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# Fourier Analysis of RPMIX (Royce Pennsylvania Mutual Fd In)

RPMIX (Royce Pennsylvania Mutual Fd In) appears to have interesting cyclic behaviour every 23 weeks (.1782*sine), 30 weeks (.1261*sine), and 28 weeks (.0788*sine).

RPMIX (Royce Pennsylvania Mutual Fd In) has an average price of 8.67 (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 6/3/2011 to 3/20/2017 for RPMIX (Royce Pennsylvania Mutual Fd In), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
08.66574   0
1-.69931 -1.2398 (1*2π)/304304 weeks
2.58065 -.61689 (2*2π)/304152 weeks
3.21903 -.47624 (3*2π)/304101 weeks
4.00295 -.59815 (4*2π)/30476 weeks
5-.09433 -.3076 (5*2π)/30461 weeks
6.11214 -.3044 (6*2π)/30451 weeks
7.14554 -.29226 (7*2π)/30443 weeks
8.05108 -.19056 (8*2π)/30438 weeks
9.07099 -.20243 (9*2π)/30434 weeks
10-.01708 -.12605 (10*2π)/30430 weeks
11-.07683 -.0788 (11*2π)/30428 weeks
12-.0441 -.05977 (12*2π)/30425 weeks
13.04128 -.17818 (13*2π)/30423 weeks
14-.02113 -.11386 (14*2π)/30422 weeks
15-.06212 .01458 (15*2π)/30420 weeks
16-.04471 .01051 (16*2π)/30419 weeks
17.06417 .01064 (17*2π)/30418 weeks
18.01136 -.08245 (18*2π)/30417 weeks
19-.04496 -.03836 (19*2π)/30416 weeks
20-.03357 -.04949 (20*2π)/30415 weeks
21-.0235 -.06638 (21*2π)/30414 weeks
22-.03156 -.05406 (22*2π)/30414 weeks
23-.01082 -.09669 (23*2π)/30413 weeks
24-.0738 -.08777 (24*2π)/30413 weeks
25-.01929 -.07164 (25*2π)/30412 weeks
26-.06799 -.08957 (26*2π)/30412 weeks
27.0166 -.03247 (27*2π)/30411 weeks
28-.05692 -.04392 (28*2π)/30411 weeks
29-.02857 -.04475 (29*2π)/30410 weeks
30-.04135 -.04437 (30*2π)/30410 weeks
31-.06588 -.01788 (31*2π)/30410 weeks
32.00466 -.04038 (32*2π)/30410 weeks
33-.02907 -.01211 (33*2π)/3049 weeks
34-.02495 -.03516 (34*2π)/3049 weeks
35-.03989 -.05427 (35*2π)/3049 weeks
36.02158 -.01874 (36*2π)/3048 weeks
37-.04159 -.08881 (37*2π)/3048 weeks
38-.00581 -.05152 (38*2π)/3048 weeks
39-.00822 -.0603 (39*2π)/3048 weeks
40-.03167 -.06578 (40*2π)/3048 weeks
41-.00594 -.04084 (41*2π)/3047 weeks
42-.0034 -.06039 (42*2π)/3047 weeks
43-.00165 -.0158 (43*2π)/3047 weeks
44.01685 -.04456 (44*2π)/3047 weeks
45-.00048 -.01813 (45*2π)/3047 weeks
46-.00297 .00114 (46*2π)/3047 weeks
47-.01263 -.01313 (47*2π)/3046 weeks
48-.02413 -.00208 (48*2π)/3046 weeks
49.01596 -.01375 (49*2π)/3046 weeks
50-.00352 -.03427 (50*2π)/3046 weeks
51-.00588 -.03364 (51*2π)/3046 weeks
52-.02121 -.03559 (52*2π)/3046 weeks
53-.032 -.04134 (53*2π)/3046 weeks
54-.02572 -.02097 (54*2π)/3046 weeks
55-.01856 -.00337 (55*2π)/3046 weeks
56-.00092 -.02 (56*2π)/3045 weeks
57-.01159 -.03345 (57*2π)/3045 weeks
58-.00162 -.03559 (58*2π)/3045 weeks
59-.02022 .00775 (59*2π)/3045 weeks
60-.00771 -.00941 (60*2π)/3045 weeks
61-.01555 -.0306 (61*2π)/3045 weeks
62-.02409 -.02611 (62*2π)/3045 weeks
63-.00953 -.0289 (63*2π)/3045 weeks
64-.00285 -.00545 (64*2π)/3045 weeks
65-.00483 -.02936 (65*2π)/3045 weeks
66-.00381 -.03459 (66*2π)/3045 weeks
67-.02934 -.01348 (67*2π)/3045 weeks
68-.01762 -.02461 (68*2π)/3044 weeks
69-.0035 .00011 (69*2π)/3044 weeks
70-.0019 -.02019 (70*2π)/3044 weeks
71-.02105 -.0206 (71*2π)/3044 weeks
72-.01645 -.02543 (72*2π)/3044 weeks
73-.03394 -.00438 (73*2π)/3044 weeks
74-.01475 .00626 (74*2π)/3044 weeks
75.0005 -.02781 (75*2π)/3044 weeks
76-.0286 -.02277 (76*2π)/3044 weeks
77-.01903 -.01345 (77*2π)/3044 weeks
78.008 -.00261 (78*2π)/3044 weeks
79.0099 -.00561 (79*2π)/3044 weeks
80.00693 -.02756 (80*2π)/3044 weeks
81-.01001 -.02525 (81*2π)/3044 weeks
82.00137 -.00091 (82*2π)/3044 weeks
83-.00464 -.01004 (83*2π)/3044 weeks
84-.0171 -.01277 (84*2π)/3044 weeks
85-.02754 -.0155 (85*2π)/3044 weeks
86-.02957 -.00973 (86*2π)/3044 weeks
87-.01879 .01083 (87*2π)/3043 weeks
88-.02353 -.01268 (88*2π)/3043 weeks
89-.02102 -.00977 (89*2π)/3043 weeks
90-.01971 -.00985 (90*2π)/3043 weeks
91.00137 -.00131 (91*2π)/3043 weeks
92-.01351 .00152 (92*2π)/3043 weeks
93-.01234 -.00666 (93*2π)/3043 weeks
94-.02247 -.01151 (94*2π)/3043 weeks
95-.00294 -.00763 (95*2π)/3043 weeks
96-.01421 -.01606 (96*2π)/3043 weeks
97-.0182 -.0062 (97*2π)/3043 weeks
98-.01184 -.00234 (98*2π)/3043 weeks
99-.01792 -.00755 (99*2π)/3043 weeks
100-.01469 -.01068 (100*2π)/3043 weeks
101-.02512 -.01505 (101*2π)/3043 weeks
102-.00879 -.00313 (102*2π)/3043 weeks
103-.00524 .00546 (103*2π)/3043 weeks
104-.01821 -.00754 (104*2π)/3043 weeks
105-.01201 .0075 (105*2π)/3043 weeks
106-.00864 .00333 (106*2π)/3043 weeks
107-.02632 -.00068 (107*2π)/3043 weeks
108-.02941 .00897 (108*2π)/3043 weeks
109-.02463 -.01209 (109*2π)/3043 weeks
110-.01735 -.00338 (110*2π)/3043 weeks
111-.02467 -.01413 (111*2π)/3043 weeks
112-.00907 -.02413 (112*2π)/3043 weeks
113-.012 -.02137 (113*2π)/3043 weeks
114-.01549 -.00126 (114*2π)/3043 weeks
115-.00935 -.01203 (115*2π)/3043 weeks
116-.01406 -.00927 (116*2π)/3043 weeks
117-.00917 -.00321 (117*2π)/3043 weeks
118-.00743 -.01332 (118*2π)/3043 weeks
119-.01021 -.00178 (119*2π)/3043 weeks
120-.01686 -.00362 (120*2π)/3043 weeks
121-.00928 -.00245 (121*2π)/3043 weeks
122-.01449 -.0059 (122*2π)/3042 weeks
123-.00391 -.00395 (123*2π)/3042 weeks
124-.01436 -.01114 (124*2π)/3042 weeks
125.0002 -.00449 (125*2π)/3042 weeks
126-.0055 -.01092 (126*2π)/3042 weeks
127-.02744 -.00003 (127*2π)/3042 weeks
128-.01125 .01531 (128*2π)/3042 weeks
129-.00524 .00997 (129*2π)/3042 weeks
130-.00877 .00758 (130*2π)/3042 weeks
131-.00566 .00222 (131*2π)/3042 weeks
132-.01157 .03087 (132*2π)/3042 weeks
133-.01707 .0074 (133*2π)/3042 weeks
134-.01538 -.00298 (134*2π)/3042 weeks
135-.00832 -.00662 (135*2π)/3042 weeks
136-.00452 -.0051 (136*2π)/3042 weeks
137-.01889 -.01823 (137*2π)/3042 weeks
138-.00292 .00477 (138*2π)/3042 weeks
139-.01317 -.01331 (139*2π)/3042 weeks
140-.0101 .00502 (140*2π)/3042 weeks
141-.0093 -.02282 (141*2π)/3042 weeks
142-.00857 -.00694 (142*2π)/3042 weeks
143-.0132 -.01429 (143*2π)/3042 weeks
144-.01528 .00479 (144*2π)/3042 weeks
145-.02352 .01032 (145*2π)/3042 weeks
146-.00532 .00199 (146*2π)/3042 weeks
147-.0004 -.00519 (147*2π)/3042 weeks
148-.01628 .00507 (148*2π)/3042 weeks
149-.01389 .01491 (149*2π)/3042 weeks
150.00502 .01432 (150*2π)/3042 weeks
151-.01093 .00449 (151*2π)/3042 weeks
152-.01832   (152*2π)/3042 weeks
153-.01093 -.00449 (153*2π)/3042 weeks
154.00502 -.01432 (154*2π)/3042 weeks
155-.01389 -.01491 (155*2π)/3042 weeks
156-.01628 -.00507 (156*2π)/3042 weeks
157-.0004 .00519 (157*2π)/3042 weeks
158-.00532 -.00199 (158*2π)/3042 weeks
159-.02352 -.01032 (159*2π)/3042 weeks
160-.01528 -.00479 (160*2π)/3042 weeks
161-.0132 .01429 (161*2π)/3042 weeks
162-.00857 .00694 (162*2π)/3042 weeks
163-.0093 .02282 (163*2π)/3042 weeks
164-.0101 -.00502 (164*2π)/3042 weeks
165-.01317 .01331 (165*2π)/3042 weeks
166-.00292 -.00477 (166*2π)/3042 weeks
167-.01889 .01823 (167*2π)/3042 weeks
168-.00452 .0051 (168*2π)/3042 weeks
169-.00832 .00662 (169*2π)/3042 weeks
170-.01538 .00298 (170*2π)/3042 weeks
171-.01707 -.0074 (171*2π)/3042 weeks
172-.01157 -.03087 (172*2π)/3042 weeks
173-.00566 -.00222 (173*2π)/3042 weeks
174-.00877 -.00758 (174*2π)/3042 weeks
175-.00524 -.00997 (175*2π)/3042 weeks
176-.01125 -.01531 (176*2π)/3042 weeks
177-.02744 .00003 (177*2π)/3042 weeks
178-.0055 .01092 (178*2π)/3042 weeks
179.0002 .00449 (179*2π)/3042 weeks
180-.01436 .01114 (180*2π)/3042 weeks
181-.00391 .00395 (181*2π)/3042 weeks
182-.01449 .0059 (182*2π)/3042 weeks
183-.00928 .00245 (183*2π)/3042 weeks
184-.01686 .00362 (184*2π)/3042 weeks
185-.01021 .00178 (185*2π)/3042 weeks
186-.00743 .01332 (186*2π)/3042 weeks
187-.00917 .00321 (187*2π)/3042 weeks
188-.01406 .00927 (188*2π)/3042 weeks
189-.00935 .01203 (189*2π)/3042 weeks
190-.01549 .00126 (190*2π)/3042 weeks
191-.012 .02137 (191*2π)/3042 weeks
192-.00907 .02413 (192*2π)/3042 weeks
193-.02467 .01413 (193*2π)/3042 weeks
194-.01735 .00338 (194*2π)/3042 weeks
195-.02463 .01209 (195*2π)/3042 weeks
196-.02941 -.00897 (196*2π)/3042 weeks
197-.02632 .00068 (197*2π)/3042 weeks
198-.00864 -.00333 (198*2π)/3042 weeks
199-.01201 -.0075 (199*2π)/3042 weeks
200-.01821 .00754 (200*2π)/3042 weeks
201-.00524 -.00546 (201*2π)/3042 weeks
202-.00879 .00313 (202*2π)/3042 weeks
203-.02512 .01505 (203*2π)/3041 weeks
204-.01469 .01068 (204*2π)/3041 weeks
205-.01792 .00755 (205*2π)/3041 weeks
206-.01184 .00234 (206*2π)/3041 weeks
207-.0182 .0062 (207*2π)/3041 weeks
208-.01421 .01606 (208*2π)/3041 weeks
209-.00294 .00763 (209*2π)/3041 weeks
210-.02247 .01151 (210*2π)/3041 weeks
211-.01234 .00666 (211*2π)/3041 weeks
212-.01351 -.00152 (212*2π)/3041 weeks
213.00137 .00131 (213*2π)/3041 weeks
214-.01971 .00985 (214*2π)/3041 weeks
215-.02102 .00977 (215*2π)/3041 weeks
216-.02353 .01268 (216*2π)/3041 weeks
217-.01879 -.01083 (217*2π)/3041 weeks
218-.02957 .00973 (218*2π)/3041 weeks
219-.02754 .0155 (219*2π)/3041 weeks
220-.0171 .01277 (220*2π)/3041 weeks
221-.00464 .01004 (221*2π)/3041 weeks
222.00137 .00091 (222*2π)/3041 weeks
223-.01001 .02525 (223*2π)/3041 weeks
224.00693 .02756 (224*2π)/3041 weeks
225.0099 .00561 (225*2π)/3041 weeks
226.008 .00261 (226*2π)/3041 weeks
227-.01903 .01345 (227*2π)/3041 weeks
228-.0286 .02277 (228*2π)/3041 weeks
229.0005 .02781 (229*2π)/3041 weeks
230-.01475 -.00626 (230*2π)/3041 weeks
231-.03394 .00438 (231*2π)/3041 weeks
232-.01645 .02543 (232*2π)/3041 weeks
233-.02105 .0206 (233*2π)/3041 weeks
234-.0019 .02019 (234*2π)/3041 weeks
235-.0035 -.00011 (235*2π)/3041 weeks
236-.01762 .02461 (236*2π)/3041 weeks
237-.02934 .01348 (237*2π)/3041 weeks
238-.00381 .03459 (238*2π)/3041 weeks
239-.00483 .02936 (239*2π)/3041 weeks
240-.00285 .00545 (240*2π)/3041 weeks
241-.00953 .0289 (241*2π)/3041 weeks
242-.02409 .02611 (242*2π)/3041 weeks
243-.01555 .0306 (243*2π)/3041 weeks
244-.00771 .00941 (244*2π)/3041 weeks
245-.02022 -.00775 (245*2π)/3041 weeks
246-.00162 .03559 (246*2π)/3041 weeks
247-.01159 .03345 (247*2π)/3041 weeks
248-.00092 .02 (248*2π)/3041 weeks
249-.01856 .00337 (249*2π)/3041 weeks
250-.02572 .02097 (250*2π)/3041 weeks
251-.032 .04134 (251*2π)/3041 weeks
252-.02121 .03559 (252*2π)/3041 weeks
253-.00588 .03364 (253*2π)/3041 weeks
254-.00352 .03427 (254*2π)/3041 weeks
255.01596 .01375 (255*2π)/3041 weeks
256-.02413 .00208 (256*2π)/3041 weeks
257-.01263 .01313 (257*2π)/3041 weeks
258-.00297 -.00114 (258*2π)/3041 weeks
259-.00048 .01813 (259*2π)/3041 weeks
260.01685 .04456 (260*2π)/3041 weeks
261-.00165 .0158 (261*2π)/3041 weeks
262-.0034 .06039 (262*2π)/3041 weeks
263-.00594 .04084 (263*2π)/3041 weeks
264-.03167 .06578 (264*2π)/3041 weeks
265-.00822 .0603 (265*2π)/3041 weeks
266-.00581 .05152 (266*2π)/3041 weeks
267-.04159 .08881 (267*2π)/3041 weeks
268.02158 .01874 (268*2π)/3041 weeks
269-.03989 .05427 (269*2π)/3041 weeks
270-.02495 .03516 (270*2π)/3041 weeks
271-.02907 .01211 (271*2π)/3041 weeks
272.00466 .04038 (272*2π)/3041 weeks
273-.06588 .01788 (273*2π)/3041 weeks
274-.04135 .04437 (274*2π)/3041 weeks
275-.02857 .04475 (275*2π)/3041 weeks
276-.05692 .04392 (276*2π)/3041 weeks
277.0166 .03247 (277*2π)/3041 weeks
278-.06799 .08957 (278*2π)/3041 weeks
279-.01929 .07164 (279*2π)/3041 weeks
280-.0738 .08777 (280*2π)/3041 weeks
281-.01082 .09669 (281*2π)/3041 weeks
282-.03156 .05406 (282*2π)/3041 weeks
283-.0235 .06638 (283*2π)/3041 weeks
284-.03357 .04949 (284*2π)/3041 weeks
285-.04496 .03836 (285*2π)/3041 weeks
286.01136 .08245 (286*2π)/3041 weeks
287.06417 -.01064 (287*2π)/3041 weeks
288-.04471 -.01051 (288*2π)/3041 weeks
289-.06212 -.01458 (289*2π)/3041 weeks
290-.02113 .11386 (290*2π)/3041 weeks
291.04128 .17818 (291*2π)/3041 weeks
292-.0441 .05977 (292*2π)/3041 weeks
293-.07683 .0788 (293*2π)/3041 weeks
294-.01708 .12605 (294*2π)/3041 weeks
295.07099 .20243 (295*2π)/3041 weeks
296.05108 .19056 (296*2π)/3041 weeks
297.14554 .29226 (297*2π)/3041 weeks
298.11214 .3044 (298*2π)/3041 weeks
299-.09433 .3076 (299*2π)/3041 weeks
300.00295 .59815 (300*2π)/3041 weeks
301.21903 .47624 (301*2π)/3041 weeks
302.58065 .61689 (302*2π)/3041 weeks