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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 159 weeks (2.8783*sine), 159 weeks (2.2967*cosine), and 172 weeks (1.4001*cosine).

NC (NACCO Industries, Inc. Common S) has an average price of 16.76 (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 6/17/1977 to 1/9/2017 for NC (NACCO Industries, Inc. Common S), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
016.76283   0 
15.99682 -12.30045 (1*2π)/20652,065 weeks
24.31966 -8.16722 (2*2π)/20651,033 weeks
33.16519 -5.83985 (3*2π)/2065688 weeks
43.23837 -6.84797 (4*2π)/2065516 weeks
5-2.56493 -6.90679 (5*2π)/2065413 weeks
6-1.59222 -1.0266 (6*2π)/2065344 weeks
7.35142 -1.53914 (7*2π)/2065295 weeks
8.90379 -1.45365 (8*2π)/2065258 weeks
9.25342 -3.03649 (9*2π)/2065229 weeks
10-.12336 -.03636 (10*2π)/2065207 weeks
111.35102 -1.33545 (11*2π)/2065188 weeks
121.40008 -.84251 (12*2π)/2065172 weeks
132.29675 -2.87826 (13*2π)/2065159 weeks
14-.58089 -2.00601 (14*2π)/2065148 weeks
15.38178 -1.7483 (15*2π)/2065138 weeks
16-.37329 -1.25939 (16*2π)/2065129 weeks
17.21337 -.45687 (17*2π)/2065121 weeks
18.59688 -.47801 (18*2π)/2065115 weeks
191.3937 -1.09262 (19*2π)/2065109 weeks
20.45052 -.98964 (20*2π)/2065103 weeks
211.07541 -1.58352 (21*2π)/206598 weeks
22.28635 -1.31074 (22*2π)/206594 weeks
23.69222 -1.0794 (23*2π)/206590 weeks
24.2037 -1.49431 (24*2π)/206586 weeks
25.61637 -1.24301 (25*2π)/206583 weeks
26-.12108 -1.18391 (26*2π)/206579 weeks
27.44977 -.88131 (27*2π)/206576 weeks
28.3991 -1.30567 (28*2π)/206574 weeks
29.19127 -1.08629 (29*2π)/206571 weeks
30.10456 -1.54411 (30*2π)/206569 weeks
31-.35851 -.73136 (31*2π)/206567 weeks
32.24995 -.65044 (32*2π)/206565 weeks
33.50997 -1.11915 (33*2π)/206563 weeks
34-.2546 -1.43677 (34*2π)/206561 weeks
35-.54521 -.63704 (35*2π)/206559 weeks
36-.09401 -.45055 (36*2π)/206557 weeks
37.28766 -.39047 (37*2π)/206556 weeks
38.23806 -.62974 (38*2π)/206554 weeks
39-.03115 -.84139 (39*2π)/206553 weeks
40.50072 -.28465 (40*2π)/206552 weeks
41.26896 -.93064 (41*2π)/206550 weeks
42.1216 -.946 (42*2π)/206549 weeks
43.13061 -.97106 (43*2π)/206548 weeks
44-.52562 -.78479 (44*2π)/206547 weeks
45-.24785 -.45988 (45*2π)/206546 weeks
46-.042 -.15363 (46*2π)/206545 weeks
47.17806 -.14744 (47*2π)/206544 weeks
48.54876 -.44584 (48*2π)/206543 weeks
49.38251 -.62069 (49*2π)/206542 weeks
50.09019 -.70292 (50*2π)/206541 weeks
51.32649 -.59866 (51*2π)/206540 weeks
52.05665 -.73234 (52*2π)/206540 weeks
53.22201 -.53228 (53*2π)/206539 weeks
54-.02387 -.82746 (54*2π)/206538 weeks
55.20289 -.38244 (55*2π)/206538 weeks
56.03064 -.5792 (56*2π)/206537 weeks
57.32538 -.53622 (57*2π)/206536 weeks
58.28628 -.73691 (58*2π)/206536 weeks
59.28755 -.70022 (59*2π)/206535 weeks
60-.09299 -1.04825 (60*2π)/206534 weeks
61.07194 -.53088 (61*2π)/206534 weeks
62.0136 -.95645 (62*2π)/206533 weeks
63-.3874 -.69182 (63*2π)/206533 weeks
64-.26749 -.50937 (64*2π)/206532 weeks
65-.12585 -.06166 (65*2π)/206532 weeks
66.37699 -.79033 (66*2π)/206531 weeks
67-.17457 -.60548 (67*2π)/206531 weeks
68-.36856 -.6036 (68*2π)/206530 weeks
69-.16652 -.21199 (69*2π)/206530 weeks
70.27359 -.40284 (70*2π)/206530 weeks
71-.18678 -.76131 (71*2π)/206529 weeks
72-.17905 -.51934 (72*2π)/206529 weeks
73-.271 -.39537 (73*2π)/206528 weeks
74-.17097 -.22722 (74*2π)/206528 weeks
75-.02797 -.19803 (75*2π)/206528 weeks
76.13059 -.2454 (76*2π)/206527 weeks
77.07281 -.30284 (77*2π)/206527 weeks
78.24405 -.47291 (78*2π)/206526 weeks
79.03949 -.52706 (79*2π)/206526 weeks
80.00297 -.47875 (80*2π)/206526 weeks
81-.02595 -.56182 (81*2π)/206525 weeks
82-.02929 -.58516 (82*2π)/206525 weeks
83-.43492 -.53905 (83*2π)/206525 weeks
84-.2063 -.25083 (84*2π)/206525 weeks
85-.15118 -.29099 (85*2π)/206524 weeks
86-.11953 -.21361 (86*2π)/206524 weeks
87-.10267 -.30939 (87*2π)/206524 weeks
88-.06603 -.17306 (88*2π)/206523 weeks
89.0838 -.26681 (89*2π)/206523 weeks
90.00783 -.28975 (90*2π)/206523 weeks
91.06915 -.31359 (91*2π)/206523 weeks
92.05099 -.37026 (92*2π)/206522 weeks
93-.03097 -.34854 (93*2π)/206522 weeks
94.05453 -.29502 (94*2π)/206522 weeks
95.04864 -.45857 (95*2π)/206522 weeks
96-.17993 -.34835 (96*2π)/206522 weeks
97.00061 -.24541 (97*2π)/206521 weeks
98.00295 -.23453 (98*2π)/206521 weeks
99.09717 -.24363 (99*2π)/206521 weeks
100.13202 -.44934 (100*2π)/206521 weeks
101-.06048 -.48306 (101*2π)/206520 weeks
102-.05474 -.36808 (102*2π)/206520 weeks
103.02866 -.34852 (103*2π)/206520 weeks
104-.01132 -.45163 (104*2π)/206520 weeks
105-.08989 -.50363 (105*2π)/206520 weeks
106-.23401 -.24856 (106*2π)/206519 weeks
107.04821 -.36368 (107*2π)/206519 weeks
108-.17403 -.36172 (108*2π)/206519 weeks
109-.06204 -.29081 (109*2π)/206519 weeks
110-.111 -.38413 (110*2π)/206519 weeks
111-.19088 -.30518 (111*2π)/206519 weeks
112-.10921 -.24985 (112*2π)/206518 weeks
113-.0447 -.26443 (113*2π)/206518 weeks
114-.00773 -.33955 (114*2π)/206518 weeks
115-.16677 -.41228 (115*2π)/206518 weeks
116-.20768 -.29229 (116*2π)/206518 weeks
117-.12416 -.15664 (117*2π)/206518 weeks
118-.05175 -.23104 (118*2π)/206518 weeks
119-.05283 -.34027 (119*2π)/206517 weeks
120-.19226 -.23068 (120*2π)/206517 weeks
121-.0519 -.24613 (121*2π)/206517 weeks
122-.07602 -.18123 (122*2π)/206517 weeks
123.05836 -.26536 (123*2π)/206517 weeks
124-.05563 -.44112 (124*2π)/206517 weeks
125-.23395 -.32936 (125*2π)/206517 weeks
126-.23475 -.19054 (126*2π)/206516 weeks
127-.04484 -.11224 (127*2π)/206516 weeks
128-.01237 -.2722 (128*2π)/206516 weeks
129-.09239 -.29708 (129*2π)/206516 weeks
130-.09055 -.3215 (130*2π)/206516 weeks
131-.15861 -.23865 (131*2π)/206516 weeks
132-.09008 -.27696 (132*2π)/206516 weeks
133-.06823 -.30044 (133*2π)/206516 weeks
134-.2886 -.33541 (134*2π)/206515 weeks
135-.25197 -.22487 (135*2π)/206515 weeks
136-.18594 -.06472 (136*2π)/206515 weeks
137-.14453 -.14623 (137*2π)/206515 weeks
138-.16568 -.20056 (138*2π)/206515 weeks
139-.11685 -.03947 (139*2π)/206515 weeks
140-.05775 -.16374 (140*2π)/206515 weeks
141-.12539 -.14686 (141*2π)/206515 weeks
142-.09807 -.15088 (142*2π)/206515 weeks
143-.09203 -.14005 (143*2π)/206514 weeks
144-.08538 -.12017 (144*2π)/206514 weeks
145-.07171 -.11536 (145*2π)/206514 weeks
146-.01621 -.12932 (146*2π)/206514 weeks
147-.03156 -.11583 (147*2π)/206514 weeks
148.00033 -.1871 (148*2π)/206514 weeks
149-.01274 -.17866 (149*2π)/206514 weeks
150.00447 -.20461 (150*2π)/206514 weeks
151-.0129 -.29475 (151*2π)/206514 weeks
152-.08939 -.30788 (152*2π)/206514 weeks
153-.23097 -.2725 (153*2π)/206513 weeks
154-.1442 -.16724 (154*2π)/206513 weeks
155-.16092 -.13514 (155*2π)/206513 weeks
156-.15106 -.10381 (156*2π)/206513 weeks
157-.10406 -.08455 (157*2π)/206513 weeks
158-.01798 -.09852 (158*2π)/206513 weeks
159.00091 -.17998 (159*2π)/206513 weeks
160-.11175 -.26112 (160*2π)/206513 weeks
161-.13317 -.17609 (161*2π)/206513 weeks
162-.18249 -.10693 (162*2π)/206513 weeks
163-.06731 -.06708 (163*2π)/206513 weeks
164-.05108 -.10306 (164*2π)/206513 weeks
165-.0545 -.1049 (165*2π)/206513 weeks
166-.04799 -.15912 (166*2π)/206512 weeks
167-.02987 -.12882 (167*2π)/206512 weeks
168-.04329 -.25032 (168*2π)/206512 weeks
169-.13131 -.1384 (169*2π)/206512 weeks
170-.06296 -.23045 (170*2π)/206512 weeks
171-.17642 -.14356 (171*2π)/206512 weeks
172-.12535 -.1214 (172*2π)/206512 weeks
173-.14323 -.06307 (173*2π)/206512 weeks
174-.02361 -.11476 (174*2π)/206512 weeks
175-.15125 -.14484 (175*2π)/206512 weeks
176-.07245 -.04631 (176*2π)/206512 weeks
177-.07208 -.11655 (177*2π)/206512 weeks
178-.06783 -.04982 (178*2π)/206512 weeks
179-.05904 -.09555 (179*2π)/206512 weeks
180-.01734 -.0944 (180*2π)/206511 weeks
181-.0733 -.11159 (181*2π)/206511 weeks
182.02224 -.10358 (182*2π)/206511 weeks
183-.09144 -.16114 (183*2π)/206511 weeks
184-.08762 -.16032 (184*2π)/206511 weeks
185-.13939 -.10905 (185*2π)/206511 weeks
186-.07001 -.02452 (186*2π)/206511 weeks
187-.07167 -.15818 (187*2π)/206511 weeks
188-.12098 -.06696 (188*2π)/206511 weeks
189-.09603 -.09247 (189*2π)/206511 weeks
190-.08788 -.01143 (190*2π)/206511 weeks
191-.00189 -.05281 (191*2π)/206511 weeks
192-.04888 -.042 (192*2π)/206511 weeks
193-.01456 -.13244 (193*2π)/206511 weeks
194-.0689 .01411 (194*2π)/206511 weeks
195.04833 -.11138 (195*2π)/206511 weeks
196-.0516 -.08503 (196*2π)/206511 weeks
197.02155 -.06547 (197*2π)/206510 weeks
198-.07777 -.07594 (198*2π)/206510 weeks
199.12593 -.0602 (199*2π)/206510 weeks
200-.09949 -.18547 (200*2π)/206510 weeks
201.02396 -.04871 (201*2π)/206510 weeks
202-.02271 -.08984 (202*2π)/206510 weeks
203.08924 -.11878 (203*2π)/206510 weeks
204-.06254 -.22128 (204*2π)/206510 weeks
205-.06079 -.07767 (205*2π)/206510 weeks
206-.04726 -.11002 (206*2π)/206510 weeks
207.04104 -.07248 (207*2π)/206510 weeks
208.03149 -.20706 (208*2π)/206510 weeks
209-.03801 -.13618 (209*2π)/206510 weeks
210-.09566 -.22072 (210*2π)/206510 weeks
211-.11017 -.07735 (211*2π)/206510 weeks
212-.03085 -.05452 (212*2π)/206510 weeks
213-.04339 -.04117 (213*2π)/206510 weeks
214.05601 -.13911 (214*2π)/206510 weeks
215-.01347 -.07753 (215*2π)/206510 weeks
216.00761 -.20771 (216*2π)/206510 weeks
217-.05815 -.15022 (217*2π)/206510 weeks
218-.03002 -.14462 (218*2π)/20659 weeks
219-.08184 -.09803 (219*2π)/20659 weeks
220.04863 -.17256 (220*2π)/20659 weeks
221-.07362 -.16128 (221*2π)/20659 weeks
222-.07069 -.17135 (222*2π)/20659 weeks
223-.12523 -.15298 (223*2π)/20659 weeks
224-.09387 -.0738 (224*2π)/20659 weeks
225-.14205 -.0923 (225*2π)/20659 weeks
226-.01745 -.02953 (226*2π)/20659 weeks
227-.04125 -.09559 (227*2π)/20659 weeks
228-.06854 -.04863 (228*2π)/20659 weeks
229.00705 -.09225 (229*2π)/20659 weeks
230.00919 -.07291 (230*2π)/20659 weeks
231.00027 -.16906 (231*2π)/20659 weeks
232-.09871 -.13443 (232*2π)/20659 weeks
233-.05318 -.09653 (233*2π)/20659 weeks
234-.04387 -.07068 (234*2π)/20659 weeks
235.03147 -.12692 (235*2π)/20659 weeks
236-.08551 -.18759 (236*2π)/20659 weeks
237-.11082 -.13138 (237*2π)/20659 weeks
238-.10985 -.068 (238*2π)/20659 weeks
239-.02823 -.01778 (239*2π)/20659 weeks
240-.01612 -.14501 (240*2π)/20659 weeks
241-.04097 -.08172 (241*2π)/20659 weeks
242-.0331 -.08937 (242*2π)/20659 weeks
243-.02731 -.09878 (243*2π)/20658 weeks
244-.00176 -.16859 (244*2π)/20658 weeks
245-.13448 -.17277 (245*2π)/20658 weeks
246-.1544 -.07964 (246*2π)/20658 weeks
247-.13486 -.01117 (247*2π)/20658 weeks
248-.00603 -.01722 (248*2π)/20658 weeks
249-.06968 -.09085 (249*2π)/20658 weeks
250-.05191 -.04319 (250*2π)/20658 weeks
251-.07787 -.03642 (251*2π)/20658 weeks
252-.00061 .00563 (252*2π)/20658 weeks
253-.00555 -.09132 (253*2π)/20658 weeks
254.02527 -.05016 (254*2π)/20658 weeks
255-.01112 -.15142 (255*2π)/20658 weeks
256-.05479 -.07723 (256*2π)/20658 weeks
257-.02441 -.10207 (257*2π)/20658 weeks
258-.0536 -.0447 (258*2π)/20658 weeks
259.00032 -.08156 (259*2π)/20658 weeks
260-.01284 -.08368 (260*2π)/20658 weeks
261.00351 -.09716 (261*2π)/20658 weeks
262-.04965 -.13383 (262*2π)/20658 weeks
263-.03826 -.09314 (263*2π)/20658 weeks
264-.07695 -.0804 (264*2π)/20658 weeks
265-.01052 -.02814 (265*2π)/20658 weeks
266.02214 -.10402 (266*2π)/20658 weeks
267-.03654 -.154 (267*2π)/20658 weeks
268-.11043 -.0791 (268*2π)/20658 weeks
269-.03811 -.03165 (269*2π)/20658 weeks
270.01468 -.0742 (270*2π)/20658 weeks
271-.04607 -.09618 (271*2π)/20658 weeks
272-.02978 -.06829 (272*2π)/20658 weeks
273.01349 -.07093 (273*2π)/20658 weeks
274-.02578 -.12158 (274*2π)/20658 weeks
275-.00224 -.12226 (275*2π)/20658 weeks
276-.08942 -.09953 (276*2π)/20657 weeks
277-.05184 -.07955 (277*2π)/20657 weeks
278-.01692 -.05126 (278*2π)/20657 weeks
279-.02346 -.07086 (279*2π)/20657 weeks
280.00748 -.09389 (280*2π)/20657 weeks
281-.03426 -.08716 (281*2π)/20657 weeks
282-.0362 -.08362 (282*2π)/20657 weeks
283.01969 -.0806 (283*2π)/20657 weeks
284-.05524 -.10276 (284*2π)/20657 weeks
285.00006 -.06618 (285*2π)/20657 weeks
286.00508 -.07488 (286*2π)/20657 weeks
287.02694 -.10038 (287*2π)/20657 weeks
288.05608 -.16757 (288*2π)/20657 weeks
289-.0448 -.17583 (289*2π)/20657 weeks
290-.06782 -.18083 (290*2π)/20657 weeks
291-.10137 -.139 (291*2π)/20657 weeks
292-.13006 -.09583 (292*2π)/20657 weeks
293-.05226 -.03403 (293*2π)/20657 weeks
294-.02213 -.07184 (294*2π)/20657 weeks
295-.02538 -.11135 (295*2π)/20657 weeks
296-.01135 -.15208 (296*2π)/20657 weeks
297-.12793 -.13829 (297*2π)/20657 weeks
298-.11994 -.07061 (298*2π)/20657 weeks
299-.07078 -.039 (299*2π)/20657 weeks
300-.04314 -.05231 (300*2π)/20657 weeks
301-.08088 -.07274 (301*2π)/20657 weeks
302-.04515 -.04146 (302*2π)/20657 weeks
303-.00725 -.04445 (303*2π)/20657 weeks
304-.00867 -.08209 (304*2π)/20657 weeks
305-.03897 -.09771 (305*2π)/20657 weeks
306-.01413 -.0653 (306*2π)/20657 weeks
307.0074 -.10832 (307*2π)/20657 weeks
308-.03863 -.14783 (308*2π)/20657 weeks
309-.08585 -.1159 (309*2π)/20657 weeks
310-.08088 -.07195 (310*2π)/20657 weeks
311-.05822 -.04807 (311*2π)/20657 weeks
312-.00934 -.06533 (312*2π)/20657 weeks
313-.03735 -.07471 (313*2π)/20657 weeks
314-.0115 -.12618 (314*2π)/20657 weeks
315-.06451 -.09112 (315*2π)/20657 weeks
316-.03412 -.07407 (316*2π)/20657 weeks
317-.06013 -.14702 (317*2π)/20657 weeks
318-.06929 -.07914 (318*2π)/20656 weeks
319-.07038 -.11695 (319*2π)/20656 weeks
320-.09117 -.08945 (320*2π)/2065