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# Fourier Analysis of NC (NACCO Industries, Inc. Common S)

NC (NACCO Industries, Inc. Common S) appears to have interesting cyclic behaviour every 160 weeks (3.4282*sine), 99 weeks (2.0376*sine), and 148 weeks (1.923*sine).

NC (NACCO Industries, Inc. Common S) has an average price of 16.92 (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 6/17/1977 to 3/13/2017 for NC (NACCO Industries, Inc. Common S), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
016.92379   0
16.24284 -12.43082 (1*2π)/20742,074 weeks
24.46718 -8.35436 (2*2π)/20741,037 weeks
33.24585 -6.06087 (3*2π)/2074691 weeks
43.07671 -7.07745 (4*2π)/2074519 weeks
5-2.76257 -6.63548 (5*2π)/2074415 weeks
6-1.25563 -.83528 (6*2π)/2074346 weeks
7.64054 -1.6294 (7*2π)/2074296 weeks
81.12009 -1.66538 (8*2π)/2074259 weeks
9.24851 -3.09977 (9*2π)/2074230 weeks
10.30174 -.12127 (10*2π)/2074207 weeks
111.54653 -1.73323 (11*2π)/2074189 weeks
121.56499 -1.32853 (12*2π)/2074173 weeks
131.90371 -3.42823 (13*2π)/2074160 weeks
14-.7848 -1.92304 (14*2π)/2074148 weeks
15.28839 -1.8366 (15*2π)/2074138 weeks
16-.31359 -1.18742 (16*2π)/2074130 weeks
17.48795 -.62205 (17*2π)/2074122 weeks
18.81778 -.86413 (18*2π)/2074115 weeks
191.29754 -1.67834 (19*2π)/2074109 weeks
20.3368 -1.3336 (20*2π)/2074104 weeks
21.72522 -2.0376 (21*2π)/207499 weeks
22.01721 -1.48166 (22*2π)/207494 weeks
23.44714 -1.40704 (23*2π)/207490 weeks
24-.16569 -1.62351 (24*2π)/207486 weeks
25.28067 -1.46345 (25*2π)/207483 weeks
26-.38222 -1.1518 (26*2π)/207480 weeks
27.2635 -1.11772 (27*2π)/207477 weeks
28-.02336 -1.46611 (28*2π)/207474 weeks
29-.15985 -1.14451 (29*2π)/207472 weeks
30-.40005 -1.44091 (30*2π)/207469 weeks
31-.40628 -.51 (31*2π)/207467 weeks
32.16292 -.82336 (32*2π)/207465 weeks
33.04318 -1.30431 (33*2π)/207463 weeks
34-.74758 -1.08044 (34*2π)/207461 weeks
35-.46133 -.25692 (35*2π)/207459 weeks
36.06603 -.45137 (36*2π)/207458 weeks
37.31634 -.64659 (37*2π)/207456 weeks
38.04552 -.82918 (38*2π)/207455 weeks
39-.24084 -.83397 (39*2π)/207453 weeks
40.42221 -.66183 (40*2π)/207452 weeks
41-.24275 -1.0639 (41*2π)/207451 weeks
42-.32958 -.88447 (42*2π)/207449 weeks
43-.31917 -.80446 (43*2π)/207448 weeks
44-.62536 -.27822 (44*2π)/207447 weeks
45-.07363 -.28214 (45*2π)/207446 weeks
46.22151 -.27936 (46*2π)/207445 weeks
47.28278 -.53047 (47*2π)/207444 weeks
48.24091 -.96113 (48*2π)/207443 weeks
49-.09941 -.87083 (49*2π)/207442 weeks
50-.32819 -.70631 (50*2π)/207441 weeks
51-.07897 -.74823 (51*2π)/207441 weeks
52-.369 -.63991 (52*2π)/207440 weeks
53-.11679 -.597 (53*2π)/207439 weeks
54-.45572 -.6252 (54*2π)/207438 weeks
55.01255 -.46183 (55*2π)/207438 weeks
56-.30655 -.54388 (56*2π)/207437 weeks
57-.1002 -.70178 (57*2π)/207436 weeks
58-.34069 -.72014 (58*2π)/207436 weeks
59-.35362 -.59775 (59*2π)/207435 weeks
60-.74773 -.48176 (60*2π)/207435 weeks
61-.19901 -.26151 (61*2π)/207434 weeks
62-.57611 -.4416 (62*2π)/207433 weeks
63-.47189 .03929 (63*2π)/207433 weeks
64-.16628 -.07832 (64*2π)/207432 weeks
65.1206 -.08347 (65*2π)/207432 weeks
66-.28104 -.79538 (66*2π)/207431 weeks
67-.40523 -.04841 (67*2π)/207431 weeks
68-.35732 -.0265 (68*2π)/207431 weeks
69.07225 -.11037 (69*2π)/207430 weeks
70-.04127 -.5202 (70*2π)/207430 weeks
71-.5333 -.19523 (71*2π)/207429 weeks
72-.15342 -.08292 (72*2π)/207429 weeks
73-.0796 -.02858 (73*2π)/207428 weeks
74.07969 -.13636 (74*2π)/207428 weeks
75.06973 -.29345 (75*2π)/207428 weeks
76-.00407 -.40685 (76*2π)/207427 weeks
77-.15146 -.33873 (77*2π)/207427 weeks
78-.23276 -.46105 (78*2π)/207427 weeks
79-.33059 -.19742 (79*2π)/207426 weeks
80-.25296 -.14894 (80*2π)/207426 weeks
81-.29783 -.1428 (81*2π)/207426 weeks
82-.24809 -.08102 (82*2π)/207425 weeks
83-.23715 .20382 (83*2π)/207425 weeks
84.13334 -.05785 (84*2π)/207425 weeks
85.01223 -.14831 (85*2π)/207424 weeks
86.03886 -.1604 (86*2π)/207424 weeks
87-.06239 -.2197 (87*2π)/207424 weeks
88.04192 -.2199 (88*2π)/207424 weeks
89-.07047 -.34538 (89*2π)/207423 weeks
90-.12701 -.21973 (90*2π)/207423 weeks
91-.13026 -.25815 (91*2π)/207423 weeks
92-.17332 -.20027 (92*2π)/207423 weeks
93-.14159 -.1218 (93*2π)/207422 weeks
94-.09406 -.18912 (94*2π)/207422 weeks
95-.22225 -.15216 (95*2π)/207422 weeks
96-.09022 .03173 (96*2π)/207422 weeks
97.00692 -.19632 (97*2π)/207421 weeks
98-.07471 -.16497 (98*2π)/207421 weeks
99-.13464 -.21324 (99*2π)/207421 weeks
100-.29399 -.16681 (100*2π)/207421 weeks
101-.22078 .03399 (101*2π)/207421 weeks
102-.06522 -.02886 (102*2π)/207420 weeks
103-.08461 -.08902 (103*2π)/207420 weeks
104-.16544 -.01307 (104*2π)/207420 weeks
105-.10371 .0503 (105*2π)/207420 weeks
106.10498 .08942 (106*2π)/207420 weeks
107-.05434 -.18672 (107*2π)/207419 weeks
108-.03225 .07613 (108*2π)/207419 weeks
109.03081 -.08103 (109*2π)/207419 weeks
110-.05251 -.01244 (110*2π)/207419 weeks
111.05371 .00198 (111*2π)/207419 weeks
112.05524 -.11761 (112*2π)/207419 weeks
113-.00592 -.12622 (113*2π)/207418 weeks
114-.05496 -.07914 (114*2π)/207418 weeks
115-.02447 .05339 (115*2π)/207418 weeks
116.12831 -.03202 (116*2π)/207418 weeks
117.13739 -.14838 (117*2π)/207418 weeks
118-.018 -.15124 (118*2π)/207418 weeks
119-.04577 -.08502 (119*2π)/207417 weeks
120.09153 -.02059 (120*2π)/207417 weeks
121.02009 -.18226 (121*2π)/207417 weeks
122.04183 -.10767 (122*2π)/207417 weeks
123-.06976 -.14101 (123*2π)/207417 weeks
124-.07101 .04492 (124*2π)/207417 weeks
125.15468 .05294 (125*2π)/207417 weeks
126.1769 -.11711 (126*2π)/207416 weeks
127.07407 -.2489 (127*2π)/207416 weeks
128-.07634 -.11226 (128*2π)/207416 weeks
129.01535 -.02987 (129*2π)/207416 weeks
130.04791 -.06686 (130*2π)/207416 weeks
131.12669 -.0597 (131*2π)/207416 weeks
132.05108 -.12472 (132*2π)/207416 weeks
133.08274 -.08323 (133*2π)/207416 weeks
134.14784 .01734 (134*2π)/207415 weeks
135.20563 -.20473 (135*2π)/207415 weeks
136.18376 -.26952 (136*2π)/207415 weeks
137.01235 -.21624 (137*2π)/207415 weeks
138.02678 -.19245 (138*2π)/207415 weeks
139.09928 -.26186 (139*2π)/207415 weeks
140-.06531 -.19331 (140*2π)/207415 weeks
141.02473 -.14276 (141*2π)/207415 weeks
142-.00138 -.18996 (142*2π)/207415 weeks
143.00576 -.18428 (143*2π)/207415 weeks
144-.00022 -.18276 (144*2π)/207414 weeks
145-.02558 -.17685 (145*2π)/207414 weeks
146-.05081 -.17288 (146*2π)/207414 weeks
147-.03002 -.11942 (147*2π)/207414 weeks
148-.07258 -.10185 (148*2π)/207414 weeks
149-.00786 -.08307 (149*2π)/207414 weeks
150-.01432 -.07021 (150*2π)/207414 weeks
151.00646 -.02982 (151*2π)/207414 weeks
152.11027 -.04362 (152*2π)/207414 weeks
153.16347 -.09815 (153*2π)/207414 weeks
154.11049 -.26685 (154*2π)/207413 weeks
155.06757 -.20647 (155*2π)/207413 weeks
156.01945 -.21805 (156*2π)/207413 weeks
157-.03225 -.21822 (157*2π)/207413 weeks
158-.06892 -.18358 (158*2π)/207413 weeks
159-.04748 -.0916 (159*2π)/207413 weeks
160.03967 -.05727 (160*2π)/207413 weeks
161.09395 -.19213 (161*2π)/207413 weeks
162.05278 -.20361 (162*2π)/207413 weeks
163-.05295 -.24454 (163*2π)/207413 weeks
164-.05827 -.14029 (164*2π)/207413 weeks
165-.03447 -.12162 (165*2π)/207413 weeks
166-.04512 -.10489 (166*2π)/207412 weeks
167-.0014 -.12694 (167*2π)/207412 weeks
168-.01223 -.07347 (168*2π)/207412 weeks
169.10297 -.15325 (169*2π)/207412 weeks
170-.02575 -.15905 (170*2π)/207412 weeks
171.09813 -.17998 (171*2π)/207412 weeks
172-.02254 -.22724 (172*2π)/207412 weeks
173-.02097 -.19967 (173*2π)/207412 weeks
174-.10527 -.17598 (174*2π)/207412 weeks
175.00846 -.10902 (175*2π)/207412 weeks
176-.0482 -.22705 (176*2π)/207412 weeks
177-.07521 -.11365 (177*2π)/207412 weeks
178-.03258 -.15517 (178*2π)/207412 weeks
179-.07663 -.09864 (179*2π)/207412 weeks
180-.05412 -.11745 (180*2π)/207412 weeks
181-.01597 -.08079 (181*2π)/207411 weeks
182-.04973 -.12594 (182*2π)/207411 weeks
183.03014 -.04712 (183*2π)/207411 weeks
184-.00763 -.15118 (184*2π)/207411 weeks
185.00323 -.17165 (185*2π)/207411 weeks
186-.07226 -.18335 (186*2π)/207411 weeks
187-.08579 -.06399 (187*2π)/207411 weeks
188-.00795 -.16683 (188*2π)/207411 weeks
189-.09589 -.13185 (189*2π)/207411 weeks
190-.07432 -.14818 (190*2π)/207411 weeks
191-.12481 -.07505 (191*2π)/207411 weeks
192-.03461 -.04996 (192*2π)/207411 weeks
193-.07726 -.04871 (193*2π)/207411 weeks
194.00383 -.11807 (194*2π)/207411 weeks
195-.12002 -.01306 (195*2π)/207411 weeks
196.04017 -.05442 (196*2π)/207411 weeks
197-.04746 -.08103 (197*2π)/207411 weeks
198.01036 -.02899 (198*2π)/207410 weeks
199-.08393 -.07918 (199*2π)/207410 weeks
200.10326 .03339 (200*2π)/207410 weeks
201-.03834 -.17553 (201*2π)/207410 weeks
202.01402 -.01548 (202*2π)/207410 weeks
203-.01635 -.05675 (203*2π)/207410 weeks
204.10975 -.03474 (204*2π)/207410 weeks
205.02001 -.19545 (205*2π)/207410 weeks
206-.03543 -.07448 (206*2π)/207410 weeks
207-.02427 -.09631 (207*2π)/207410 weeks
208.0486 -.02447 (208*2π)/207410 weeks
209.09463 -.15422 (209*2π)/207410 weeks
210.01709 -.11388 (210*2π)/207410 weeks
211-.01933 -.22241 (211*2π)/207410 weeks
212-.08115 -.09915 (212*2π)/207410 weeks
213-.01722 -.04991 (213*2π)/207410 weeks
214-.03511 -.02934 (214*2π)/207410 weeks
215.08752 -.1009 (215*2π)/207410 weeks
216.01454 -.05344 (216*2π)/207410 weeks
217.06185 -.17908 (217*2π)/207410 weeks
218-.01201 -.1428 (218*2π)/207410 weeks
219.01249 -.13492 (219*2π)/20749 weeks
220-.04923 -.09525 (220*2π)/20749 weeks
221.09111 -.15095 (221*2π)/20749 weeks
222-.02746 -.15807 (222*2π)/20749 weeks
223-.02654 -.17018 (223*2π)/20749 weeks
224-.08559 -.15946 (224*2π)/20749 weeks
225-.06374 -.07728 (225*2π)/20749 weeks
226-.11275 -.0966 (226*2π)/20749 weeks
227.00733 -.02578 (227*2π)/20749 weeks
228-.01174 -.09167 (228*2π)/20749 weeks
229-.03991 -.04573 (229*2π)/20749 weeks
230.03622 -.08843 (230*2π)/20749 weeks
231.03851 -.07063 (231*2π)/20749 weeks
232.02696 -.16696 (232*2π)/20749 weeks
233-.07121 -.129 (233*2π)/20749 weeks
234-.02381 -.09288 (234*2π)/20749 weeks
235-.01296 -.06943 (235*2π)/20749 weeks
236.05457 -.13207 (236*2π)/20749 weeks
237-.06931 -.17947 (237*2π)/20749 weeks
238-.0863 -.11675 (238*2π)/20749 weeks
239-.07385 -.05417 (239*2π)/20749 weeks
240.01372 -.02102 (240*2π)/20749 weeks
241.00453 -.14868 (241*2π)/20749 weeks
242-.01214 -.07978 (242*2π)/20749 weeks
243-.00656 -.0912 (243*2π)/20749 weeks
244-.00515 -.10342 (244*2π)/20749 weeks
245-.00101 -.17136 (245*2π)/20748 weeks
246-.12971 -.13606 (246*2π)/20748 weeks
247-.11497 -.03727 (247*2π)/20748 weeks
248-.06837 .0149 (248*2π)/20748 weeks
249.05022 -.03309 (249*2π)/20748 weeks
250-.03545 -.08618 (250*2π)/20748 weeks
251-.00219 -.04313 (251*2π)/20748 weeks
252-.0205 -.03501 (252*2π)/20748 weeks
253.06298 -.02967 (253*2π)/20748 weeks
254.02088 -.12247 (254*2π)/20748 weeks
255.05486 -.09197 (255*2π)/20748 weeks
256-.01922 -.16678 (256*2π)/20748 weeks
257-.02771 -.076 (257*2π)/20748 weeks
258-.00557 -.11131 (258*2π)/20748 weeks
259-.00978 -.0526 (259*2π)/20748 weeks
260.02233 -.11398 (260*2π)/20748 weeks
261.00276 -.10829 (261*2π)/20748 weeks
262.00489 -.12489 (262*2π)/20748 weeks
263-.05611 -.12685 (263*2π)/20748 weeks
264-.02124 -.09041 (264*2π)/20748 weeks
265-.04239 -.06756 (265*2π)/20748 weeks
266.0373 -.06698 (266*2π)/20748 weeks
267.00944 -.14845 (267*2π)/20748 weeks
268-.0658 -.13977 (268*2π)/20748 weeks
269-.06917 -.03817 (269*2π)/20748 weeks
270.02241 -.05756 (270*2π)/20748 weeks
271.02472 -.12376 (271*2π)/20748 weeks
272-.04071 -.10209 (272*2π)/20748 weeks
273-.00506 -.09223 (273*2π)/20748 weeks
274.0148 -.12106 (274*2π)/20748 weeks
275-.05099 -.13218 (275*2π)/20748 weeks
276-.0292 -.12943 (276*2π)/20748 weeks
277-.075 -.05973 (277*2π)/20747 weeks
278-.01779 -.08004 (278*2π)/20747 weeks
279.01579 -.08615 (279*2π)/20747 weeks
280-.01332 -.10303 (280*2π)/20747 weeks
281-.01058 -.13173 (281*2π)/20747 weeks
282-.03946 -.09368 (282*2π)/20747 weeks
283-.03135 -.09798 (283*2π)/20747 weeks
284.00035 -.12791 (284*2π)/20747 weeks
285-.06781 -.09154 (285*2π)/20747 weeks
286.00043 -.11076 (286*2π)/20747 weeks
287-.02271 -.12306 (287*2π)/20747 weeks
288-.04128 -.15079 (288*2π)/20747 weeks
289-.08149 -.18093 (289*2π)/20747 weeks
290-.14164 -.08407 (290*2π)/20747 weeks
291-.1254 -.06643 (291*2π)/20747 weeks
292-.08985 -.01801 (292*2π)/20747 weeks
293-.05507 .0009 (293*2π)/20747 weeks
294.02665 -.04842 (294*2π)/20747 weeks
295-.01953 -.09634 (295*2π)/20747 weeks
296-.06035 -.10057 (296*2π)/20747 weeks
297-.07638 -.10065 (297*2π)/20747 weeks
298-.10102 .00642 (298*2π)/20747 weeks
299-.01373 .00001 (299*2π)/20747 weeks
300.02258 -.04749 (300*2π)/20747 weeks
301.00141 -.07688 (301*2π)/20747 weeks
302-.03382 -.05946 (302*2π)/20747 weeks
303.01155 -.08367 (303*2π)/20747 weeks
304.00119 -.11184 (304*2π)/20747 weeks
305-.04496 -.1108 (305*2π)/20747 weeks
306-.06019 -.08395 (306*2π)/20747 weeks
307-.02354 -.09066 (307*2π)/20747 weeks
308-.06527 -.10942 (308*2π)/20747 weeks
309-.09775 -.06127 (309*2π)/20747 weeks
310-.0558 -.01549 (310*2π)/20747 weeks
311-.0093 -.03125 (311*2π)/20747 weeks
312.00086 -.0622 (312*2π)/20747 weeks
313-.01902 -.10237 (313*2π)/20747 weeks
314-.05041 -.06735 (314*2π)/20747 weeks
315-.07203 -.0925 (315*2π)/20747 weeks
316-.04444