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# Fourier Analysis of TXI (Texas Industries, Inc. Common S)

TXI (Texas Industries, Inc. Common S) appears to have interesting cyclic behaviour every 157 weeks (4.1783*sine), 169 weeks (2.9447*sine), and 169 weeks (2.0551*cosine).

TXI (Texas Industries, Inc. Common S) has an average price of 18.64 (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 6/1/1972 to 6/30/2014 for TXI (Texas Industries, Inc. Common S), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
018.64357   0
18.22 -18.81835 (1*2π)/21962,196 weeks
2-.67607 -9.3559 (2*2π)/21961,098 weeks
3-1.07622 -5.61605 (3*2π)/2196732 weeks
4-.32705 .75095 (4*2π)/2196549 weeks
56.39553 -.77506 (5*2π)/2196439 weeks
64.3396 -5.00438 (6*2π)/2196366 weeks
71.55755 -5.60709 (7*2π)/2196314 weeks
8-.33083 -4.06362 (8*2π)/2196275 weeks
9-.67738 -1.68772 (9*2π)/2196244 weeks
101.45749 -1.54124 (10*2π)/2196220 weeks
111.22037 -2.02464 (11*2π)/2196200 weeks
121.3258 -1.78189 (12*2π)/2196183 weeks
132.05511 -2.94468 (13*2π)/2196169 weeks
14.0824 -4.17827 (14*2π)/2196157 weeks
15-1.10474 -2.55079 (15*2π)/2196146 weeks
16-1.07163 -1.08035 (16*2π)/2196137 weeks
17-.29154 -.4688 (17*2π)/2196129 weeks
181.0625 -1.27708 (18*2π)/2196122 weeks
19.01817 -2.00569 (19*2π)/2196116 weeks
20.21522 -.71379 (20*2π)/2196110 weeks
21-.0544 -2.16585 (21*2π)/2196105 weeks
22-1.34057 -.49923 (22*2π)/2196100 weeks
23.81994 .04237 (23*2π)/219695 weeks
24.36832 -1.18055 (24*2π)/219692 weeks
25.33877 -.15653 (25*2π)/219688 weeks
26.89896 -1.12274 (26*2π)/219684 weeks
27.26119 -.90813 (27*2π)/219681 weeks
28.9243 -.72302 (28*2π)/219678 weeks
29.64023 -1.60995 (29*2π)/219676 weeks
30-.02788 -1.33931 (30*2π)/219673 weeks
31.21926 -1.32044 (31*2π)/219671 weeks
32-.71953 -1.06721 (32*2π)/219669 weeks
33-.20342 .15379 (33*2π)/219667 weeks
34.78797 -.25506 (34*2π)/219665 weeks
35.99751 -.72233 (35*2π)/219663 weeks
36.86865 -1.50409 (36*2π)/219661 weeks
37.02049 -1.61902 (37*2π)/219659 weeks
38-.43148 -.89193 (38*2π)/219658 weeks
39.1923 -.64316 (39*2π)/219656 weeks
40.3167 -.75078 (40*2π)/219655 weeks
41.34057 -.89321 (41*2π)/219654 weeks
42.45357 -1.2315 (42*2π)/219652 weeks
43-.12012 -1.10373 (43*2π)/219651 weeks
44.11686 -1.18599 (44*2π)/219650 weeks
45-.24909 -1.24127 (45*2π)/219649 weeks
46-.6081 -.8926 (46*2π)/219648 weeks
47-.2674 -.36666 (47*2π)/219647 weeks
48.00091 -.50992 (48*2π)/219646 weeks
49.16638 -.71716 (49*2π)/219645 weeks
50-.07993 -.95633 (50*2π)/219644 weeks
51-.14805 -.69146 (51*2π)/219643 weeks
52-.09773 -.84158 (52*2π)/219642 weeks
53-.41565 -.80698 (53*2π)/219641 weeks
54-.45078 -.39327 (54*2π)/219641 weeks
55-.02347 -.3932 (55*2π)/219640 weeks
56-.07653 -.55113 (56*2π)/219639 weeks
57-.02999 -.48268 (57*2π)/219639 weeks
58-.08849 -.77256 (58*2π)/219638 weeks
59-.53899 -.50057 (59*2π)/219637 weeks
60-.16566 -.15173 (60*2π)/219637 weeks
61.22214 -.24678 (61*2π)/219636 weeks
62.20709 -.6263 (62*2π)/219635 weeks
63-.15225 -1.0185 (63*2π)/219635 weeks
64-.70713 -.46415 (64*2π)/219634 weeks
65-.2108 -.14197 (65*2π)/219634 weeks
66-.11161 -.18344 (66*2π)/219633 weeks
67-.0132 -.16381 (67*2π)/219633 weeks
68.10364 -.44682 (68*2π)/219632 weeks
69-.15553 -.36585 (69*2π)/219632 weeks
70.14033 -.21473 (70*2π)/219631 weeks
71.07511 -.63497 (71*2π)/219631 weeks
72-.04691 -.47907 (72*2π)/219631 weeks
73-.17694 -.70348 (73*2π)/219630 weeks
74-.66638 -.23755 (74*2π)/219630 weeks
75.0366 .19315 (75*2π)/219629 weeks
76.40427 -.48656 (76*2π)/219629 weeks
77-.22684 -.60041 (77*2π)/219629 weeks
78-.23127 -.40312 (78*2π)/219628 weeks
79-.39628 -.33208 (79*2π)/219628 weeks
80-.22272 .14598 (80*2π)/219627 weeks
81.26229 -.15763 (81*2π)/219627 weeks
82-.05355 -.3362 (82*2π)/219627 weeks
83-.01939 -.23181 (83*2π)/219626 weeks
84.00704 -.19311 (84*2π)/219626 weeks
85.06361 -.34476 (85*2π)/219626 weeks
86-.12216 -.29756 (86*2π)/219626 weeks
87-.0682 -.14154 (87*2π)/219625 weeks
88.13602 -.07444 (88*2π)/219625 weeks
89.23988 -.2341 (89*2π)/219625 weeks
90.19351 -.45098 (90*2π)/219624 weeks
91.02338 -.51544 (91*2π)/219624 weeks
92-.15284 -.4969 (92*2π)/219624 weeks
93-.23332 -.20116 (93*2π)/219624 weeks
94.07064 -.08296 (94*2π)/219623 weeks
95.10165 -.35521 (95*2π)/219623 weeks
96-.03719 -.39796 (96*2π)/219623 weeks
97-.07657 -.36677 (97*2π)/219623 weeks
98-.18676 -.29713 (98*2π)/219622 weeks
99-.13943 -.21163 (99*2π)/219622 weeks
100-.03501 -.11692 (100*2π)/219622 weeks
101-.04463 -.21359 (101*2π)/219622 weeks
102-.11067 -.18688 (102*2π)/219622 weeks
103.04064 -.05512 (103*2π)/219621 weeks
104.0917 -.26042 (104*2π)/219621 weeks
105-.03637 -.23472 (105*2π)/219621 weeks
106.00842 -.06028 (106*2π)/219621 weeks
107.15205 -.13773 (107*2π)/219621 weeks
108.20803 -.29231 (108*2π)/219620 weeks
109.10935 -.38689 (109*2π)/219620 weeks
110.00929 -.40914 (110*2π)/219620 weeks
111-.17435 -.30868 (111*2π)/219620 weeks
112-.09254 -.09827 (112*2π)/219620 weeks
113.14196 -.11744 (113*2π)/219619 weeks
114.17761 -.26733 (114*2π)/219619 weeks
115.05487 -.38901 (115*2π)/219619 weeks
116.08639 -.32054 (116*2π)/219619 weeks
117-.04093 -.47159 (117*2π)/219619 weeks
118-.22166 -.31584 (118*2π)/219619 weeks
119-.18999 -.16176 (119*2π)/219618 weeks
120-.02738 -.02034 (120*2π)/219618 weeks
121.21137 -.09362 (121*2π)/219618 weeks
122.21996 -.38758 (122*2π)/219618 weeks
123-.04367 -.44007 (123*2π)/219618 weeks
124-.04262 -.32114 (124*2π)/219618 weeks
125-.1928 -.35265 (125*2π)/219618 weeks
126-.1895 -.1601 (126*2π)/219617 weeks
127-.01104 -.07321 (127*2π)/219617 weeks
128.03955 -.16555 (128*2π)/219617 weeks
129.02172 -.15444 (129*2π)/219617 weeks
130.13156 -.13585 (130*2π)/219617 weeks
131.25505 -.38413 (131*2π)/219617 weeks
132-.0563 -.64517 (132*2π)/219617 weeks
133-.31305 -.36111 (133*2π)/219617 weeks
134-.29554 -.23122 (134*2π)/219616 weeks
135-.29962 .04015 (135*2π)/219616 weeks
136.02529 .10126 (136*2π)/219616 weeks
137.24962 -.12149 (137*2π)/219616 weeks
138.08216 -.35417 (138*2π)/219616 weeks
139-.07 -.33471 (139*2π)/219616 weeks
140-.12501 -.23344 (140*2π)/219616 weeks
141-.18295 -.1509 (141*2π)/219616 weeks
142-.05803 .02791 (142*2π)/219615 weeks
143.12019 -.07714 (143*2π)/219615 weeks
144.14276 -.24989 (144*2π)/219615 weeks
145-.00296 -.24813 (145*2π)/219615 weeks
146-.031 -.27327 (146*2π)/219615 weeks
147-.08587 -.1651 (147*2π)/219615 weeks
148-.02464 -.14399 (148*2π)/219615 weeks
149-.00726 -.15658 (149*2π)/219615 weeks
150-.01714 -.06022 (150*2π)/219615 weeks
151.09941 -.10857 (151*2π)/219615 weeks
152.1431 -.16006 (152*2π)/219614 weeks
153.20263 -.20273 (153*2π)/219614 weeks
154.14114 -.47039 (154*2π)/219614 weeks
155-.12918 -.33324 (155*2π)/219614 weeks
156-.05148 -.23422 (156*2π)/219614 weeks
157-.04697 -.21493 (157*2π)/219614 weeks
158-.02777 -.22826 (158*2π)/219614 weeks
159.01448 -.23242 (159*2π)/219614 weeks
160-.0158 -.27634 (160*2π)/219614 weeks
161-.10882 -.27227 (161*2π)/219614 weeks
162-.14775 -.19218 (162*2π)/219614 weeks
163-.03869 -.1137 (163*2π)/219613 weeks
164-.01451 -.15685 (164*2π)/219613 weeks
165-.06525 -.17227 (165*2π)/219613 weeks
166.04954 -.09167 (166*2π)/219613 weeks
167.09583 -.22968 (167*2π)/219613 weeks
168.01869 -.32319 (168*2π)/219613 weeks
169-.07522 -.24582 (169*2π)/219613 weeks
170-.07718 -.22112 (170*2π)/219613 weeks
171-.02292 -.15002 (171*2π)/219613 weeks
172.05392 -.29871 (172*2π)/219613 weeks
173-.0973 -.30721 (173*2π)/219613 weeks
174-.10951 -.21561 (174*2π)/219613 weeks
175-.13311 -.25606 (175*2π)/219613 weeks
176-.16521 -.11729 (176*2π)/219612 weeks
177-.02475 -.1494 (177*2π)/219612 weeks
178-.1415 -.18842 (178*2π)/219612 weeks
179-.08763 -.04541 (179*2π)/219612 weeks
180.08357 -.08846 (180*2π)/219612 weeks
181.0325 -.28345 (181*2π)/219612 weeks
182-.12782 -.26165 (182*2π)/219612 weeks
183-.1568 -.14895 (183*2π)/219612 weeks
184-.09769 -.07174 (184*2π)/219612 weeks
185-.01087 -.07464 (185*2π)/219612 weeks
186.0475 -.11559 (186*2π)/219612 weeks
187.00426 -.21175 (187*2π)/219612 weeks
188-.06529 -.20333 (188*2π)/219612 weeks
189-.05936 -.19725 (189*2π)/219612 weeks
190-.11072 -.13624 (190*2π)/219612 weeks
191-.07154 -.06906 (191*2π)/219611 weeks
192-.00687 -.08494 (192*2π)/219611 weeks
193.06624 -.1339 (193*2π)/219611 weeks
194.04396 -.18446 (194*2π)/219611 weeks
195-.00404 -.26276 (195*2π)/219611 weeks
196-.10151 -.20876 (196*2π)/219611 weeks
197-.05826 -.1778 (197*2π)/219611 weeks
198-.07048 -.16027 (198*2π)/219611 weeks
199-.01723 -.12567 (199*2π)/219611 weeks
200-.02854 -.26107 (200*2π)/219611 weeks
201-.15537 -.21171 (201*2π)/219611 weeks
202-.11513 -.10448 (202*2π)/219611 weeks
203-.11227 -.13032 (203*2π)/219611 weeks
204-.1019 -.04449 (204*2π)/219611 weeks
205.09063 -.05137 (205*2π)/219611 weeks
206.03267 -.29563 (206*2π)/219611 weeks
207-.19332 -.19649 (207*2π)/219611 weeks
208-.14827 -.0961 (208*2π)/219611 weeks
209-.10509 -.01507 (209*2π)/219611 weeks
210-.00284 .00284 (210*2π)/219610 weeks
211.04771 -.09465 (211*2π)/219610 weeks
212.03843 -.10249 (212*2π)/219610 weeks
213.02792 -.20281 (213*2π)/219610 weeks
214-.07104 -.11012 (214*2π)/219610 weeks
215.04176 -.10032 (215*2π)/219610 weeks
216.00812 -.19657 (216*2π)/219610 weeks
217-.04217 -.14024 (217*2π)/219610 weeks
218.00378 -.15507 (218*2π)/219610 weeks
219-.06723 -.18402 (219*2π)/219610 weeks
220-.04855 -.09138 (220*2π)/219610 weeks
221-.00379 -.14353 (221*2π)/219610 weeks
222-.06763 -.10169 (222*2π)/219610 weeks
223.04456 -.04663 (223*2π)/219610 weeks
224.09914 -.17369 (224*2π)/219610 weeks
225.05386 -.20308 (225*2π)/219610 weeks
226.01737 -.29082 (226*2π)/219610 weeks
227-.12958 -.2806 (227*2π)/219610 weeks
228-.14292 -.10136 (228*2π)/219610 weeks
229-.0236 -.10106 (229*2π)/219610 weeks
230-.00639 -.11031 (230*2π)/219610 weeks
231.09563 -.18804 (231*2π)/219610 weeks
232-.03256 -.34218 (232*2π)/21969 weeks
233-.1628 -.23625 (233*2π)/21969 weeks
234-.12317 -.17703 (234*2π)/21969 weeks
235-.18779 -.10828 (235*2π)/21969 weeks
236-.04013 -.06257 (236*2π)/21969 weeks
237-.01702 -.18257 (237*2π)/21969 weeks
238-.10401 -.18353 (238*2π)/21969 weeks
239-.05109 -.14524 (239*2π)/21969 weeks
240-.15964 -.22116 (240*2π)/21969 weeks
241-.17833 -.05374 (241*2π)/21969 weeks
242-.05562 -.10002 (242*2π)/21969 weeks
243-.11319 -.12278 (243*2π)/21969 weeks
244-.10009 -.09257 (244*2π)/21969 weeks
245-.14272 -.14663 (245*2π)/21969 weeks
246-.19152 .00499 (246*2π)/21969 weeks
247-.04576 .05769 (247*2π)/21969 weeks
248.00453 -.01228 (248*2π)/21969 weeks
249.02242 -.05362 (249*2π)/21969 weeks
250.02103 -.11908 (250*2π)/21969 weeks
251-.06065 -.12938 (251*2π)/21969 weeks
252-.04126 -.05446 (252*2π)/21969 weeks
253-.00672 -.07299 (253*2π)/21969 weeks
254-.03968 -.04107 (254*2π)/21969 weeks
255.06107 -.03484 (255*2π)/21969 weeks
256.08449 -.1382 (256*2π)/21969 weeks
257.05646 -.14953 (257*2π)/21969 weeks
258.05121 -.21057 (258*2π)/21969 weeks
259-.05881 -.2518 (259*2π)/21968 weeks
260-.12028 -.15444 (260*2π)/21968 weeks
261-.08027 -.1043 (261*2π)/21968 weeks
262-.05748 -.06506 (262*2π)/21968 weeks
263.07085 -.10461 (263*2π)/21968 weeks
264.01047 -.2468 (264*2π)/21968 weeks
265-.11284 -.17326 (265*2π)/21968 weeks
266-.05449 -.15825 (266*2π)/21968 weeks
267