4. Consider the monthly log returns of U.S. CRSP equal-weighted index from January 1962 to December 1999 for 456 observations. The data le is m-ew6299.txt. (a) Build an AR model for the series. Check the estimated model. Is the estimated model a good/adequate model? Write down the estimated model. (b) Build an MA model for the series. Check the estimated model. Is the estimated model a good/adequate model? Write down the estimated model. (c) Build an ARMA model for the series and check whether the model is the same as the model in part (a) or part (b). (d) Compute 1- and 12-step-ahead forecasts of the AR and MA models built in part (a) and part (b). Are the forecasts in the AR and MA models similar?

plz use R program to answer questions, Here is the data below

-0.792 1.532 -0.596 -7.049 -10.319 -8.880 6.183 3.666 -6.603 -4.050 11.430 -2.593 8.539 -1.459 1.196 2.653 3.180 -1.043 -0.632 4.144 -1.042 1.214 -1.627 -0.424 3.159 2.486 2.519 0.100 0.748 1.036 2.971 -0.606 3.754 1.865 -0.052 -1.244 6.897 3.181 1.527 4.072 -0.587 -8.743 2.823 4.099 2.705 5.702 4.549 4.208 6.220 2.845 -0.893 4.557 -8.995 -0.500 -1.645 -10.615 -1.833 -1.449 3.991 1.716 15.880 4.150 5.661 4.107 -0.813 7.877 7.997 0.629 6.106 -2.080 0.088 7.738 2.362 -5.776 -1.128 13.368 8.738 1.609 -2.656 3.529 6.655 0.689 6.952 0.588 -0.169 -8.963 2.009 0.345 0.624 -12.036 -10.073 5.086 -2.493 8.850 -5.666 -6.847 -3.960 3.941 -2.400 -17.669 -9.488 -7.677 5.757 5.980 11.876 -6.039 0.302 7.818 12.760 4.680 5.506 2.673 -5.070 -1.739 -5.512 4.034 -0.466 -5.919 -3.475 11.076 9.884 4.096 -0.095 0.123 -1.829 -3.435 -2.993 1.218 -3.121 -1.387 4.984 -2.007 -2.652 -7.564 -2.943 -7.327 -8.730 -3.849 10.069 -4.541 7.046 0.031 -19.264 -4.272 12.430 0.857 0.835 -5.711 -7.533 -3.406 -5.332 -8.973 -8.230 8.521 -5.275 -8.416 26.175 5.256 7.837 3.063 7.036 6.928 -0.897 -4.931 -3.965 1.459 1.668 -0.058 17.395 10.093 1.800 -0.382 -1.987 2.617 0.222 -1.683 1.685 -2.279 2.628 9.762 3.623 0.442 1.054 1.679 0.287 5.026 1.228 -0.125 1.488 -2.348 6.845 2.084 -1.127 2.568 6.562 7.633 6.539 1.024 5.105 8.946 0.608 -19.513 3.749 1.425 8.956 -1.646 8.073 2.842 -0.699 5.319 2.119 7.298 -0.128 -10.299 6.328 6.523 9.985 -0.629 -18.036 5.216 6.869 4.515 8.561 6.176 5.117 4.637 6.684 -3.290 0.558 0.208 7.017 2.766 2.682 -1.319 -2.000 -7.463 -9.408 6.757 2.147 -1.982 -1.743 -4.894 -1.216 5.108 -2.246 -3.720 -1.512 6.150 3.238 12.100 8.807 2.249 10.350 5.128 4.900 7.828 8.692 4.764 -1.805 -3.411 0.298 -5.807 3.013 -1.941 0.574 -5.531 0.707 -1.961 -5.210 1.371 -4.861 8.583 0.027 -2.111 -3.191 0.504 11.579 4.606 -0.857 -1.135 2.267 0.346 1.932 -0.342 -5.778 1.878 5.190 2.871 4.248 6.049 4.662 1.572 3.598 0.892 -7.646 2.187 -6.240 2.432 -0.630 -3.514 11.049 7.227 3.255 -1.980 0.071 2.177 3.411 1.547 -1.563 -31.588 -5.372 2.756 7.521 6.016 3.379 1.513 -1.717 4.734 0.055 -2.400 1.853 -1.185 -3.739 1.935 6.122 0.279 1.689 3.022 2.700 -0.836 3.112 1.911 0.446 -5.229 -0.825 -1.224 -4.689 1.563 2.180 -2.708 4.559 0.537 -2.767 -11.630 -8.391 -5.798 3.599 -0.388 8.181 12.544 7.494 3.055 2.989 -3.511 3.432 2.817 0.863 2.358 -2.572 3.580 13.931 5.070 -1.422 -3.344 0.548 -4.051 2.691 -2.474 1.186 1.619 6.553 3.503 6.461 -0.794 3.041 -1.284 3.725 1.190 1.400 3.961 2.546 3.931 -2.467 1.599 4.776 -0.954 -4.711 -1.088 -0.027 -2.693 1.535 3.613 0.449 -0.240 -4.142 -1.294 2.733 2.761 1.857 2.565 2.029 4.754 5.371 2.993 2.566 -4.143 1.705 0.973 3.275 3.105 2.383 5.575 5.926 -3.108 -8.188 4.380 2.856 -2.017 2.447 -0.142 5.989 -1.048 -4.906 -2.162 8.174 4.329 4.748 2.666 7.825 -2.594 -2.002 -2.318 1.501 5.782 4.640 2.267 -4.323 -2.794 -5.110 -21.650 4.246 3.758 7.390 1.885 6.170 -4.319 -0.182 8.038 2.458 3.726 0.656 -3.129 -1.510 -0.182 8.420 7.853