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Fourier Analysis of ^TYX (Treasury Yield 30 Years)


^TYX (Treasury Yield 30 Years) appears to have interesting cyclic behaviour every 190 weeks (.4758*sine), 174 weeks (.4627*sine), and 161 weeks (.2277*cosine).

^TYX (Treasury Yield 30 Years) has an average price of 6.82 (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 2/15/1977 to 3/20/2017 for ^TYX (Treasury Yield 30 Years), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
06.81621   0 
1.2544 3.17719 (1*2π)/20922,092 weeks
2-.47801 1.7056 (2*2π)/20921,046 weeks
3-.66099 1.03257 (3*2π)/2092697 weeks
4-.57479 .40654 (4*2π)/2092523 weeks
5-.26545 -.03502 (5*2π)/2092418 weeks
6.06914 -.00708 (6*2π)/2092349 weeks
7-.00103 .29506 (7*2π)/2092299 weeks
8-.09296 .00945 (8*2π)/2092262 weeks
9-.00348 .07856 (9*2π)/2092232 weeks
10.18552 .13349 (10*2π)/2092209 weeks
11.20434 .47579 (11*2π)/2092190 weeks
12-.01524 .46269 (12*2π)/2092174 weeks
13-.22769 -.02615 (13*2π)/2092161 weeks
14-.00451 -.07731 (14*2π)/2092149 weeks
15-.01047 -.05386 (15*2π)/2092139 weeks
16.15817 .12133 (16*2π)/2092131 weeks
17-.09024 .05577 (17*2π)/2092123 weeks
18.09658 .19063 (18*2π)/2092116 weeks
19-.08049 .17305 (19*2π)/2092110 weeks
20-.08345 .09548 (20*2π)/2092105 weeks
21-.02997 .13889 (21*2π)/2092100 weeks
22-.00625 -.07297 (22*2π)/209295 weeks
23.12328 .01796 (23*2π)/209291 weeks
24.00445 .09136 (24*2π)/209287 weeks
25.0139 .12561 (25*2π)/209284 weeks
26-.00162 .02607 (26*2π)/209280 weeks
27.13246 .01661 (27*2π)/209277 weeks
28.05391 .05701 (28*2π)/209275 weeks
29-.00072 .02334 (29*2π)/209272 weeks
30.02131 .04531 (30*2π)/209270 weeks
31-.01551 .1036 (31*2π)/209267 weeks
32.032 .1013 (32*2π)/209265 weeks
33.03552 .03499 (33*2π)/209263 weeks
34-.02979 .04598 (34*2π)/209262 weeks
35-.06667 -.00658 (35*2π)/209260 weeks
36-.02594 -.02229 (36*2π)/209258 weeks
37.0439 -.03505 (37*2π)/209257 weeks
38.04972 .02933 (38*2π)/209255 weeks
39.01435 .0341 (39*2π)/209254 weeks
40.0132 .11145 (40*2π)/209252 weeks
41.03174 -.01566 (41*2π)/209251 weeks
42.04596 .0117 (42*2π)/209250 weeks
43-.00534 .03222 (43*2π)/209249 weeks
44-.01289 .08405 (44*2π)/209248 weeks
45.04561 .09188 (45*2π)/209246 weeks
46.01881 .1005 (46*2π)/209245 weeks
47-.03315 .03698 (47*2π)/209245 weeks
48-.07083 -.00469 (48*2π)/209244 weeks
49-.02602 -.06609 (49*2π)/209243 weeks
50.02854 .0271 (50*2π)/209242 weeks
51.01676 .01259 (51*2π)/209241 weeks
52-.01091 -.02248 (52*2π)/209240 weeks
53.02662 .00045 (53*2π)/209239 weeks
54.04011 .02527 (54*2π)/209239 weeks
55-.01141 .07505 (55*2π)/209238 weeks
56.06131 .08323 (56*2π)/209237 weeks
57-.05254 .03395 (57*2π)/209237 weeks
58-.051 -.01407 (58*2π)/209236 weeks
59-.00658 .02109 (59*2π)/209235 weeks
60-.00199 .01362 (60*2π)/209235 weeks
61-.00631 .05374 (61*2π)/209234 weeks
62-.01614 .04162 (62*2π)/209234 weeks
63.00277 -.00661 (63*2π)/209233 weeks
64.00478 .00181 (64*2π)/209233 weeks
65.01358 .02337 (65*2π)/209232 weeks
66.03438 .00484 (66*2π)/209232 weeks
67.02429 .02502 (67*2π)/209231 weeks
68.00541 .05157 (68*2π)/209231 weeks
69-.02391 .04599 (69*2π)/209230 weeks
70-.00935 .03357 (70*2π)/209230 weeks
71.00325 .01458 (71*2π)/209229 weeks
72-.03285 .01745 (72*2π)/209229 weeks
73-.02873 -.0091 (73*2π)/209229 weeks
74.00992 .01944 (74*2π)/209228 weeks
75-.01401 .00832 (75*2π)/209228 weeks
76.00584 .02705 (76*2π)/209228 weeks
77-.0042 .02069 (77*2π)/209227 weeks
78.00417 -.00036 (78*2π)/209227 weeks
79.03563 .00078 (79*2π)/209226 weeks
80.01367 .05764 (80*2π)/209226 weeks
81.00069 .03794 (81*2π)/209226 weeks
82-.00025 .03891 (82*2π)/209226 weeks
83-.02778 .05438 (83*2π)/209225 weeks
84-.02692 .04459 (84*2π)/209225 weeks
85-.04573 -.00684 (85*2π)/209225 weeks
86.02053 -.01569 (86*2π)/209224 weeks
87.00744 .00115 (87*2π)/209224 weeks
88.03714 -.00129 (88*2π)/209224 weeks
89.04471 .01909 (89*2π)/209224 weeks
90.01835 .04143 (90*2π)/209223 weeks
91.00962 .02336 (91*2π)/209223 weeks
92-.02515 .00751 (92*2π)/209223 weeks
93-.00539 .01124 (93*2π)/209222 weeks
94.01745 .02503 (94*2π)/209222 weeks
95.02491 .03088 (95*2π)/209222 weeks
96-.00911 .04388 (96*2π)/209222 weeks
97-.00657 .01959 (97*2π)/209222 weeks
98.0151 .01234 (98*2π)/209221 weeks
99-.00452 .02408 (99*2π)/209221 weeks
100-.0108 .01444 (100*2π)/209221 weeks
101-.04231 -.01474 (101*2π)/209221 weeks
102-.02678 -.00336 (102*2π)/209221 weeks
103.02603 -.00428 (103*2π)/209220 weeks
104.0229 .00228 (104*2π)/209220 weeks
105.02803 .01778 (105*2π)/209220 weeks
106.0317 .0272 (106*2π)/209220 weeks
107.00377 .04134 (107*2π)/209220 weeks
108-.02022 .03753 (108*2π)/209219 weeks
109-.00519 .04011 (109*2π)/209219 weeks
110-.02583 .0047 (110*2π)/209219 weeks
111-.02441 -.00163 (111*2π)/209219 weeks
112.00569 -.00595 (112*2π)/209219 weeks
113.00765 .01628 (113*2π)/209219 weeks
114.01839 .01002 (114*2π)/209218 weeks
115.02444 .00209 (115*2π)/209218 weeks
116-.01992 .01085 (116*2π)/209218 weeks
117.01306 .01435 (117*2π)/209218 weeks
118.01602 .02613 (118*2π)/209218 weeks
119.00999 .01117 (119*2π)/209218 weeks
120.00899 .00457 (120*2π)/209217 weeks
121.01312 .00004 (121*2π)/209217 weeks
122.00446 .03062 (122*2π)/209217 weeks
123-.01453 .04011 (123*2π)/209217 weeks
124-.00604 -.00147 (124*2π)/209217 weeks
125-.00417 .00546 (125*2π)/209217 weeks
126-.00142 .03289 (126*2π)/209217 weeks
127-.00991 .0017 (127*2π)/209216 weeks
128.00081 -.01004 (128*2π)/209216 weeks
129.02608 -.00491 (129*2π)/209216 weeks
130.00218 .01702 (130*2π)/209216 weeks
131.0086 .03401 (131*2π)/209216 weeks
132-.00374 .00886 (132*2π)/209216 weeks
133.02726 .02654 (133*2π)/209216 weeks
134.0095 .0181 (134*2π)/209216 weeks
135-.01252 .00345 (135*2π)/209215 weeks
136.00124 -.00214 (136*2π)/209215 weeks
137.01281 .02728 (137*2π)/209215 weeks
138.0019 .00271 (138*2π)/209215 weeks
139.00822 .00879 (139*2π)/209215 weeks
140-.01149 .00506 (140*2π)/209215 weeks
141-.00238 .00128 (141*2π)/209215 weeks
142-.00124 .00493 (142*2π)/209215 weeks
143.01947 .00896 (143*2π)/209215 weeks
144.00834 .01773 (144*2π)/209215 weeks
145-.01406 -.00957 (145*2π)/209214 weeks
146-.01006 .01988 (146*2π)/209214 weeks
147.0221 -.00577 (147*2π)/209214 weeks
148.01394 .0146 (148*2π)/209214 weeks
149.01375 .01715 (149*2π)/209214 weeks
150-.00297 .00879 (150*2π)/209214 weeks
151-.01375 .01065 (151*2π)/209214 weeks
152-.00033 .02192 (152*2π)/209214 weeks
153.0073 .01084 (153*2π)/209214 weeks
154-.00363 .01263 (154*2π)/209214 weeks
155-.00391 .00857 (155*2π)/209213 weeks
156-.004 .00327 (156*2π)/209213 weeks
157.00668 .00776 (157*2π)/209213 weeks
158.00749 -.00177 (158*2π)/209213 weeks
159.00046 -.00799 (159*2π)/209213 weeks
160-.00302 -.00334 (160*2π)/209213 weeks
161.01995 .00976 (161*2π)/209213 weeks
162.00983 .00083 (162*2π)/209213 weeks
163.0089 .00058 (163*2π)/209213 weeks
164.00666 .01129 (164*2π)/209213 weeks
165-.009 .01071 (165*2π)/209213 weeks
166-.00811 .02578 (166*2π)/209213 weeks
167-.01347 .01926 (167*2π)/209213 weeks
168-.00166 .00677 (168*2π)/209212 weeks
169-.0039 -.01619 (169*2π)/209212 weeks
170.01184 -.00175 (170*2π)/209212 weeks
171.00899 .00773 (171*2π)/209212 weeks
172.01365 .01434 (172*2π)/209212 weeks
173.02013 .00114 (173*2π)/209212 weeks
174.00638 .01999 (174*2π)/209212 weeks
175-.01869 .0285 (175*2π)/209212 weeks
176-.00222 .01553 (176*2π)/209212 weeks
177.00142 -.00422 (177*2π)/209212 weeks
178.00149 -.00407 (178*2π)/209212 weeks
179.00812 -.0084 (179*2π)/209212 weeks
180.00449 .01081 (180*2π)/209212 weeks
181.01564 .01619 (181*2π)/209212 weeks
182.00434 .01929 (182*2π)/209211 weeks
183-.00617 .02169 (183*2π)/209211 weeks
184-.0014 .00794 (184*2π)/209211 weeks
185-.00282 .01294 (185*2π)/209211 weeks
186-.0064 .01756 (186*2π)/209211 weeks
187-.00559 -.00517 (187*2π)/209211 weeks
188-.00093 .00551 (188*2π)/209211 weeks
189.01999 .0106 (189*2π)/209211 weeks
190.00206 .01114 (190*2π)/209211 weeks
191.00335 .0066 (191*2π)/209211 weeks
192.00479 .00264 (192*2π)/209211 weeks
193.00507 .00867 (193*2π)/209211 weeks
194.00129 .01111 (194*2π)/209211 weeks
195.00189 .00236 (195*2π)/209211 weeks
196.00776 .00848 (196*2π)/209211 weeks
197.00094 .01012 (197*2π)/209211 weeks
198-.00697 .00366 (198*2π)/209211 weeks
199.00182 .0053 (199*2π)/209211 weeks
200.01097 .01264 (200*2π)/209210 weeks
201-.00016 .01279 (201*2π)/209210 weeks
202-.00167 .01122 (202*2π)/209210 weeks
203.00151 -.00144 (203*2π)/209210 weeks
204.00534 .0169 (204*2π)/209210 weeks
205.00222 .01557 (205*2π)/209210 weeks
206-.00732 .01397 (206*2π)/209210 weeks
207.00348 .00202 (207*2π)/209210 weeks
208-.00493 .00769 (208*2π)/209210 weeks
209.00553 .00197 (209*2π)/209210 weeks
210.00905 .00164 (210*2π)/209210 weeks
211.01057 .00936 (211*2π)/209210 weeks
212.00263 .00835 (212*2π)/209210 weeks
213-.00771 .00786 (213*2π)/209210 weeks
214-.00211 .00732 (214*2π)/209210 weeks
215.00108 .01066 (215*2π)/209210 weeks
216.0065 .00786 (216*2π)/209210 weeks
217.0038 .00144 (217*2π)/209210 weeks
218-.01645 .00725 (218*2π)/209210 weeks
219.0047 .00135 (219*2π)/209210 weeks
220.00341 .01726 (220*2π)/209210 weeks
221.00522 -.00512 (221*2π)/20929 weeks
222.00035 .00453 (222*2π)/20929 weeks
223.00509 .01414 (223*2π)/20929 weeks
224.00332 .01631 (224*2π)/20929 weeks
225-.00031 .01591 (225*2π)/20929 weeks
226-.0001 .01125 (226*2π)/20929 weeks
227-.00442 .00111 (227*2π)/20929 weeks
228.00303 .00639 (228*2π)/20929 weeks
229.0067 .01117 (229*2π)/20929 weeks
230.00633 .00957 (230*2π)/20929 weeks
231-.00042 .00053 (231*2π)/20929 weeks
232-.0022 .00517 (232*2π)/20929 weeks
233.01359 -.00011 (233*2π)/20929 weeks
234.00874 .00653 (234*2π)/20929 weeks
235.00359 .01531 (235*2π)/20929 weeks
236.00163 .00015 (236*2π)/20929 weeks
237.00544 .00164 (237*2π)/20929 weeks
238.01098 .0019 (238*2π)/20929 weeks
239-.00325 .00095 (239*2π)/20929 weeks
240.00149 .01026 (240*2π)/20929 weeks
241-.00321 .00127 (241*2π)/20929 weeks
242.00918 .00576 (242*2π)/20929 weeks
243-.00215 .01039 (243*2π)/20929 weeks
244-.00542 .01166 (244*2π)/20929 weeks
245-.00465 .01039 (245*2π)/20929 weeks
246.00009 .00504 (246*2π)/20929 weeks
247-.00358 .00392 (247*2π)/20928 weeks
248.00275 -.00481 (248*2π)/20928 weeks
249.01141 .01061 (249*2π)/20928 weeks
250.00645 .0138 (250*2π)/20928 weeks
251.00121 .00486 (251*2π)/20928 weeks
252-.00471 .00858 (252*2π)/20928 weeks
253-.00316 .00366 (253*2π)/20928 weeks
254.00486 -.00433 (254*2π)/20928 weeks
255.00531 -.00303 (255*2π)/20928 weeks
256.0117 .00252 (256*2π)/20928 weeks
257.00697 .01505 (257*2π)/20928 weeks
258.00073 .00704 (258*2π)/20928 weeks
259.00612 .013 (259*2π)/20928 weeks
260.0025 -.00075 (260*2π)/20928 weeks
261-.00002 .01114 (261*2π)/20928 weeks
262-.00524 .00071 (262*2π)/20928 weeks
263-.00336 .00283 (263*2π)/20928 weeks
264.00677 .0065 (264*2π)/20928 weeks
265.00187 .00433 (265*2π)/20928 weeks
266.00068 .00884 (266*2π)/20928 weeks
267.00068 -.00172 (267*2π)/20928 weeks
268.00578 .00681 (268*2π)/20928 weeks
269.00945 .00406 (269*2π)/20928 weeks
270.00149 .00357 (270*2π)/20928 weeks
271.00513 .00508 (271*2π)/20928 weeks
272.00203 .01014 (272*2π)/20928 weeks
273.00626 -.00482 (273*2π)/20928 weeks
274-.00389 .0098 (274*2π)/20928 weeks
275-.00146 .00316 (275*2π)/20928 weeks
276.00043 .00662 (276*2π)/20928 weeks
277-.00263 .00974 (277*2π)/20928 weeks
278-.00439 -.00257 (278*2π)/20928 weeks
279-.00631 -.00149 (279*2π)/20927 weeks
280.00722 .00354 (280*2π)/20927 weeks
281.00442 .00005 (281*2π)/20927 weeks
282.0162 .00455 (282*2π)/20927 weeks
283.01202 .00773 (283*2π)/20927 weeks
284-.00608 .01155 (284*2π)/20927 weeks
285-.00127 .01279 (285*2π)/20927 weeks
286-.00422 .01213 (286*2π)/20927 weeks
287.00561 .00662 (287*2π)/20927 weeks
288.00683 -.00094 (288*2π)/20927 weeks
289.00623 -.00166 (289*2π)/20927 weeks
290-.00518 .00494 (290*2π)/20927 weeks
291-.00438 .00224 (291*2π)/20927 weeks
292-.0004 .00001 (292*2π)/20927 weeks
293.00573 .00218 (293*2π)/20927 weeks
294.00757 .0127 (294*2π)/20927 weeks
295.00331 .00739 (295*2π)/20927 weeks
296-.00159 .00683 (296*2π)/20927 weeks
297.00539 -.00303 (297*2π)/20927 weeks
298-.00179 .00768 (298*2π)/20927 weeks
299.00378 .00773 (299*2π)/20927 weeks
300.00359 .00451 (300*2π)/20927 weeks
301.00759 .00988 (301*2π)/20927 weeks
302.00059 .00683 (302*2π)/20927 weeks
303-.00161 .00196 (303*2π)/20927 weeks
304.00171 -.0004 (304*2π)/20927 weeks
305.00165 .00289 (305*2π)/20927 weeks
306-.00033 .0021 (306*2π)/20927 weeks
307-.00693 .00397 (307*2π)/20927 weeks
308.00122 -.00057 (308*2π)/20927 weeks
309.01328 .00144 (309*2π)/20927 weeks
310.00722 .00733 (310*2π)/20927 weeks
311.00171 .00671 (311*2π)/20927 weeks
312-.00151