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Fourier Analysis of VTIPX (Vanguard Short-Term Inflation-P)


VTIPX (Vanguard Short-Term Inflation-P) appears to have interesting cyclic behaviour every 13 weeks (.0253*cosine), 17 weeks (.0252*sine), and 12 weeks (.0231*cosine).

VTIPX (Vanguard Short-Term Inflation-P) has an average price of 24.43 (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 1/17/2017 for VTIPX (Vanguard Short-Term Inflation-P), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
024.43455   0 
1.1716 .17552 (1*2π)/223223 weeks
2.13714 -.08568 (2*2π)/223112 weeks
3.02657 .06282 (3*2π)/22374 weeks
4-.09893 .00748 (4*2π)/22356 weeks
5.00548 .06937 (5*2π)/22345 weeks
6-.04939 -.0085 (6*2π)/22337 weeks
7.00518 -.0258 (7*2π)/22332 weeks
8.00609 -.01634 (8*2π)/22328 weeks
9-.00565 .01117 (9*2π)/22325 weeks
10.02176 .01248 (10*2π)/22322 weeks
11-.00922 .01085 (11*2π)/22320 weeks
12-.00844 .00348 (12*2π)/22319 weeks
13.00759 .0252 (13*2π)/22317 weeks
14-.00832 .00091 (14*2π)/22316 weeks
15.00879 -.0031 (15*2π)/22315 weeks
16.02097 -.01639 (16*2π)/22314 weeks
17.0253 .00603 (17*2π)/22313 weeks
18-.02312 -.01696 (18*2π)/22312 weeks
19-.00137 .01295 (19*2π)/22312 weeks
20-.01189 -.02017 (20*2π)/22311 weeks
21.00282 -.0028 (21*2π)/22311 weeks
22.01336 -.01257 (22*2π)/22310 weeks
23.00317 .00693 (23*2π)/22310 weeks
24-.00964 .00202 (24*2π)/2239 weeks
25-.01007 -.0005 (25*2π)/2239 weeks
26-.00217 -.01005 (26*2π)/2239 weeks
27.00398 -.01091 (27*2π)/2238 weeks
28.00747 .00063 (28*2π)/2238 weeks
29.00107 .00864 (29*2π)/2238 weeks
30.00574 -.00739 (30*2π)/2237 weeks
31-.00198 -.00212 (31*2π)/2237 weeks
32-.00063 -.00335 (32*2π)/2237 weeks
33-.00235 .00693 (33*2π)/2237 weeks
34.00055 -.00764 (34*2π)/2237 weeks
35-.00005 .00768 (35*2π)/2236 weeks
36.00128 .0017 (36*2π)/2236 weeks
37.001 -.00284 (37*2π)/2236 weeks
38-.00082 -.00452 (38*2π)/2236 weeks
39-.00175 -.00308 (39*2π)/2236 weeks
40.00555 -.00276 (40*2π)/2236 weeks
41.00256 -.0012 (41*2π)/2235 weeks
42-.00851 -.00021 (42*2π)/2235 weeks
43.0022 .00031 (43*2π)/2235 weeks
44-.01496 .00284 (44*2π)/2235 weeks
45-.00732 -.00463 (45*2π)/2235 weeks
46.00299 .00302 (46*2π)/2235 weeks
47.00349 .00356 (47*2π)/2235 weeks
48.00183 .00279 (48*2π)/2235 weeks
49-.00276 -.00087 (49*2π)/2235 weeks
50-.00867 .00284 (50*2π)/2234 weeks
51-.0003 .00386 (51*2π)/2234 weeks
52.00321 -.00215 (52*2π)/2234 weeks
53.00221 .00234 (53*2π)/2234 weeks
54.00336 -.0068 (54*2π)/2234 weeks
55.00132 .00268 (55*2π)/2234 weeks
56.00475 -.00112 (56*2π)/2234 weeks
57-.00864 .00257 (57*2π)/2234 weeks
58.00241 -.00515 (58*2π)/2234 weeks
59.00423 -.00198 (59*2π)/2234 weeks
60.00758 .00592 (60*2π)/2234 weeks
61.00057 -.00496 (61*2π)/2234 weeks
62-.00219 .00002 (62*2π)/2234 weeks
63-.0011 -.00962 (63*2π)/2234 weeks
64.00116 -.00013 (64*2π)/2233 weeks
65.00484 -.00193 (65*2π)/2233 weeks
66-.0002 -.00303 (66*2π)/2233 weeks
67-.00055 .00034 (67*2π)/2233 weeks
68-.00247 -.00046 (68*2π)/2233 weeks
69.00579 -.00484 (69*2π)/2233 weeks
70-.005 -.00604 (70*2π)/2233 weeks
71-.00379 -.00012 (71*2π)/2233 weeks
72-.00362 -.00264 (72*2π)/2233 weeks
73.00017 -.00034 (73*2π)/2233 weeks
74.00511 .00271 (74*2π)/2233 weeks
75.00367 -.00033 (75*2π)/2233 weeks
76-.00413 .00545 (76*2π)/2233 weeks
77-.00515 .0035 (77*2π)/2233 weeks
78-.00431 -.00069 (78*2π)/2233 weeks
79.00202 -.00569 (79*2π)/2233 weeks
80.00296 .00041 (80*2π)/2233 weeks
81-.00219 .00029 (81*2π)/2233 weeks
82-.00305 .00372 (82*2π)/2233 weeks
83-.00655 -.00255 (83*2π)/2233 weeks
84.00087 .0008 (84*2π)/2233 weeks
85.00555 -.00332 (85*2π)/2233 weeks
86-.00091 .0005 (86*2π)/2233 weeks
87.00128 .00375 (87*2π)/2233 weeks
88-.00245 .00119 (88*2π)/2233 weeks
89.00035 .00235 (89*2π)/2233 weeks
90.0003 -.00059 (90*2π)/2232 weeks
91.00054 -.00372 (91*2π)/2232 weeks
92.00355 .00171 (92*2π)/2232 weeks
93.00051 .00469 (93*2π)/2232 weeks
94.00402 .0028 (94*2π)/2232 weeks
95-.00174 -.00226 (95*2π)/2232 weeks
96-.0032 -.00084 (96*2π)/2232 weeks
97.00146 -.00477 (97*2π)/2232 weeks
98.0047 .00019 (98*2π)/2232 weeks
99.00209 -.00186 (99*2π)/2232 weeks
100-.00083 .00242 (100*2π)/2232 weeks
101-.00015 -.00315 (101*2π)/2232 weeks
102-.00648 .00496 (102*2π)/2232 weeks
103.00363 -.00373 (103*2π)/2232 weeks
104.00189 -.00541 (104*2π)/2232 weeks
105.00064 -.00037 (105*2π)/2232 weeks
106.00114 -.00225 (106*2π)/2232 weeks
107.00096 .00201 (107*2π)/2232 weeks
108-.00012 .00158 (108*2π)/2232 weeks
109-.00003 .0024 (109*2π)/2232 weeks
110.00027 -.00401 (110*2π)/2232 weeks
111-.00199 .00166 (111*2π)/2232 weeks
112-.00199 -.00166 (112*2π)/2232 weeks
113.00027 .00401 (113*2π)/2232 weeks
114-.00003 -.0024 (114*2π)/2232 weeks
115-.00012 -.00158 (115*2π)/2232 weeks
116.00096 -.00201 (116*2π)/2232 weeks
117.00114 .00225 (117*2π)/2232 weeks
118.00064 .00037 (118*2π)/2232 weeks
119.00189 .00541 (119*2π)/2232 weeks
120.00363 .00373 (120*2π)/2232 weeks
121-.00648 -.00496 (121*2π)/2232 weeks
122-.00015 .00315 (122*2π)/2232 weeks
123-.00083 -.00242 (123*2π)/2232 weeks
124.00209 .00186 (124*2π)/2232 weeks
125.0047 -.00019 (125*2π)/2232 weeks
126.00146 .00477 (126*2π)/2232 weeks
127-.0032 .00084 (127*2π)/2232 weeks
128-.00174 .00226 (128*2π)/2232 weeks
129.00402 -.0028 (129*2π)/2232 weeks
130.00051 -.00469 (130*2π)/2232 weeks
131.00355 -.00171 (131*2π)/2232 weeks
132.00054 .00372 (132*2π)/2232 weeks
133.0003 .00059 (133*2π)/2232 weeks
134.00035 -.00235 (134*2π)/2232 weeks
135-.00245 -.00119 (135*2π)/2232 weeks
136.00128 -.00375 (136*2π)/2232 weeks
137-.00091 -.0005 (137*2π)/2232 weeks
138.00555 .00332 (138*2π)/2232 weeks
139.00087 -.0008 (139*2π)/2232 weeks
140-.00655 .00255 (140*2π)/2232 weeks
141-.00305 -.00372 (141*2π)/2232 weeks
142-.00219 -.00029 (142*2π)/2232 weeks
143.00296 -.00041 (143*2π)/2232 weeks
144.00202 .00569 (144*2π)/2232 weeks
145-.00431 .00069 (145*2π)/2232 weeks
146-.00515 -.0035 (146*2π)/2232 weeks
147-.00413 -.00545 (147*2π)/2232 weeks
148.00367 .00033 (148*2π)/2232 weeks
149.00511 -.00271 (149*2π)/2231 weeks
150.00017 .00034 (150*2π)/2231 weeks
151-.00362 .00264 (151*2π)/2231 weeks
152-.00379 .00012 (152*2π)/2231 weeks
153-.005 .00604 (153*2π)/2231 weeks
154.00579 .00484 (154*2π)/2231 weeks
155-.00247 .00046 (155*2π)/2231 weeks
156-.00055 -.00034 (156*2π)/2231 weeks
157-.0002 .00303 (157*2π)/2231 weeks
158.00484 .00193 (158*2π)/2231 weeks
159.00116 .00013 (159*2π)/2231 weeks
160-.0011 .00962 (160*2π)/2231 weeks
161-.00219 -.00002 (161*2π)/2231 weeks
162.00057 .00496 (162*2π)/2231 weeks
163.00758 -.00592 (163*2π)/2231 weeks
164.00423 .00198 (164*2π)/2231 weeks
165.00241 .00515 (165*2π)/2231 weeks
166-.00864 -.00257 (166*2π)/2231 weeks
167.00475 .00112 (167*2π)/2231 weeks
168.00132 -.00268 (168*2π)/2231 weeks
169.00336 .0068 (169*2π)/2231 weeks
170.00221 -.00234 (170*2π)/2231 weeks
171.00321 .00215 (171*2π)/2231 weeks
172-.0003 -.00386 (172*2π)/2231 weeks
173-.00867 -.00284 (173*2π)/2231 weeks
174-.00276 .00087 (174*2π)/2231 weeks
175.00183 -.00279 (175*2π)/2231 weeks
176.00349 -.00356 (176*2π)/2231 weeks
177.00299 -.00302 (177*2π)/2231 weeks
178-.00732 .00463 (178*2π)/2231 weeks
179-.01496 -.00284 (179*2π)/2231 weeks
180.0022 -.00031 (180*2π)/2231 weeks
181-.00851 .00021 (181*2π)/2231 weeks
182.00256 .0012 (182*2π)/2231 weeks
183.00555 .00276 (183*2π)/2231 weeks
184-.00175 .00308 (184*2π)/2231 weeks
185-.00082 .00452 (185*2π)/2231 weeks
186.001 .00284 (186*2π)/2231 weeks
187.00128 -.0017 (187*2π)/2231 weeks
188-.00005 -.00768 (188*2π)/2231 weeks
189.00055 .00764 (189*2π)/2231 weeks
190-.00235 -.00693 (190*2π)/2231 weeks
191-.00063 .00335 (191*2π)/2231 weeks
192-.00198 .00212 (192*2π)/2231 weeks
193.00574 .00739 (193*2π)/2231 weeks
194.00107 -.00864 (194*2π)/2231 weeks
195.00747 -.00063 (195*2π)/2231 weeks
196.00398 .01091 (196*2π)/2231 weeks
197-.00217 .01005 (197*2π)/2231 weeks
198-.01007 .0005 (198*2π)/2231 weeks
199-.00964 -.00202 (199*2π)/2231 weeks
200.00317 -.00693 (200*2π)/2231 weeks
201.01336 .01257 (201*2π)/2231 weeks
202.00282 .0028 (202*2π)/2231 weeks
203-.01189 .02017 (203*2π)/2231 weeks
204-.00137 -.01295 (204*2π)/2231 weeks
205-.02312 .01696 (205*2π)/2231 weeks
206.0253 -.00603 (206*2π)/2231 weeks
207.02097 .01639 (207*2π)/2231 weeks
208.00879 .0031 (208*2π)/2231 weeks
209-.00832 -.00091 (209*2π)/2231 weeks
210.00759 -.0252 (210*2π)/2231 weeks
211-.00844 -.00348 (211*2π)/2231 weeks
212-.00922 -.01085 (212*2π)/2231 weeks
213.02176 -.01248 (213*2π)/2231 weeks
214-.00565 -.01117 (214*2π)/2231 weeks
215.00609 .01634 (215*2π)/2231 weeks
216.00518 .0258 (216*2π)/2231 weeks
217-.04939 .0085 (217*2π)/2231 weeks
218.00548 -.06937 (218*2π)/2231 weeks
219-.09893 -.00748 (219*2π)/2231 weeks
220.02657 -.06282 (220*2π)/2231 weeks
221.13714 .08568 (221*2π)/2231 weeks

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