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# Fourier Analysis of RPGAX (T. ROWE PRICE GLOBAL ALLOCATION FUND)

RPGAX (T. ROWE PRICE GLOBAL ALLOCATION FUND) appears to have interesting cyclic behaviour every 21 weeks (.1253*sine), 17 weeks (.0932*sine), and 19 weeks (.0412*cosine).

RPGAX (T. ROWE PRICE GLOBAL ALLOCATION FUND) has an average price of 11.04 (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 1/2/2014 to 4/23/2018 for RPGAX (T. ROWE PRICE GLOBAL ALLOCATION FUND), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
011.03962   0
1.51801 -.70058 (1*2π)/226226 weeks
2-.13255 -.57243 (2*2π)/226113 weeks
3.05341 -.39162 (3*2π)/22675 weeks
4-.12835 -.13133 (4*2π)/22657 weeks
5-.03548 -.24221 (5*2π)/22645 weeks
6-.0563 -.21911 (6*2π)/22638 weeks
7.00869 -.10255 (7*2π)/22632 weeks
8-.03548 -.09625 (8*2π)/22628 weeks
9.00981 -.12542 (9*2π)/22625 weeks
10-.02533 -.00893 (10*2π)/22623 weeks
11-.00621 -.12535 (11*2π)/22621 weeks
12-.04124 -.01372 (12*2π)/22619 weeks
13-.02195 -.09318 (13*2π)/22617 weeks
14.01628 -.03079 (14*2π)/22616 weeks
15-.01421 -.06303 (15*2π)/22615 weeks
16-.01421 -.05859 (16*2π)/22614 weeks
17-.0172 -.05672 (17*2π)/22613 weeks
18-.01364 -.07609 (18*2π)/22613 weeks
19.01518 -.08178 (19*2π)/22612 weeks
20.0029 -.02671 (20*2π)/22611 weeks
21-.03872 -.03706 (21*2π)/22611 weeks
22-.00449 -.02733 (22*2π)/22610 weeks
23-.02955 -.05745 (23*2π)/22610 weeks
24-.00656 -.0408 (24*2π)/2269 weeks
25-.00275 -.03299 (25*2π)/2269 weeks
26-.00762 -.02059 (26*2π)/2269 weeks
27.00719 -.00627 (27*2π)/2268 weeks
28-.00473 -.02366 (28*2π)/2268 weeks
29-.00819 -.03176 (29*2π)/2268 weeks
30.01145 -.03725 (30*2π)/2268 weeks
31.00608 -.02629 (31*2π)/2267 weeks
32.00012 -.0253 (32*2π)/2267 weeks
33-.00743 -.0284 (33*2π)/2267 weeks
34.00227 -.03622 (34*2π)/2267 weeks
35-.0218 -.03952 (35*2π)/2266 weeks
36-.01393 -.01872 (36*2π)/2266 weeks
37-.03579 -.03084 (37*2π)/2266 weeks
38-.01494 -.00957 (38*2π)/2266 weeks
39-.01462 -.01962 (39*2π)/2266 weeks
40-.02087 -.01099 (40*2π)/2266 weeks
41-.01071 -.03268 (41*2π)/2266 weeks
42-.0255 .01022 (42*2π)/2265 weeks
43-.00865 -.01803 (43*2π)/2265 weeks
44-.01396 .00071 (44*2π)/2265 weeks
45-.02979 -.01795 (45*2π)/2265 weeks
46-.00316 -.01561 (46*2π)/2265 weeks
47-.01893 -.01867 (47*2π)/2265 weeks
48-.0016 -.01744 (48*2π)/2265 weeks
49-.02272 -.00584 (49*2π)/2265 weeks
50-.00993 -.01981 (50*2π)/2265 weeks
51-.02335 -.00959 (51*2π)/2264 weeks
52-.01123 -.03071 (52*2π)/2264 weeks
53-.01012 -.01692 (53*2π)/2264 weeks
54-.0047 -.00876 (54*2π)/2264 weeks
55-.02569 .00457 (55*2π)/2264 weeks
56-.01964 -.02214 (56*2π)/2264 weeks
57-.00257 -.00592 (57*2π)/2264 weeks
58-.02833 -.01056 (58*2π)/2264 weeks
59-.00804 .00444 (59*2π)/2264 weeks
60-.0228 -.01006 (60*2π)/2264 weeks
61-.01031 -.01068 (61*2π)/2264 weeks
62-.01014 -.00299 (62*2π)/2264 weeks
63-.00893 -.01303 (63*2π)/2264 weeks
64-.01497 -.00202 (64*2π)/2264 weeks
65-.0053 -.00856 (65*2π)/2263 weeks
66-.01007 -.01623 (66*2π)/2263 weeks
67-.01821 -.01555 (67*2π)/2263 weeks
68-.00661 -.01423 (68*2π)/2263 weeks
69-.01061 -.01832 (69*2π)/2263 weeks
70-.01548 -.0194 (70*2π)/2263 weeks
71-.00734 -.02375 (71*2π)/2263 weeks
72-.02421 -.01102 (72*2π)/2263 weeks
73-.02184 -.01544 (73*2π)/2263 weeks
74-.02615 -.00535 (74*2π)/2263 weeks
75-.0218 -.00725 (75*2π)/2263 weeks
76-.01121 -.00299 (76*2π)/2263 weeks
77-.02048 .00113 (77*2π)/2263 weeks
78-.01552 -.0061 (78*2π)/2263 weeks
79-.00693 .00157 (79*2π)/2263 weeks
80-.01342 .01108 (80*2π)/2263 weeks
81-.00866 -.00729 (81*2π)/2263 weeks
82-.01278 .00172 (82*2π)/2263 weeks
83-.0103 -.00495 (83*2π)/2263 weeks
84-.01287 -.00337 (84*2π)/2263 weeks
85-.0074 -.00575 (85*2π)/2263 weeks
86-.00354 -.00361 (86*2π)/2263 weeks
87-.00793 .00095 (87*2π)/2263 weeks
88-.01697 -.00532 (88*2π)/2263 weeks
89-.00719 -.01323 (89*2π)/2263 weeks
90-.00597 -.00412 (90*2π)/2263 weeks
91-.01438 -.00305 (91*2π)/2262 weeks
92-.0111 -.00571 (92*2π)/2262 weeks
93-.01246 -.00683 (93*2π)/2262 weeks
94-.00588 -.00755 (94*2π)/2262 weeks
95-.01844 .0028 (95*2π)/2262 weeks
96-.0089 -.00515 (96*2π)/2262 weeks
97-.01153 -.0063 (97*2π)/2262 weeks
98-.02091 -.00196 (98*2π)/2262 weeks
99-.00371 -.00889 (99*2π)/2262 weeks
100-.01207 -.00576 (100*2π)/2262 weeks
101-.02216 -.00443 (101*2π)/2262 weeks
102-.00598 -.00901 (102*2π)/2262 weeks
103-.00901 -.00642 (103*2π)/2262 weeks
104-.00516 -.00606 (104*2π)/2262 weeks
105-.0123 .00267 (105*2π)/2262 weeks
106-.00912 -.00431 (106*2π)/2262 weeks
107-.02201 -.00103 (107*2π)/2262 weeks
108-.00252 .00087 (108*2π)/2262 weeks
109-.02271 -.00058 (109*2π)/2262 weeks
110-.01126 -.00599 (110*2π)/2262 weeks
111-.01138 .00794 (111*2π)/2262 weeks
112-.01964 -.00642 (112*2π)/2262 weeks
113-.01436   (113*2π)/2262 weeks
114-.01964 .00642 (114*2π)/2262 weeks
115-.01138 -.00794 (115*2π)/2262 weeks
116-.01126 .00599 (116*2π)/2262 weeks
117-.02271 .00058 (117*2π)/2262 weeks
118-.00252 -.00087 (118*2π)/2262 weeks
119-.02201 .00103 (119*2π)/2262 weeks
120-.00912 .00431 (120*2π)/2262 weeks
121-.0123 -.00267 (121*2π)/2262 weeks
122-.00516 .00606 (122*2π)/2262 weeks
123-.00901 .00642 (123*2π)/2262 weeks
124-.00598 .00901 (124*2π)/2262 weeks
125-.02216 .00443 (125*2π)/2262 weeks
126-.01207 .00576 (126*2π)/2262 weeks
127-.00371 .00889 (127*2π)/2262 weeks
128-.02091 .00196 (128*2π)/2262 weeks
129-.01153 .0063 (129*2π)/2262 weeks
130-.0089 .00515 (130*2π)/2262 weeks
131-.01844 -.0028 (131*2π)/2262 weeks
132-.00588 .00755 (132*2π)/2262 weeks
133-.01246 .00683 (133*2π)/2262 weeks
134-.0111 .00571 (134*2π)/2262 weeks
135-.01438 .00305 (135*2π)/2262 weeks
136-.00597 .00412 (136*2π)/2262 weeks
137-.00719 .01323 (137*2π)/2262 weeks
138-.01697 .00532 (138*2π)/2262 weeks
139-.00793 -.00095 (139*2π)/2262 weeks
140-.00354 .00361 (140*2π)/2262 weeks
141-.0074 .00575 (141*2π)/2262 weeks
142-.01287 .00337 (142*2π)/2262 weeks
143-.0103 .00495 (143*2π)/2262 weeks
144-.01278 -.00172 (144*2π)/2262 weeks
145-.00866 .00729 (145*2π)/2262 weeks
146-.01342 -.01108 (146*2π)/2262 weeks
147-.00693 -.00157 (147*2π)/2262 weeks
148-.01552 .0061 (148*2π)/2262 weeks
149-.02048 -.00113 (149*2π)/2262 weeks
150-.01121 .00299 (150*2π)/2262 weeks
151-.0218 .00725 (151*2π)/2261 weeks
152-.02615 .00535 (152*2π)/2261 weeks
153-.02184 .01544 (153*2π)/2261 weeks
154-.02421 .01102 (154*2π)/2261 weeks
155-.00734 .02375 (155*2π)/2261 weeks
156-.01548 .0194 (156*2π)/2261 weeks
157-.01061 .01832 (157*2π)/2261 weeks
158-.00661 .01423 (158*2π)/2261 weeks
159-.01821 .01555 (159*2π)/2261 weeks
160-.01007 .01623 (160*2π)/2261 weeks
161-.0053 .00856 (161*2π)/2261 weeks
162-.01497 .00202 (162*2π)/2261 weeks
163-.00893 .01303 (163*2π)/2261 weeks
164-.01014 .00299 (164*2π)/2261 weeks
165-.01031 .01068 (165*2π)/2261 weeks
166-.0228 .01006 (166*2π)/2261 weeks
167-.00804 -.00444 (167*2π)/2261 weeks
168-.02833 .01056 (168*2π)/2261 weeks
169-.00257 .00592 (169*2π)/2261 weeks
170-.01964 .02214 (170*2π)/2261 weeks
171-.02569 -.00457 (171*2π)/2261 weeks
172-.0047 .00876 (172*2π)/2261 weeks
173-.01012 .01692 (173*2π)/2261 weeks
174-.01123 .03071 (174*2π)/2261 weeks
175-.02335 .00959 (175*2π)/2261 weeks
176-.00993 .01981 (176*2π)/2261 weeks
177-.02272 .00584 (177*2π)/2261 weeks
178-.0016 .01744 (178*2π)/2261 weeks
179-.01893 .01867 (179*2π)/2261 weeks
180-.00316 .01561 (180*2π)/2261 weeks
181-.02979 .01795 (181*2π)/2261 weeks
182-.01396 -.00071 (182*2π)/2261 weeks
183-.00865 .01803 (183*2π)/2261 weeks
184-.0255 -.01022 (184*2π)/2261 weeks
185-.01071 .03268 (185*2π)/2261 weeks
186-.02087 .01099 (186*2π)/2261 weeks
187-.01462 .01962 (187*2π)/2261 weeks
188-.01494 .00957 (188*2π)/2261 weeks
189-.03579 .03084 (189*2π)/2261 weeks
190-.01393 .01872 (190*2π)/2261 weeks
191-.0218 .03952 (191*2π)/2261 weeks
192.00227 .03622 (192*2π)/2261 weeks
193-.00743 .0284 (193*2π)/2261 weeks
194.00012 .0253 (194*2π)/2261 weeks
195.00608 .02629 (195*2π)/2261 weeks
196.01145 .03725 (196*2π)/2261 weeks
197-.00819 .03176 (197*2π)/2261 weeks
198-.00473 .02366 (198*2π)/2261 weeks
199.00719 .00627 (199*2π)/2261 weeks
200-.00762 .02059 (200*2π)/2261 weeks
201-.00275 .03299 (201*2π)/2261 weeks
202-.00656 .0408 (202*2π)/2261 weeks
203-.02955 .05745 (203*2π)/2261 weeks
204-.00449 .02733 (204*2π)/2261 weeks
205-.03872 .03706 (205*2π)/2261 weeks
206.0029 .02671 (206*2π)/2261 weeks
207.01518 .08178 (207*2π)/2261 weeks
208-.01364 .07609 (208*2π)/2261 weeks
209-.0172 .05672 (209*2π)/2261 weeks
210-.01421 .05859 (210*2π)/2261 weeks
211-.01421 .06303 (211*2π)/2261 weeks
212.01628 .03079 (212*2π)/2261 weeks
213-.02195 .09318 (213*2π)/2261 weeks
214-.04124 .01372 (214*2π)/2261 weeks
215-.00621 .12535 (215*2π)/2261 weeks
216-.02533 .00893 (216*2π)/2261 weeks
217.00981 .12542 (217*2π)/2261 weeks
218-.03548 .09625 (218*2π)/2261 weeks
219.00869 .10255 (219*2π)/2261 weeks
220-.0563 .21911 (220*2π)/2261 weeks
221-.03548 .24221 (221*2π)/2261 weeks
222-.12835 .13133 (222*2π)/2261 weeks
223.05341 .39162 (223*2π)/2261 weeks
224-.13255 .57243 (224*2π)/2261 weeks