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# Fourier Analysis of PXNIX (PAX MSCI EAFE ESG LEADERS INDEX FUND INSTITUTIONAL CLASS)

PXNIX (PAX MSCI EAFE ESG LEADERS INDEX FUND INSTITUTIONAL CLASS) appears to have interesting cyclic behaviour every 21 weeks (.1153*sine), 25 weeks (.1019*sine), and 33 weeks (.0975*sine).

PXNIX (PAX MSCI EAFE ESG LEADERS INDEX FUND INSTITUTIONAL CLASS) has an average price of 7.32 (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 1/3/2012 to 4/16/2018 for PXNIX (PAX MSCI EAFE ESG LEADERS INDEX FUND INSTITUTIONAL CLASS), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
07.3214   0
1-.37391 -.74069 (1*2π)/329329 weeks
2.29204 -.94783 (2*2π)/329165 weeks
3-.00411 -.55269 (3*2π)/329110 weeks
4-.03275 -.35694 (4*2π)/32982 weeks
5.03753 -.38204 (5*2π)/32966 weeks
6-.03123 -.05813 (6*2π)/32955 weeks
7.02762 -.25394 (7*2π)/32947 weeks
8.02105 -.10405 (8*2π)/32941 weeks
9-.09322 -.18074 (9*2π)/32937 weeks
10.01035 -.09746 (10*2π)/32933 weeks
11-.00642 -.06413 (11*2π)/32930 weeks
12-.08638 -.04925 (12*2π)/32927 weeks
13-.01318 -.10188 (13*2π)/32925 weeks
14-.08523 -.06877 (14*2π)/32924 weeks
15-.03561 -.03365 (15*2π)/32922 weeks
16-.0075 -.11529 (16*2π)/32921 weeks
17-.08055 -.08824 (17*2π)/32919 weeks
18-.01325 -.03883 (18*2π)/32918 weeks
19.01397 -.07774 (19*2π)/32917 weeks
20-.00791 -.0196 (20*2π)/32916 weeks
21-.01227 -.06645 (21*2π)/32916 weeks
22-.01048 -.0555 (22*2π)/32915 weeks
23-.00287 -.06358 (23*2π)/32914 weeks
24.00806 -.06566 (24*2π)/32914 weeks
25.0025 -.03179 (25*2π)/32913 weeks
26-.00093 -.05508 (26*2π)/32913 weeks
27-.02087 -.04831 (27*2π)/32912 weeks
28.02243 -.07666 (28*2π)/32912 weeks
29-.02995 -.00327 (29*2π)/32911 weeks
30-.02349 -.07802 (30*2π)/32911 weeks
31-.04677 -.04649 (31*2π)/32911 weeks
32-.01835 -.03646 (32*2π)/32910 weeks
33.00781 -.04654 (33*2π)/32910 weeks
34-.03936 -.03797 (34*2π)/32910 weeks
35-.01849 -.0555 (35*2π)/3299 weeks
36-.01915 -.04389 (36*2π)/3299 weeks
37-.01646 -.03889 (37*2π)/3299 weeks
38-.01811 -.02561 (38*2π)/3299 weeks
39-.02282 -.0208 (39*2π)/3298 weeks
40.00411 -.03081 (40*2π)/3298 weeks
41.00087 -.0261 (41*2π)/3298 weeks
42.004 -.01813 (42*2π)/3298 weeks
43-.01873 -.01193 (43*2π)/3298 weeks
44-.00464 -.0301 (44*2π)/3297 weeks
45-.00695 -.01117 (45*2π)/3297 weeks
46-.02798 -.03087 (46*2π)/3297 weeks
47.00893 -.03743 (47*2π)/3297 weeks
48-.014 -.02298 (48*2π)/3297 weeks
49-.02383 -.0199 (49*2π)/3297 weeks
50-.00558 -.03483 (50*2π)/3297 weeks
51-.0088 -.03972 (51*2π)/3296 weeks
52-.02679 -.04427 (52*2π)/3296 weeks
53.00839 -.03977 (53*2π)/3296 weeks
54-.01322 -.03815 (54*2π)/3296 weeks
55-.03285 -.0245 (55*2π)/3296 weeks
56-.00137 -.02481 (56*2π)/3296 weeks
57-.013 -.01399 (57*2π)/3296 weeks
58-.03145 -.03248 (58*2π)/3296 weeks
59-.00545 -.01075 (59*2π)/3296 weeks
60-.00356 -.02813 (60*2π)/3295 weeks
61-.04529 -.02893 (61*2π)/3295 weeks
62-.00405 -.01375 (62*2π)/3295 weeks
63-.00358 -.01686 (63*2π)/3295 weeks
64-.02405 -.01211 (64*2π)/3295 weeks
65.0018 -.01008 (65*2π)/3295 weeks
66-.03253 -.01962 (66*2π)/3295 weeks
67-.01559 -.00785 (67*2π)/3295 weeks
68-.01472 -.00628 (68*2π)/3295 weeks
69-.03069 -.0239 (69*2π)/3295 weeks
70.00106 -.0221 (70*2π)/3295 weeks
71-.01187 -.00963 (71*2π)/3295 weeks
72-.02723 -.00524 (72*2π)/3295 weeks
73-.00977 -.0288 (73*2π)/3295 weeks
74-.0084 -.02161 (74*2π)/3294 weeks
75-.02051 .00316 (75*2π)/3294 weeks
76-.00615 -.03165 (76*2π)/3294 weeks
77-.01233 -.01084 (77*2π)/3294 weeks
78-.02155 -.02771 (78*2π)/3294 weeks
79-.00023 -.01559 (79*2π)/3294 weeks
80-.02515 -.02461 (80*2π)/3294 weeks
81-.00949 -.00835 (81*2π)/3294 weeks
82-.01541 -.02478 (82*2π)/3294 weeks
83-.01761 -.00719 (83*2π)/3294 weeks
84-.00201 -.02274 (84*2π)/3294 weeks
85-.0192 -.01769 (85*2π)/3294 weeks
86-.02658 -.00766 (86*2π)/3294 weeks
87-.01064 -.01623 (87*2π)/3294 weeks
88-.02226 -.00926 (88*2π)/3294 weeks
89-.01606 -.01262 (89*2π)/3294 weeks
90-.01452 -.01531 (90*2π)/3294 weeks
91-.01365 -.00261 (91*2π)/3294 weeks
92-.01015 -.00735 (92*2π)/3294 weeks
93-.00883 -.01178 (93*2π)/3294 weeks
94-.01873 .00471 (94*2π)/3294 weeks
95-.01773 -.00469 (95*2π)/3293 weeks
96-.00249 -.00775 (96*2π)/3293 weeks
97-.01181 -.00284 (97*2π)/3293 weeks
98-.01913 -.01947 (98*2π)/3293 weeks
99-.0057 -.01069 (99*2π)/3293 weeks
100-.00601 -.00007 (100*2π)/3293 weeks
101-.00837 -.01131 (101*2π)/3293 weeks
102-.00188 -.00075 (102*2π)/3293 weeks
103-.0173 .00462 (103*2π)/3293 weeks
104.00194 -.01732 (104*2π)/3293 weeks
105-.00655 -.01486 (105*2π)/3293 weeks
106-.00155 -.00498 (106*2π)/3293 weeks
107-.00799 -.01189 (107*2π)/3293 weeks
108-.01131 -.01477 (108*2π)/3293 weeks
109-.0122 -.01382 (109*2π)/3293 weeks
110-.01581 -.01878 (110*2π)/3293 weeks
111-.01025 -.00494 (111*2π)/3293 weeks
112-.01569 -.01995 (112*2π)/3293 weeks
113-.01389 -.00853 (113*2π)/3293 weeks
114-.01808 -.01308 (114*2π)/3293 weeks
115-.02289 -.00614 (115*2π)/3293 weeks
116-.00891 -.01622 (116*2π)/3293 weeks
117-.03038 -.00043 (117*2π)/3293 weeks
118-.0174 -.01007 (118*2π)/3293 weeks
119-.00856 -.00876 (119*2π)/3293 weeks
120-.01766 -.00031 (120*2π)/3293 weeks
121-.01571 -.00532 (121*2π)/3293 weeks
122-.01612 -.00323 (122*2π)/3293 weeks
123-.02366 -.01135 (123*2π)/3293 weeks
124-.01856 -.00945 (124*2π)/3293 weeks
125-.01824 -.00512 (125*2π)/3293 weeks
126-.01827 -.00189 (126*2π)/3293 weeks
127-.01534 -.00754 (127*2π)/3293 weeks
128-.00392 -.00605 (128*2π)/3293 weeks
129-.01517 -.00087 (129*2π)/3293 weeks
130-.00574 -.00116 (130*2π)/3293 weeks
131-.01619 -.00202 (131*2π)/3293 weeks
132-.01049 -.00304 (132*2π)/3292 weeks
133-.01283 -.00517 (133*2π)/3292 weeks
134-.01247 -.00011 (134*2π)/3292 weeks
135-.01144 -.00586 (135*2π)/3292 weeks
136-.00891 -.00377 (136*2π)/3292 weeks
137-.01966 .01036 (137*2π)/3292 weeks
138-.01181 -.00382 (138*2π)/3292 weeks
139-.01371 -.00714 (139*2π)/3292 weeks
140-.01823 .00222 (140*2π)/3292 weeks
141-.01402 -.00301 (141*2π)/3292 weeks
142-.0095 -.0003 (142*2π)/3292 weeks
143-.01688 -.01609 (143*2π)/3292 weeks
144-.01123 .00128 (144*2π)/3292 weeks
145-.00487 .00343 (145*2π)/3292 weeks
146-.01672 .00742 (146*2π)/3292 weeks
147-.00495 -.00424 (147*2π)/3292 weeks
148-.02038 -.00346 (148*2π)/3292 weeks
149-.00781 -.00732 (149*2π)/3292 weeks
150-.01121 -.00108 (150*2π)/3292 weeks
151-.01692 .0027 (151*2π)/3292 weeks
152-.01045 .00217 (152*2π)/3292 weeks
153-.01246 -.00266 (153*2π)/3292 weeks
154-.01223 -.00272 (154*2π)/3292 weeks
155-.01421 .00699 (155*2π)/3292 weeks
156-.00861 -.00877 (156*2π)/3292 weeks
157-.02673 -.00748 (157*2π)/3292 weeks
158-.01318 .00407 (158*2π)/3292 weeks
159-.00063 -.00397 (159*2π)/3292 weeks
160-.01131 .00605 (160*2π)/3292 weeks
161-.00868 -.00375 (161*2π)/3292 weeks
162-.0109 -.00033 (162*2π)/3292 weeks
163-.00395 .00448 (163*2π)/3292 weeks
164-.01047 -.00505 (164*2π)/3292 weeks
165-.01047 .00505 (165*2π)/3292 weeks
166-.00395 -.00448 (166*2π)/3292 weeks
167-.0109 .00033 (167*2π)/3292 weeks
168-.00868 .00375 (168*2π)/3292 weeks
169-.01131 -.00605 (169*2π)/3292 weeks
170-.00063 .00397 (170*2π)/3292 weeks
171-.01318 -.00407 (171*2π)/3292 weeks
172-.02673 .00748 (172*2π)/3292 weeks
173-.00861 .00877 (173*2π)/3292 weeks
174-.01421 -.00699 (174*2π)/3292 weeks
175-.01223 .00272 (175*2π)/3292 weeks
176-.01246 .00266 (176*2π)/3292 weeks
177-.01045 -.00217 (177*2π)/3292 weeks
178-.01692 -.0027 (178*2π)/3292 weeks
179-.01121 .00108 (179*2π)/3292 weeks
180-.00781 .00732 (180*2π)/3292 weeks
181-.02038 .00346 (181*2π)/3292 weeks
182-.00495 .00424 (182*2π)/3292 weeks
183-.01672 -.00742 (183*2π)/3292 weeks
184-.00487 -.00343 (184*2π)/3292 weeks
185-.01123 -.00128 (185*2π)/3292 weeks
186-.01688 .01609 (186*2π)/3292 weeks
187-.0095 .0003 (187*2π)/3292 weeks
188-.01402 .00301 (188*2π)/3292 weeks
189-.01823 -.00222 (189*2π)/3292 weeks
190-.01371 .00714 (190*2π)/3292 weeks
191-.01181 .00382 (191*2π)/3292 weeks
192-.01966 -.01036 (192*2π)/3292 weeks
193-.00891 .00377 (193*2π)/3292 weeks
194-.01144 .00586 (194*2π)/3292 weeks
195-.01247 .00011 (195*2π)/3292 weeks
196-.01283 .00517 (196*2π)/3292 weeks
197-.01049 .00304 (197*2π)/3292 weeks
198-.01619 .00202 (198*2π)/3292 weeks
199-.00574 .00116 (199*2π)/3292 weeks
200-.01517 .00087 (200*2π)/3292 weeks
201-.00392 .00605 (201*2π)/3292 weeks
202-.01534 .00754 (202*2π)/3292 weeks
203-.01827 .00189 (203*2π)/3292 weeks
204-.01824 .00512 (204*2π)/3292 weeks
205-.01856 .00945 (205*2π)/3292 weeks
206-.02366 .01135 (206*2π)/3292 weeks
207-.01612 .00323 (207*2π)/3292 weeks
208-.01571 .00532 (208*2π)/3292 weeks
209-.01766 .00031 (209*2π)/3292 weeks
210-.00856 .00876 (210*2π)/3292 weeks
211-.0174 .01007 (211*2π)/3292 weeks
212-.03038 .00043 (212*2π)/3292 weeks
213-.00891 .01622 (213*2π)/3292 weeks
214-.02289 .00614 (214*2π)/3292 weeks
215-.01808 .01308 (215*2π)/3292 weeks
216-.01389 .00853 (216*2π)/3292 weeks
217-.01569 .01995 (217*2π)/3292 weeks
218-.01025 .00494 (218*2π)/3292 weeks
219-.01581 .01878 (219*2π)/3292 weeks
220-.0122 .01382 (220*2π)/3291 weeks
221-.01131 .01477 (221*2π)/3291 weeks
222-.00799 .01189 (222*2π)/3291 weeks
223-.00155 .00498 (223*2π)/3291 weeks
224-.00655 .01486 (224*2π)/3291 weeks
225.00194 .01732 (225*2π)/3291 weeks
226-.0173 -.00462 (226*2π)/3291 weeks
227-.00188 .00075 (227*2π)/3291 weeks
228-.00837 .01131 (228*2π)/3291 weeks
229-.00601 .00007 (229*2π)/3291 weeks
230-.0057 .01069 (230*2π)/3291 weeks
231-.01913 .01947 (231*2π)/3291 weeks
232-.01181 .00284 (232*2π)/3291 weeks
233-.00249 .00775 (233*2π)/3291 weeks
234-.01773 .00469 (234*2π)/3291 weeks
235-.01873 -.00471 (235*2π)/3291 weeks
236-.00883 .01178 (236*2π)/3291 weeks
237-.01015 .00735 (237*2π)/3291 weeks
238-.01365 .00261 (238*2π)/3291 weeks
239-.01452 .01531 (239*2π)/3291 weeks
240-.01606 .01262 (240*2π)/3291 weeks
241-.02226 .00926 (241*2π)/3291 weeks
242-.01064 .01623 (242*2π)/3291 weeks
243-.02658 .00766 (243*2π)/3291 weeks
244-.0192 .01769 (244*2π)/3291 weeks
245-.00201 .02274 (245*2π)/3291 weeks
246-.01761 .00719 (246*2π)/3291 weeks
247-.01541 .02478 (247*2π)/3291 weeks
248-.00949 .00835 (248*2π)/3291 weeks
249-.02515 .02461 (249*2π)/3291 weeks
250-.00023 .01559 (250*2π)/3291 weeks
251-.02155 .02771 (251*2π)/3291 weeks
252-.01233 .01084 (252*2π)/3291 weeks
253-.00615 .03165 (253*2π)/3291 weeks
254-.02051 -.00316 (254*2π)/3291 weeks
255-.0084 .02161 (255*2π)/3291 weeks
256-.00977 .0288 (256*2π)/3291 weeks
257-.02723 .00524 (257*2π)/3291 weeks
258-.01187 .00963 (258*2π)/3291 weeks
259.00106 .0221 (259*2π)/3291 weeks
260-.03069 .0239 (260*2π)/3291 weeks
261-.01472 .00628 (261*2π)/3291 weeks
262-.01559 .00785 (262*2π)/3291 weeks
263-.03253 .01962 (263*2π)/3291 weeks
264.0018 .01008 (264*2π)/3291 weeks
265-.02405 .01211 (265*2π)/3291 weeks
266-.00358 .01686 (266*2π)/3291 weeks
267-.00405 .01375 (267*2π)/3291 weeks
268-.04529 .02893 (268*2π)/3291 weeks
269-.00356 .02813 (269*2π)/3291 weeks
270-.00545 .01075 (270*2π)/3291 weeks
271-.03145 .03248 (271*2π)/3291 weeks
272-.013 .01399 (272*2π)/3291 weeks
273-.00137 .02481 (273*2π)/3291 weeks
274-.03285 .0245 (274*2π)/3291 weeks
275-.01322 .03815 (275*2π)/3291 weeks
276.00839 .03977 (276*2π)/3291 weeks
277-.02679 .04427 (277*2π)/3291 weeks
278-.0088 .03972 (278*2π)/3291 weeks
279-.00558 .03483 (279*2π)/3291 weeks
280-.02383 .0199 (280*2π)/3291 weeks
281-.014 .02298 (281*2π)/3291 weeks
282.00893 .03743 (282*2π)/3291 weeks
283-.02798 .03087 (283*2π)/3291 weeks
284-.00695 .01117 (284*2π)/3291 weeks
285-.00464 .0301 (285*2π)/3291 weeks
286-.01873 .01193 (286*2π)/3291 weeks
287.004 .01813 (287*2π)/3291 weeks
288.00087 .0261 (288*2π)/3291 weeks
289.00411 .03081 (289*2π)/3291 weeks
290-.02282 .0208 (290*2π)/3291 weeks
291-.01811 .02561 (291*2π)/3291 weeks
292-.01646 .03889 (292*2π)/3291 weeks
293-.01915 .04389 (293*2π)/3291 weeks
294-.01849 .0555 (294*2π)/3291 weeks
295-.03936 .03797 (295*2π)/3291 weeks
296.00781 .04654 (296*2π)/3291 weeks
297-.01835 .03646 (297*2π)/3291 weeks
298-.04677 .04649 (298*2π)/3291 weeks
299-.02349 .07802 (299*2π)/3291 weeks
300-.02995 .00327 (300*2π)/3291 weeks
301.02243 .07666 (301*2π)/3291 weeks
302-.02087 .04831 (302*2π)/3291 weeks
303-.00093 .05508 (303*2π)/3291 weeks
304.0025 .03179 (304*2π)/3291 weeks
305.00806 .06566 (305*2π)/3291 weeks
306-.00287 .06358 (306*2π)/3291 weeks
307-.01048 .0555 (307*2π)/3291 weeks
308-.01227 .06645 (308*2π)/3291 weeks
309-.00791 .0196 (309*2π)/3291 weeks
310.01397 .07774 (310*2π)/3291 weeks
311-.01325 .03883 (311*2π)/3291 weeks
312-.08055 .08824 (312*2π)/3291 weeks
313-.0075 .11529 (313*2π)/3291 weeks
314-.03561 .03365 (314*2π)/3291 weeks
315-.08523 .06877 (315*2π)/3291 weeks
316-.01318 .10188 (316*2π)/3291 weeks
317-.08638 .04925 (317*2π)/3291 weeks
318-.00642 .06413 (318*2π)/3291 weeks
319.01035 .09746 (319*2π)/3291 weeks
320-.09322 .18074 (320*2π)/3291 weeks
321.02105 .10405 (321*2π)/3291 weeks
322.02762 .25394 (322*2π)/3291 weeks
323-.03123 .05813 (323*2π)/3291 weeks
324.03753 .38204 (324*2π)/3291 weeks
325-.03275 .35694 (325*2π)/3291 weeks
326-.00411 .55269 (326*2π)/3291 weeks
327.29204 .94783 (327*2π)/3291 weeks