -.00462 (224*2π)/4052 weeks
225.01461 .02893 (225*2π)/4052 weeks
226.01082 -.02898 (226*2π)/4052 weeks
227-.00666 .03927 (227*2π)/4052 weeks
228-.00072 -.01465 (228*2π)/4052 weeks
229-.02727 -.00171 (229*2π)/4052 weeks
230.00588 -.00477 (230*2π)/4052 weeks
231.00267 .00089 (231*2π)/4052 weeks
232.00804 .00491 (232*2π)/4052 weeks
233-.0255 .00106 (233*2π)/4052 weeks
234.01472 -.00754 (234*2π)/4052 weeks
235-.02048 -.00991 (235*2π)/4052 weeks
236.01065 .01533 (236*2π)/4052 weeks
237-.01413 -.02255 (237*2π)/4052 weeks
238-.02578 .01666 (238*2π)/4052 weeks
239-.00483 .01767 (239*2π)/4052 weeks
240.02775 -.01403 (240*2π)/4052 weeks
241-.02117 -.0106 (241*2π)/4052 weeks
242-.01935 .00017 (242*2π)/4052 weeks
243-.00102 -.00292 (243*2π)/4052 weeks
244-.02594 .01689 (244*2π)/4052 weeks
245-.01244 -.01438 (245*2π)/4052 weeks
246-.03556 -.01666 (246*2π)/4052 weeks
247-.01849 .00961 (247*2π)/4052 weeks
248-.0172 -.02192 (248*2π)/4052 weeks
249-.01433 .02441 (249*2π)/4052 weeks
250-.01548 .05198 (250*2π)/4052 weeks
251.02613 .00246 (251*2π)/4052 weeks
252-.04037 -.01565 (252*2π)/4052 weeks
253.00972 .01138 (253*2π)/4052 weeks
254-.01436 -.01116 (254*2π)/4052 weeks
255-.03776 .01051 (255*2π)/4052 weeks
256.04582 .02687 (256*2π)/4052 weeks
257.00108 .00469 (257*2π)/4052 weeks
258-.01718 -.00751 (258*2π)/4052 weeks
259.01052 .00898 (259*2π)/4052 weeks
260-.00923 -.0291 (260*2π)/4052 weeks
261-.00727 -.0208 (261*2π)/4052 weeks
262.00231 .00527 (262*2π)/4052 weeks
263.00454 -.023 (263*2π)/4052 weeks
264-.03255 -.02865 (264*2π)/4052 weeks
265-.0209 .01136 (265*2π)/4052 weeks
266-.0366 -.00384 (266*2π)/4052 weeks
267-.00963 -.01044 (267*2π)/4052 weeks
268-.00778 -.02255 (268*2π)/4052 weeks
269-.01816 -.01571 (269*2π)/4052 weeks
270-.03943 -.00556 (270*2π)/4052 weeks
271-.01874 -.00701 (271*2π)/4051 weeks
272-.04083 .01541 (272*2π)/4051 weeks
273-.0314 .06021 (273*2π)/4051 weeks
274-.03204 .02114 (274*2π)/4051 weeks
275-.027 -.00028 (275*2π)/4051 weeks
276-.04266 .00057 (276*2π)/4051 weeks
277-.01568 .04994 (277*2π)/4051 weeks
278.0369 .02077 (278*2π)/4051 weeks
279-.00675 .01325 (279*2π)/4051 weeks
280-.02527 .02548 (280*2π)/4051 weeks
281-.03686 .03901 (281*2π)/4051 weeks
282.01088 .02713 (282*2π)/4051 weeks
283.00175 .02859 (283*2π)/4051 weeks
284.02581 -.02198 (284*2π)/4051 weeks
285-.0414 .01889 (285*2π)/4051 weeks
286.0191 .03571 (286*2π)/4051 weeks
287-.01073 .00284 (287*2π)/4051 weeks
288-.00499 .00162 (288*2π)/4051 weeks
289.00348 .02162 (289*2π)/4051 weeks
290-.00601 -.00079 (290*2π)/4051 weeks
291-.03363 -.01969 (291*2π)/4051 weeks
292.02659 .05711 (292*2π)/4051 weeks
293.01075 -.01587 (293*2π)/4051 weeks
294-.003 .00122 (294*2π)/4051 weeks
295-.00955 .01887 (295*2π)/4051 weeks
296-.02986 -.00278 (296*2π)/4051 weeks
297-.01604 .00786 (297*2π)/4051 weeks
298-.02812 .02676 (298*2π)/4051 weeks
299.01747 -.01295 (299*2π)/4051 weeks
300-.03294 -.03565 (300*2π)/4051 weeks
301-.05355 .01167 (301*2π)/4051 weeks
302.03351 .01287 (302*2π)/4051 weeks
303-.02438 .00741 (303*2π)/4051 weeks
304-.0288 .04264 (304*2π)/4051 weeks
305.01352 .03955 (305*2π)/4051 weeks
306-.03269 -.03748 (306*2π)/4051 weeks
307-.08515 .00193 (307*2π)/4051 weeks
308.01288 .05816 (308*2π)/4051 weeks
309.01588 -.00637 (309*2π)/4051 weeks
310-.01872 .02977 (310*2π)/4051 weeks
311-.07089 .01238 (311*2π)/4051 weeks
312.08177 .05504 (312*2π)/4051 weeks
313.00008 -.06365 (313*2π)/4051 weeks
314-.03645 .00099 (314*2π)/4051 weeks
315.01308 .02711 (315*2π)/4051 weeks
316-.02087 -.00796 (316*2π)/4051 weeks
317-.00705 .01324 (317*2π)/4051 weeks
318-.06993 .03372 (318*2π)/4051 weeks
319.04958 .03855 (319*2π)/4051 weeks
320-.0522 -.03373 (320*2π)/4051 weeks
321-.00441 .05125 (321*2π)/4051 weeks
322.03059 .02658 (322*2π)/4051 weeks
323.01808 .01058 (323*2π)/4051 weeks
324-.02364 .00065 (324*2π)/4051 weeks
325.0146 .04253 (325*2π)/4051 weeks
326.02541 -.02651 (326*2π)/4051 weeks
327-.06319 -.01129 (327*2π)/4051 weeks
328-.01008 .05493 (328*2π)/4051 weeks
329.01713 -.02288 (329*2π)/4051 weeks
330-.03768 .00747 (330*2π)/4051 weeks
331-.04646 .08522 (331*2π)/4051 weeks
332.0134 .00013 (332*2π)/4051 weeks
333.00533 -.00449 (333*2π)/4051 weeks
334-.06522 .03457 (334*2π)/4051 weeks
335.04536 .06223 (335*2π)/4051 weeks
336.02315 .00259 (336*2π)/4051 weeks
337-.02548 -.00764 (337*2π)/4051 weeks
338-.03851 .01691 (338*2π)/4051 weeks
339-.00154 .08385 (339*2π)/4051 weeks
340.01879 .05461 (340*2π)/4051 weeks
341-.02003 .00354 (341*2π)/4051 weeks
342.02829 -.00683 (342*2π)/4051 weeks
343-.05649 .0411 (343*2π)/4051 weeks
344-.01897 .06864 (344*2π)/4051 weeks
345-.0588 .04151 (345*2π)/4051 weeks
346-.01929 .03235 (346*2π)/4051 weeks
347.04744 .02136 (347*2π)/4051 weeks
348-.01967 .02647 (348*2π)/4051 weeks
349.06321 .01055 (349*2π)/4051 weeks
350-.0401 .02379 (350*2π)/4051 weeks
351-.02498 .08323 (351*2π)/4051 weeks
352-.00153 .01017 (352*2π)/4051 weeks
353-.04741 .06347 (353*2π)/4051 weeks
354.02251 .05995 (354*2π)/4051 weeks
355.0663 -.01046 (355*2π)/4051 weeks
356.06613 -.0088 (356*2π)/4051 weeks
357-.05131 .01866 (357*2π)/4051 weeks
358.01282 .08748 (358*2π)/4051 weeks
359-.03519 -.09952 (359*2π)/4051 weeks
360-.07383 .04443 (360*2π)/4051 weeks
361.02443 .0375 (361*2π)/4051 weeks
362.03045 .01295 (362*2π)/4051 weeks
363-.04285 -.00757 (363*2π)/4051 weeks
364-.04642 .11486 (364*2π)/4051 weeks
365.03953 .065 (365*2π)/4051 weeks
366.01545 .04262 (366*2π)/4051 weeks
367.01952 .02288 (367*2π)/4051 weeks
368-.03605 .04911 (368*2π)/4051 weeks
369.05459 -.04355 (369*2π)/4051 weeks
370-.11193 .0053 (370*2π)/4051 weeks
371.03268 .1097 (371*2π)/4051 weeks
372.01337 .10006 (372*2π)/4051 weeks
373.04963 .06456 (373*2π)/4051 weeks
374.12361 -.00657 (374*2π)/4051 weeks
375.035 .13845 (375*2π)/4051 weeks
376.08245 -.02304 (376*2π)/4051 weeks
377.07977 .02651 (377*2π)/4051 weeks
378.03799 .01835 (378*2π)/4051 weeks
379.09149 -.05138 (379*2π)/4051 weeks
380-.00673 -.04799 (380*2π)/4051 weeks
381.14978 -.01995 (381*2π)/4051 weeks
382.0451 -.11677 (382*2π)/4051 weeks
383-.03045 -.03949 (383*2π)/4051 weeks
384-.02809 .0058 (384*2π)/4051 weeks
385-.0672 -.05676 (385*2π)/4051 weeks
386-.06073 .03083 (386*2π)/4051 weeks
387.02834 -.09405 (387*2π)/4051 weeks
388-.30669 .01423 (388*2π)/4051 weeks
389-.10953 .05455 (389*2π)/4051 weeks
390-.01345 .12349 (390*2π)/4051 weeks
391-.10064 .12987 (391*2π)/4051 weeks
392-.14738 .18963 (392*2π)/4051 weeks
393-.0062 -.06989 (393*2π)/4051 weeks
394.02439 .04889 (394*2π)/4051 weeks
395-.08132 .32725 (395*2π)/4051 weeks
396.09781 .44645 (396*2π)/4051 weeks
397.34757 .19311 (397*2π)/4051 weeks
398-.34331 .27858 (398*2π)/4051 weeks
399.02025 .10256 (399*2π)/4051 weeks
400.41824 .39881 (400*2π)/4051 weeks
401-.32515 -.52332 (401*2π)/4051 weeks
402-.89988 .91231 (402*2π)/4051 weeks
4031.14247 1.29313 (403*2π)/4051 weeks