3. Consider the monthly simple returns of the Decile 1 (CAP1RET in the data file),Decile 2 (CAP2RET in the data file), Decile 9 (CAP9RET in the data file), and Decile 101(CAP10RET in the data file) of...

3. Consider the monthly simple returns of the Decile 1 (CAP1RET in the data file),Decile 2 (CAP2RET in the data file), Decile 9 (CAP9RET in the data file), and Decile 101(CAP10RET in the data file) of U.S. stocks based on market capitalization. The data spanis from January 1970 to December 2008. The data file ism-deciles08.txt.(a) For the return series of Decile 2 and Decile 10, test the null hypothesis that the first 12lags of autocorrelations are zero at the 5% level. Draw your conclusion.(b) Build an ARMA model for the return series of Decile 2. Check the estimated model. Isthe estimated model a good/adequate model? Write down the estimated model.(c) Use the estimated ARMA model to produce 1- to 12-step-ahead forecasts of the seriesand the associated standard errors of forecasts.


date CAP1RET CAP2RET CAP9RET CAP10RET 19700130 0.054383 -0.004338 -0.073082 -0.076874 19700227 0.020264 0.020155 0.064185 0.059512 19700331 -0.031790 -0.028090 -0.004034 -0.001327 19700430 -0.184775 -0.193004 -0.115825 -0.091112 19700529 -0.088189 -0.085342 -0.085565 -0.053193 19700630 -0.059476 -0.085212 -0.046605 -0.048133 19700731 0.016092 0.017552 0.079077 0.074123 19700831 0.050133 0.051462 0.055984 0.046990 19700930 0.153767 0.142111 0.065849 0.033489 19701030 -0.069930 -0.065084 -0.038729 -0.008571 19701130 -0.069943 -0.034285 0.049899 0.055691 19701231 0.074097 0.110054 0.079993 0.052765 19710129 0.274968 0.200490 0.069375 0.037766 19710226 0.093511 0.084130 0.022567 0.013003 19710331 0.056836 0.070891 0.052102 0.040449 19710430 0.020969 -0.000620 0.031688 0.033062 19710528 -0.064048 -0.071769 -0.031629 -0.035429 19710630 -0.041963 -0.030357 0.003699 0.006193 19710730 -0.076464 -0.066261 -0.042138 -0.037006 19710831 0.036657 0.021909 0.047900 0.039228 19710930 -0.010199 0.002549 -0.004305 -0.005566 19711029 -0.071293 -0.070176 -0.048429 -0.036415 19711130 -0.055561 -0.054274 -0.009327 0.005793 19711231 0.125149 0.117853 0.099282 0.084333 19720131 0.245973 0.175307 0.030514 0.018958 19720229 0.062300 0.049447 0.031347 0.030764 19720330 -0.018404 -0.010880 0.011360 0.009400 19720428 0.001723 -0.010036 0.002856 0.006660 19720531 -0.031005 -0.042386 0.007918 0.024176 19720630 -0.031082 -0.037574 -0.031739 -0.016868 19720731 -0.027344 -0.024645 -0.021379 0.004401 19720831 -0.011429 -0.008290 0.027699 0.041497 19720929 -0.038331 -0.039753 -0.016889 -0.001947 19721031 -0.043062 -0.027085 0.000769 0.013770 19721130 0.012135 0.034602 0.071096 0.045142 19721229 -0.033087 -0.022591 -0.007774 0.018398 19730131 0.028226 -0.023813 -0.060507 -0.015484 19730228 -0.073392 -0.076155 -0.056309 -0.034403 19730330 -0.032910 -0.045229 -0.022485 0.000256 19730430 -0.072810 -0.066237 -0.062514 -0.042260 19730531 -0.116833 -0.110864 -0.051545 -0.009291 19730629 -0.031571 -0.029917 -0.029956 -0.001786 19730731 0.114619 0.102670 0.094205 0.042089 19730831 -0.060716 -0.062398 -0.021180 -0.029726 19730928 0.042153 0.050787 0.105597 0.037914 19731031 0.003839 0.019227 -0.001198 -0.000256 19731130 -0.182100 -0.187612 -0.155987 -0.103288 19731231 -0.099964 -0.071833 0.025719 0.013537 19740131 0.338967 0.211417 0.036737 -0.016155 19740228 -0.025023 -0.001287 0.010079 0.001880 19740329 0.034693 0.014044 -0.027001 -0.024193 19740430 -0.045653 -0.059859 -0.061098 -0.039066 19740531 -0.086678 -0.075841 -0.060772 -0.029546 19740628 -0.035770 -0.032652 -0.030617 -0.016024 19740731 -0.034814 -0.053258 -0.036362 -0.079295 19740830 -0.070349 -0.087916 -0.095896 -0.084247 19740930 -0.076313 -0.084996 -0.079677 -0.119121 19741031 0.070523 0.067100 0.150306 0.176525 19741129 -0.084922 -0.054956 -0.018361 -0.045791 19741231 -0.128791 -0.118327 -0.035427 -0.017931 19750131 0.534829 0.461993 0.216687 0.109855 19750228 0.047669 0.014564 0.041125 0.064469 19750331 0.166421 0.122825 0.051435 0.019301 19750430 -0.022208 -0.012919 0.055289 0.047380 19750530 0.065010 0.063360 0.055458 0.052734 19750630 0.105536 0.106876 0.076396 0.044613 19750731 0.009799 0.013279 -0.059636 -0.066956 19750829 -0.084910 -0.080159 -0.026092 -0.016596 19750930 -0.063882 -0.053649 -0.036320 -0.036223 19751031 -0.037119 -0.008659 0.058677 0.061077 19751128 0.017198 0.017138 0.037149 0.030690 19751231 -0.017993 -0.022655 -0.002395 -0.013195 19760130 0.355377 0.319604 0.155043 0.112700 19760227 0.291409