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Fourier Analysis of VTIP (Vanguard ShortTerm Inflation-Protected Securities ETF)


VTIP (Vanguard ShortTerm Inflation-Protected Securities ETF) appears to have interesting cyclic behaviour every 12 weeks (.0592*cosine), 24 weeks (.0514*sine), and 11 weeks (.0451*cosine).

VTIP (Vanguard ShortTerm Inflation-Protected Securities ETF) has an average price of 48.79 (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 10/16/2012 to 10/16/2017 for VTIP (Vanguard ShortTerm Inflation-Protected Securities ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
048.78551   0 
1.54166 -.00448 (1*2π)/262262 weeks
2-.02266 -.30075 (2*2π)/262131 weeks
3.11816 .107 (3*2π)/26287 weeks
4.00796 .14184 (4*2π)/26266 weeks
5-.08287 -.11523 (5*2π)/26252 weeks
6-.02111 .11037 (6*2π)/26244 weeks
7-.07441 -.01599 (7*2π)/26237 weeks
8.01234 -.07385 (8*2π)/26233 weeks
9.01379 -.04808 (9*2π)/26229 weeks
10.05008 -.02341 (10*2π)/26226 weeks
11-.00532 -.05142 (11*2π)/26224 weeks
12.01047 .01331 (12*2π)/26222 weeks
13-.02421 -.00044 (13*2π)/26220 weeks
14-.01853 -.00576 (14*2π)/26219 weeks
15.02292 .00325 (15*2π)/26217 weeks
16-.04313 -.01903 (16*2π)/26216 weeks
17-.04396 -.03283 (17*2π)/26215 weeks
18-.02832 .00383 (18*2π)/26215 weeks
19.0314 -.00338 (19*2π)/26214 weeks
20.04052 .015 (20*2π)/26213 weeks
21-.05921 -.0148 (21*2π)/26212 weeks
22.01905 .00909 (22*2π)/26212 weeks
23-.04506 -.00786 (23*2π)/26211 weeks
24.00587 -.02374 (24*2π)/26211 weeks
25-.00425 -.00719 (25*2π)/26210 weeks
26.0291 -.01491 (26*2π)/26210 weeks
27.00916 .01065 (27*2π)/26210 weeks
28-.01385 .00734 (28*2π)/2629 weeks
29-.00831 -.00505 (29*2π)/2629 weeks
30-.02078 -.02438 (30*2π)/2629 weeks
31-.00932 -.0212 (31*2π)/2628 weeks
32.00071 -.02032 (32*2π)/2628 weeks
33.00712 .0052 (33*2π)/2628 weeks
34-.00061 .02372 (34*2π)/2628 weeks
35.00113 -.00612 (35*2π)/2627 weeks
36.00135 .01255 (36*2π)/2627 weeks
37.00897 .00459 (37*2π)/2627 weeks
38.01324 -.00932 (38*2π)/2627 weeks
39-.00741 .00002 (39*2π)/2627 weeks
40-.00064 -.02215 (40*2π)/2627 weeks
41.00146 .01011 (41*2π)/2626 weeks
42-.00034 -.00741 (42*2π)/2626 weeks
43-.01106 -.00049 (43*2π)/2626 weeks
44-.00391 .00109 (44*2π)/2626 weeks
45.00643 -.00335 (45*2π)/2626 weeks
46-.00227 -.00835 (46*2π)/2626 weeks
47.0107 -.00891 (47*2π)/2626 weeks
48-.00283 -.00453 (48*2π)/2625 weeks
49-.00653 .00978 (49*2π)/2625 weeks
50.00411 -.0122 (50*2π)/2625 weeks
51.00443 .01085 (51*2π)/2625 weeks
52-.01918 -.01419 (52*2π)/2625 weeks
53-.01351 -.0208 (53*2π)/2625 weeks
54.00168 .00166 (54*2π)/2625 weeks
55.00456 .00004 (55*2π)/2625 weeks
56-.00819 -.00419 (56*2π)/2625 weeks
57-.00983 .00507 (57*2π)/2625 weeks
58-.0024 .00081 (58*2π)/2625 weeks
59-.01718 -.00454 (59*2π)/2624 weeks
60-.00302 .00776 (60*2π)/2624 weeks
61.00306 -.00655 (61*2π)/2624 weeks
62.00001 -.00737 (62*2π)/2624 weeks
63-.01214 -.0097 (63*2π)/2624 weeks
64.005 .0004 (64*2π)/2624 weeks
65-.01059 .00505 (65*2π)/2624 weeks
66.00769 .0101 (66*2π)/2624 weeks
67-.01776 .00455 (67*2π)/2624 weeks
68.00402 -.01057 (68*2π)/2624 weeks
69.00508 -.00831 (69*2π)/2624 weeks
70.00506 -.00701 (70*2π)/2624 weeks
71-.01716 .01516 (71*2π)/2624 weeks
72.00195 .00408 (72*2π)/2624 weeks
73-.00304 .00113 (73*2π)/2624 weeks
74-.00387 -.01199 (74*2π)/2624 weeks
75.00948 .00039 (75*2π)/2623 weeks
76.00552 -.0065 (76*2π)/2623 weeks
77.00185 .00282 (77*2π)/2623 weeks
78.0055 -.00082 (78*2π)/2623 weeks
79-.00293 -.00064 (79*2π)/2623 weeks
80-.00878 .0003 (80*2π)/2623 weeks
81.00461 -.0145 (81*2π)/2623 weeks
82-.01328 .00214 (82*2π)/2623 weeks
83.00742 .00341 (83*2π)/2623 weeks
84.00151 -.00188 (84*2π)/2623 weeks
85.00102 -.00944 (85*2π)/2623 weeks
86-.0033 -.00608 (86*2π)/2623 weeks
87.00054 .00984 (87*2π)/2623 weeks
88.00299 .00491 (88*2π)/2623 weeks
89-.00116 .01358 (89*2π)/2623 weeks
90-.00385 .00427 (90*2π)/2623 weeks
91-.00283 -.00176 (91*2π)/2623 weeks
92-.00895 -.0108 (92*2π)/2623 weeks
93.00318 -.00759 (93*2π)/2623 weeks
94.00686 -.00097 (94*2π)/2623 weeks
95-.00982 .0059 (95*2π)/2623 weeks
96-.0016 .0088 (96*2π)/2623 weeks
97-.0099 .00029 (97*2π)/2623 weeks
98-.00292 -.01407 (98*2π)/2623 weeks
99-.0062 -.00237 (99*2π)/2623 weeks
100.0123 -.00277 (100*2π)/2623 weeks
101-.00482 .00357 (101*2π)/2623 weeks
102.00582 .0073 (102*2π)/2623 weeks
103.00024 .00474 (103*2π)/2623 weeks
104-.00026 -.00404 (104*2π)/2623 weeks
105-.00482 .00167 (105*2π)/2622 weeks
106-.00453 -.00395 (106*2π)/2622 weeks
107.00233 -.00742 (107*2π)/2622 weeks
108.00523 -.00019 (108*2π)/2622 weeks
109.0051 .00878 (109*2π)/2622 weeks
110-.00231 -.00159 (110*2π)/2622 weeks
111-.00849 .0071 (111*2π)/2622 weeks
112.00014 .00261 (112*2π)/2622 weeks
113-.00271 -.00141 (113*2π)/2622 weeks
114.00431 -.00801 (114*2π)/2622 weeks
115.00678 -.00139 (115*2π)/2622 weeks
116-.00156 -.00252 (116*2π)/2622 weeks
117.00261 .00499 (117*2π)/2622 weeks
118-.00456 .0053 (118*2π)/2622 weeks
119.00682 .00066 (119*2π)/2622 weeks
120-.01687 .00369 (120*2π)/2622 weeks
121.00622 -.00717 (121*2π)/2622 weeks
122.00019 -.01078 (122*2π)/2622 weeks
123.00125 -.00013 (123*2π)/2622 weeks
124.00174 -.00442 (124*2π)/2622 weeks
125.00518 -.00299 (125*2π)/2622 weeks
126-.00084 -.00084 (126*2π)/2622 weeks
127-.00056 .00261 (127*2π)/2622 weeks
128-.00463 .00516 (128*2π)/2622 weeks
129-.00851 -.00288 (129*2π)/2622 weeks
130.00324 .00463 (130*2π)/2622 weeks
131-.002   (131*2π)/2622 weeks
132.00324 -.00463 (132*2π)/2622 weeks
133-.00851 .00288 (133*2π)/2622 weeks
134-.00463 -.00516 (134*2π)/2622 weeks
135-.00056 -.00261 (135*2π)/2622 weeks
136-.00084 .00084 (136*2π)/2622 weeks
137.00518 .00299 (137*2π)/2622 weeks
138.00174 .00442 (138*2π)/2622 weeks
139.00125 .00013 (139*2π)/2622 weeks
140.00019 .01078 (140*2π)/2622 weeks
141.00622 .00717 (141*2π)/2622 weeks
142-.01687 -.00369 (142*2π)/2622 weeks
143.00682 -.00066 (143*2π)/2622 weeks
144-.00456 -.0053 (144*2π)/2622 weeks
145.00261 -.00499 (145*2π)/2622 weeks
146-.00156 .00252 (146*2π)/2622 weeks
147.00678 .00139 (147*2π)/2622 weeks
148.00431 .00801 (148*2π)/2622 weeks
149-.00271 .00141 (149*2π)/2622 weeks
150.00014 -.00261 (150*2π)/2622 weeks
151-.00849 -.0071 (151*2π)/2622 weeks
152-.00231 .00159 (152*2π)/2622 weeks
153.0051 -.00878 (153*2π)/2622 weeks
154.00523 .00019 (154*2π)/2622 weeks
155.00233 .00742 (155*2π)/2622 weeks
156-.00453 .00395 (156*2π)/2622 weeks
157-.00482 -.00167 (157*2π)/2622 weeks
158-.00026 .00404 (158*2π)/2622 weeks
159.00024 -.00474 (159*2π)/2622 weeks
160.00582 -.0073 (160*2π)/2622 weeks
161-.00482 -.00357 (161*2π)/2622 weeks
162.0123 .00277 (162*2π)/2622 weeks
163-.0062 .00237 (163*2π)/2622 weeks
164-.00292 .01407 (164*2π)/2622 weeks
165-.0099 -.00029 (165*2π)/2622 weeks
166-.0016 -.0088 (166*2π)/2622 weeks
167-.00982 -.0059 (167*2π)/2622 weeks
168.00686 .00097 (168*2π)/2622 weeks
169.00318 .00759 (169*2π)/2622 weeks
170-.00895 .0108 (170*2π)/2622 weeks
171-.00283 .00176 (171*2π)/2622 weeks
172-.00385 -.00427 (172*2π)/2622 weeks
173-.00116 -.01358 (173*2π)/2622 weeks
174.00299 -.00491 (174*2π)/2622 weeks
175.00054 -.00984 (175*2π)/2621 weeks
176-.0033 .00608 (176*2π)/2621 weeks
177.00102 .00944 (177*2π)/2621 weeks
178.00151 .00188 (178*2π)/2621 weeks
179.00742 -.00341 (179*2π)/2621 weeks
180-.01328 -.00214 (180*2π)/2621 weeks
181.00461 .0145 (181*2π)/2621 weeks
182-.00878 -.0003 (182*2π)/2621 weeks
183-.00293 .00064 (183*2π)/2621 weeks
184.0055 .00082 (184*2π)/2621 weeks
185.00185 -.00282 (185*2π)/2621 weeks
186.00552 .0065 (186*2π)/2621 weeks
187.00948 -.00039 (187*2π)/2621 weeks
188-.00387 .01199 (188*2π)/2621 weeks
189-.00304 -.00113 (189*2π)/2621 weeks
190.00195 -.00408 (190*2π)/2621 weeks
191-.01716 -.01516 (191*2π)/2621 weeks
192.00506 .00701 (192*2π)/2621 weeks
193.00508 .00831 (193*2π)/2621 weeks
194.00402 .01057 (194*2π)/2621 weeks
195-.01776 -.00455 (195*2π)/2621 weeks
196.00769 -.0101 (196*2π)/2621 weeks
197-.01059 -.00505 (197*2π)/2621 weeks
198.005 -.0004 (198*2π)/2621 weeks
199-.01214 .0097 (199*2π)/2621 weeks
200.00001 .00737 (200*2π)/2621 weeks
201.00306 .00655 (201*2π)/2621 weeks
202-.00302 -.00776 (202*2π)/2621 weeks
203-.01718 .00454 (203*2π)/2621 weeks
204-.0024 -.00081 (204*2π)/2621 weeks
205-.00983 -.00507 (205*2π)/2621 weeks
206-.00819 .00419 (206*2π)/2621 weeks
207.00456 -.00004 (207*2π)/2621 weeks
208.00168 -.00166 (208*2π)/2621 weeks
209-.01351 .0208 (209*2π)/2621 weeks
210-.01918 .01419 (210*2π)/2621 weeks
211.00443 -.01085 (211*2π)/2621 weeks
212.00411 .0122 (212*2π)/2621 weeks
213-.00653 -.00978 (213*2π)/2621 weeks
214-.00283 .00453 (214*2π)/2621 weeks
215.0107 .00891 (215*2π)/2621 weeks
216-.00227 .00835 (216*2π)/2621 weeks
217.00643 .00335 (217*2π)/2621 weeks
218-.00391 -.00109 (218*2π)/2621 weeks
219-.01106 .00049 (219*2π)/2621 weeks
220-.00034 .00741 (220*2π)/2621 weeks
221.00146 -.01011 (221*2π)/2621 weeks
222-.00064 .02215 (222*2π)/2621 weeks
223-.00741 -.00002 (223*2π)/2621 weeks
224.01324 .00932 (224*2π)/2621 weeks
225.00897 -.00459 (225*2π)/2621 weeks
226.00135 -.01255 (226*2π)/2621 weeks
227.00113 .00612 (227*2π)/2621 weeks
228-.00061 -.02372 (228*2π)/2621 weeks
229.00712 -.0052 (229*2π)/2621 weeks
230.00071 .02032 (230*2π)/2621 weeks
231-.00932 .0212 (231*2π)/2621 weeks
232-.02078 .02438 (232*2π)/2621 weeks
233-.00831 .00505 (233*2π)/2621 weeks
234-.01385 -.00734 (234*2π)/2621 weeks
235.00916 -.01065 (235*2π)/2621 weeks
236.0291 .01491 (236*2π)/2621 weeks
237-.00425 .00719 (237*2π)/2621 weeks
238.00587 .02374 (238*2π)/2621 weeks
239-.04506 .00786 (239*2π)/2621 weeks
240.01905 -.00909 (240*2π)/2621 weeks
241-.05921 .0148 (241*2π)/2621 weeks
242.04052 -.015 (242*2π)/2621 weeks
243.0314 .00338 (243*2π)/2621 weeks
244-.02832 -.00383 (244*2π)/2621 weeks
245-.04396 .03283 (245*2π)/2621 weeks
246-.04313 .01903 (246*2π)/2621 weeks
247.02292 -.00325 (247*2π)/2621 weeks
248-.01853 .00576 (248*2π)/2621 weeks
249-.02421 .00044 (249*2π)/2621 weeks
250.01047 -.01331 (250*2π)/2621 weeks
251-.00532 .05142 (251*2π)/2621 weeks
252.05008 .02341 (252*2π)/2621 weeks
253.01379 .04808 (253*2π)/2621 weeks
254.01234 .07385 (254*2π)/2621 weeks
255-.07441 .01599 (255*2π)/2621 weeks
256-.02111 -.11037 (256*2π)/2621 weeks
257-.08287 .11523 (257*2π)/2621 weeks
258.00796 -.14184 (258*2π)/2621 weeks
259.11816 -.107 (259*2π)/2621 weeks
260-.02266 .30075 (260*2π)/2621 weeks



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