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-0.003227 0.010571 0.009803 -0.00355 0.015586 20060131 0.018365 0.049485 0.060305 0.092323 0.086504 20060228 0.002425 -0.00559 0.006175 -0.002402 0.008618 20060331 0.010697 0.018173 0.036423 0.043753 0.049733 20060428 0.013026 0.008543 0.00888 -0.004602 0.005217 20060531 -0.025278 -0.029992 -0.043427 -0.05768 -0.045821 20060630 0.001526 0.004627 -0.000694 -0.008908 -0.010139 20060731 0.011175 -0.010095 -0.036214 -0.037898 -0.032144 20060831 0.024315 0.026311 0.021473 0.02945 0.021972 20060929 0.027031 0.017125 0.009447 0.004792 0.005296 20061031 0.031948 0.036544 0.053409 0.066534 0.049277 20061130 0.013591 0.032955 0.037587 0.024599 0.026929 20061229 0.018246 0.001885 0.00023 0.01485 0.024227 20070131 0.013396 0.028011 0.045272 0.012109 0.016369 20070228 -0.026751 0.004121 0.017687 -0.005483 -0.001987 20070330 0.012305 0.007718 0.014543 0.009092 0.000612 20070430 0.042318 0.038548 0.037498 0.008079 0.022106 20070531 0.034898 0.032174 0.042686 0.034033 0.019642 20070629 -0.016701 -0.015409 -0.001781 0.000862 -0.005599 20070731 -0.026887 -0.02759 -0.045039 -0.073398 -0.059007 20070831 0.020688 -0.00176 -0.006739 0.014945 -0.01942 20070928 0.040631 0.033257 0.024592 0.00921 0.020845 20071031 0.022087 0.020425 0.022562 0.022497 0.00248 20071130 -0.038445 -0.036718 -0.059707 -0.086622 -0.087653 20071231 -0.003986 -0.008966 -0.011655 -0.003176 -0.007273 20080131 -0.062823 -0.055149 -0.042332 -0.068961 -0.049946 20080229 -0.028928 -0.032251 -0.031064 -0.057955 -0.02785 20080331 -0.003059 -0.018472 -0.023786 -0.003067 -0.027466 20080430 0.043661 0.060936 0.06733 0.025486 0.011691 20080530 0.009706 0.021634 0.044954 0.050181 0.02346 20080630 -0.080792 -0.086946 -0.073459 -0.098251 -0.088121 20080731 -0.006815 -0.021676 0.011157 0.064545 0.019489 20080829 0.012539 0.008509 0.031235 0.038554 0.03049 20080930 -0.080147 -0.121923 -0.101092 -0.076073 -0.094634 20081031 -0.150882 -0.199662 -0.19831 -0.208119 -0.232115 20081128 -0.065631 -0.091317 -0.115204 -0.126045 -0.169012 20081231 0.006305 0.038179 0.040284 0.052653 0.021658 20090130 -0.08329 -0.067699 -0.070591 -0.104326 -0.036752 20090227 -0.09942 -0.096799 -0.097931 -0.131677 -0.121569 20090331 0.087706 0.083287 0.087625 0.110757 0.106225 20090430 0.070432 0.152269 0.172946 0.240701 0.250038 20090529 0.052996 0.052954 0.044029 0.092723 0.14138 20090630 0.004333 -7e-06 0.004362 0.030105 0.054089 20090731 0.070912 0.086466 0.096222 0.098662 0.107815 20090831 0.029726 0.037306 0.032937 0.045443 0.081701 20090930 0.031177 0.049744 0.068062 0.072717 0.072239 20091030 -0.0121 -0.03944 -0.053157 -0.079612 -0.075074 20091130 0.063006 0.050556 0.049156 0.014943 0.010398 20091231 0.009555 0.047389 0.066275 0.081898 0.075438 20100129 -0.033718 -0.033408 -0.030703 -0.035973 -0.004111 20100226 0.027465 0.041523 0.048321 0.049801 0.040673 20100331 0.05771 0.064042 0.073382 0.077272 0.084015 20100430 0.007725 0.030725 0.042432 0.071347 0.094822 20100528 -0.08023 -0.075644 -0.081569 -0.084242 -0.087239 20100630 -0.049693 -0.050742 -0.057058 -0.077646 -0.080475 20100730 0.071234 0.070351 0.067586 0.063426 0.057834 20100831 -0.043646 -0.045216 -0.053122 -0.089265 -0.086733 20100930 0.085822 0.103301 0.122203 0.119975 0.10989 20101029 0.040339 0.036242 0.041202 0.058458 0.042151 20101130 -0.004714 0.012035 0.035768 0.044421 0.023797 20101231 0.064217 0.065768 0.075719 0.090362 0.096194 20110131 0.022782 0.018406 0.022135 -0.016878 -0.002642 20110228 0.029381 0.03832 0.055864 0.051159 0.044711 20110331 -0.003542 0.005935 0.026903 0.030137 0.001017 20110429 0.028783 0.031454 0.031531 0.01851 0.011663 20110531 -0.015554 -0.001103 -0.019219 -0.015234 -0.027635 20110630 -0.016157 -0.014384 -0.018463 -0.033513 -0.024262 20110729 -0.014625 -0.036875 -0.03562 -0.024969 -0.022883 20110831 -0.050087 -0.059275 -0.083436 -0.104253 -0.106379 20110930 -0.062415 -0.080109 -0.117113 -0.1095 -0.10838 

The fileassignment_3.txtcontains monthly returns for five portfolios (e.g.dec1~dec10). The data span is from 01/1961 to 09/2011. Answer following two questions:

1. For the return series ofdec5anddec9, test the null hypothesis that the first 12 lags of autocorrelations are 0 at the 5% level. Draw your conclusion.

2. Build an ARMA model for the return series ofdec1. Perform model checking and write down the fitted model.