Finance- Plagiarism free pls

C The file assignment_3.txt contains 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 of dec5 and dec9, 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 of dec1. Perform model checking and write down the fitted model

date dec1 dec2 dec5 dec9 dec10

19610131 0.058011 0.067392 0.081767 0.096754 0.087207

19610228 0.029241 0.042784 0.055524 0.056564 0.060245

19610330 0.025896 0.025474 0.041304 0.060563 0.071875

19610428 0.005667 0.001365 0.00078 0.011911 0.023328

19610531 0.019208 0.036852 0.04959 0.046248 0.050362

19610630 -0.02467 -0.025225 -0.040046 -0.050651 -0.051434

19610731 0.035668 0.027452 0.00937 0.004484 -0.008962

19610831 0.024092 0.041437 0.015614 0.008745 0.011384

19610929 -0.016177 -0.024784 -0.016758 -0.036241 -0.032031

19611031 0.028087 0.028174 0.023155 0.023609 0.027843

19611130 0.048685 0.036955 0.043721 0.052817 0.048427

19611229 0.005025 -0.011093 -0.00404 0.002387 0.002329

19620131 -0.04526 -0.022549 -0.029078 0.007979 0.048003

19620228 0.02362 0.012706 0.015649 0.01248 0.027391

19620330 -0.003898 -0.002686 -0.005748 0.004284 -0.007097

19620430 -0.06129 -0.069647 -0.059029 -0.069243 -0.072758

19620531 -0.078846 -0.085837 -0.10734 -0.100785 -0.108352

19620629 -0.083259 -0.075967 -0.085625 -0.079802 -0.075303

19620731 0.068084 0.060073 0.051869 0.072275 0.077477

19620831 0.020698 0.02718 0.022439 0.036381 0.04777

19620928 -0.044818 -0.058543 -0.059073 -0.07738 -0.073603

19621031 0.012499 -0.00814 -0.017068 -0.055811 -0.059562

19621130 0.099604 0.133502 0.125354 0.129271 0.107458

19621231 0.019592 0.01113 -0.007943 -0.038341 -0.040749

19630131 0.045429 0.055389 0.066401 0.094983 0.104486

19630228 -0.023884 -0.018394 -0.017365 -0.017808 -0.018155

19630329 0.038267 0.032237 0.018539 0.012976 0.001153

19630430 0.052166 0.039321 0.032948 0.017776 0.010118

19630531 0.015735 0.025482 0.036258 0.042853 0.036635

19630628 -0.020691 -0.006069 -0.020601 -0.006799 -0.010582

19630731 0.003275 -0.003159 -0.020085 -0.005376 -0.002477

19630830 0.052318 0.059272 0.044707 0.032852 0.026653

19630930 -0.009125 -0.020792 -0.017719 -0.019807 0.00204

19631031 0.035121 0.019602 0.013527 0.002833 0.007016

19631129 -0.005387 -0.002446 -0.017011 -0.018406 -0.022297

19631231 0.025565 0.019087 0.005644 -0.009151 -0.021819

19640131 0.031144 0.013786 0.007448 0.030904 0.046242

19640228 0.01576 0.018223 0.027548 0.017326 0.028016

19640331 0.012396 0.020256 0.026343 0.030815 0.01953

19640430 0.008592 -0.006305 -0.011836 -0.007332 -0.004249

19640528 0.017664 0.013243 0.012549 -0.008667 0.005094

19640630 0.015844 0.016313 0.016338 0.011585 0.013163

19640731 0.016735 0.034244 0.029591 0.023815 0.037029

19640831 -0.013134 -0.012906 -0.009553 -0.004772 -0.005573

19640930 0.027702 0.031828 0.029679 0.037297 0.050351

19641030 0.00624 0.007968 0.024678 0.021981 0.026918

19641130 0.003817 -0.000464 0.006991 0.007266 -0.002249

19641231 0.007182 -0.000823 -0.007063 -0.015109 -0.01998

19650129 0.03081 0.046427 0.05347 0.05712 0.084762

19650226 -0.003587 0.025498 0.035618 0.018827 0.035896

19650331 -0.015123 -0.00752 0.005503 0.030291 0.024336

19650430 0.034077 0.028259 0.040189 0.032507 0.050321

19650528 -0.002959 -0.009231 -0.000256 -0.021767 -0.002347

19650630 -0.04043 -0.057578 -0.079003 -0.092205 -0.09657

19650730 0.011193 0.024219 0.034897 0.035293 0.026863

19650831 0.024496 0.03427 0.052501 0.043122 0.040087

19650930 0.032489 0.027799 0.03242 0.019904 0.02981

19651029 0.022185 0.033503 0.043739 0.067262 0.074523

19651130 -0.010616 0.012488 0.047903 0.049592 0.059053

19651231 0.006171 0.023643 0.022772 0.05108 0.049598

19660131 -0.001079 0.018601 0.032516 0.057475 0.085423

19660228 -0.016176 -0.011238 0.006879 0.043811 0.048119

19660331 -0.02382 -0.007018 -0.026027 -0.021543 -0.002481

19660429 0.019589 0.021322 0.044579 0.053058 0.054574

19660531 -0.042101 -0.058315 -0.070124 -0.092825 -0.110102

19660630 -0.015246 -0.004762 -0.00579 0.002304 -0.00557

19660729 -0.012703 -0.008649 -0.010825 -0.016103 -0.01978

19660831 -0.067081 -0.081761 -0.086849 -0.099178 -0.118895

19660930 -0.002101 -0.012696 -0.018871 -0.017207 -0.022673

19661031 0.054016 0.050185 0.018352 -0.0282 -0.052977

19661130 0.008646 0.022892 0.033457 0.053044 0.042278

19661230 -0.004802 0.019891 0.017467 0.020857 0.019079

19670131 0.068568 0.080373 0.152216 0.180843 0.211806

19670228 0.008735 0.011044 0.014809 0.048767 0.064911

19670331 0.039698 0.035364 0.051478 0.067494 0.068904

19670428 0.04403 0.037541 0.038164 0.040785 0.044602

19670531 -0.050631 -0.036233 -0.005738 -0.002191 0.000295

19670630 0.014998 0.01887 0.057569 0.102075 0.118678

19670731 0.041034 0.051373 0.059991 0.089876 0.1048

19670831 -0.008704 -0.003777 -0.000423 -0.004674 0.011887

19670929 0.03492 0.021973 0.040354 0.073676 0.088675

19671031 -0.017631 -0.053763 -0.033172 -0.030405 -0.007511

19671130 0.007657 0.001845 0.008903 0.012547 -0.012048

19671229 0.02325 0.033111 0.049507 0.101914 0.112981

19680131 -0.046267 -0.040359 -0.01887 0.007135 0.076514

19680229 -0.024984 -0.032197 -0.046723 -0.055084 -0.075146

19680329 0.012511 -0.003027 0.001843 -0.015568 -0.016972

19680430 0.080396 0.085935 0.121345 0.161241 0.170134

19680531 0.011076 0.028609 0.073687 0.096214 0.13855

19680628 0.007917 0.023493 0.015238 0.003688 0.013114

19680730 -0.015339 -0.022999 -0.048454 -0.038548 -0.020943

19680830 0.013173 0.016034 0.025587 0.042423 0.047302

19680930 0.031751 0.053948 0.048021 0.066513 0.070898

19681031 0.00741 0.016422 0.025906 -0.00967 0.0041

19681129 0.047482 0.066408 0.075815 0.070788 0.072423

19681231 -0.044984 -0.029151 -0.013146 0.010592 0.033044

19690131 -0.008208 -0.000299 -0.020841 -0.019187 0.004643

19690228 -0.037417 -0.065761 -0.070136 -0.095074 -0.103165

19690328 0.041346 0.011199 0.008464 0.030027 0.018273

19690430 0.024883 0.018685 0.015238 -0.003889 -0.004934

19690529 0.006649 -0.001651 0.00606 0.003673 0.011502

19690630 -0.048659 -0.069702 -0.104041 -0.128577 -0.132533

19690731 -0.056311 -0.063499 -0.081753 -0.111659 -0.117458

19690829 0.050951 0.03982 0.066671 0.054845 0.041077

19690930 -0.030304 -0.00765 -0.011879 -0.033037 -0.031771

19691031 0.041143 0.071243 0.084518 0.09676 0.112035

19691128 -0.026198 -0.036227 -0.049312 -0.072298 -0.070327

19691231 -0.010351 -0.023517 -0.022934 -0.068192 -0.089239

19700130 -0.080692 -0.068004 -0.058264 -0.043693 -0.009592

19700227 0.056258 0.07707 0.054954 0.040517 0.025837

19700331 0.001078 -0.011366 -0.016616 -0.036098 -0.035673

19700430 -0.084833 -0.10964 -0.14725 -0.177406 -0.187493

19700529 -0.048462 -0.07401 -0.102908 -0.101702 -0.094647

19700630 -0.048952 -0.047306 -0.066446 -0.08531 -0.087369

19700731 0.073319 0.07313 0.065855 0.057671 0.040341

19700831 0.044079 0.055228 0.071947 0.06375 0.058201

19700930 0.029107 0.042906 0.09964 0.137416 0.163561

19701030 -0.004906 -0.024022 -0.042688 -0.068092 -0.079411

19701130 0.054586 0.060109 0.035799 0.002067 -0.031902

19701231 0.050112 0.068955 0.081347 0.093818 0.094088

19710129 0.034885 0.053614 0.095505 0.131944 0.182548

19710226 0.013189 0.015037 0.018036 0.047367 0.068243

19710331 0.041144 0.035396 0.047222 0.046002 0.063385

19710430 0.034221 0.038489 0.04736 0.029759 0.01949

19710528 -0.037548 -0.029219 -0.039358 -0.062733 -0.06478

19710630 0.006808 -0.00051 -0.013048 -0.027439 -0.030383

19710730 -0.038081 -0.037829 -0.057425 -0.065584 -0.06669

19710831 0.039668 0.038182 0.06418 0.05491 0.030787

19710930 -0.004516 -0.00809 -0.000638 0.000195 -2.8e-05

19711029 -0.032954 -0.054115 -0.054749 -0.062275 -0.068634

19711130 0.009671 -0.010698 -0.02662 -0.044812 -0.054719

19711231 0.079864 0.095033 0.111563 0.132976 0.126949

19720131 0.016369 0.028511 0.043855 0.111935 0.152311

19720229 0.030204 0.029931 0.040274 0.032985 0.042728

19720330 0.012325 -0.002066 0.003607 -0.004181 -0.00819

19720428 0.007168 0.008691 -0.000285 -0.001257 0.001503

19720531 0.027161 0.007478 0.002152 -0.025637 -0.033376

19720630 -0.014936 -0.03071 -0.018578 -0.036085 -0.040016

19720731 0.009158 -0.020557 -0.024705 -0.051803 -0.036376

19720831 0.037061 0.050653 0.024893 -0.004622 -0.001045

19720929 0.001613 -0.019101 -0.024922 -0.042264 -0.043812

19721031 0.014394 0.011725 -0.009307 -0.023347 -0.033214

19721130 0.040127 0.065779 0.056611 0.052936 0.042128

19721229 0.022182 -0.004857 -0.006384 -0.020323 -0.03189

19730131 -0.004979 -0.072329 -0.069163 -0.05205 -0.033162

19730228 -0.031568 -0.048032 -0.082459 -0.085564 -0.084468

19730330 0.002759 -0.016991 -0.031967 -0.028426 -0.030544

19730430 -0.038118 -0.056069 -0.071259 -0.081071 -0.085084

19730531 -0.006239 -0.019389 -0.066678 -0.096901 -0.104067

19730629 0.001023 -0.027391 -0.031986 -0.043801 -0.044644

19730731 0.03358 0.075324 0.098315 0.145697 0.150538

19730831 -0.034154 -0.012549 -0.030463 -0.055687 -0.073051

19730928 0.028717 0.090222 0.114051 0.105907 0.076823

19731031 0.004062 -0.02148 -0.006534 -0.008499 0.001446

19731130 -0.098924 -0.13566 -0.173255 -0.206715 -0.199853

19731231 0.015834 0.010668 0.003429 -0.029664 -0.062624

19740131 -0.021841 0.025216 0.074334 0.178253 0.202554

19740228 -0.001581 0.012267 0.010829 -0.00598 -0.008725

19740329 -0.022258 -0.031543 -0.018158 -0.001827 0.011522

19740430 -0.034169 -0.064395 -0.056497 -0.059521 -0.062462

19740531 -0.018382 -0.068651 -0.076697 -0.079307 -0.079801

19740628 -0.013298 -0.030279 -0.034713 -0.029587 -0.026679

19740731 -0.086102 -0.050734 -0.018124 -0.048179 -0.054411

19740830 -0.082207 -0.102441 -0.08281 -0.087674 -0.0824

19740930 -0.124626 -0.076541 -0.079639 -0.082329 -0.078183

19741031 0.173961 0.176748 0.143744 0.092736 0.077082

19741129 -0.047427 -0.019068 -0.024919 -0.053914 -0.072223

19741231 -0.018764 -0.019956 -0.054913 -0.089879 -0.099849

19750131 0.102644 0.174092 0.253248 0.335371 0.402605

19750228 0.068822 0.045027 0.056645 0.039284 0.025067

19750331 0.01678 0.034792 0.067473 0.099781 0.126137

19750430 0.049074 0.03937 0.049411 0.045726 0.014451

19750530 0.054235 0.049397 0.056989 0.073342 0.073454

19750630 0.040561 0.080278 0.057136 0.075801 0.101392

19750731 -0.068987 -0.059034 -0.041202 -0.033234 0.008975

19750829 -0.015699 -0.019284 -0.033207 -0.065993 -0.071067

19750930 -0.035695 -0.032386 -0.037513 -0.034944 -0.035721

19751031 0.065669 0.059346 0.031124 0.02183 -0.004053

19751128 0.029495 0.02965 0.03947 0.027153 0.02453

19751231 -0.015052 0.000157 0.007269 -0.012313 -0.018419

19760130 0.110547 0.129526 0.169527 0.22557 0.273677

19760227 -0.017872 0.018792 0.053857 0.110527 0.163815

19760331 0.039322 0.005838 0.013931 0.007587 0.00289

19760430 -0.010542 -0.010469 -0.012536 -0.022683 -0.027655

19760528 -0.007063 -0.004697 -0.006338 -0.025822 -0.035147

19760630 0.041786 0.055836 0.061827 0.029171 0.024088

19760730 -0.008924 -0.009154 -0.002631 0.002512 -0.005917

19760831 0.003661 0.000953 -0.01628 -0.017056 -0.027198

19760930 0.026106 0.02376 0.024955 0.019653 0.018059

19761029 -0.01976 -0.027805 -0.02558 -0.030639 -0.022953

19761130 -0.007277 0.024965 0.04213 0.042815 0.016488

19761231 0.047675 0.071218 0.080283 0.106467 0.111061

19770131 -0.049291 -0.039702 -0.004844 0.035524 0.053905

19770228 -0.014298 -0.025348 -0.020813 -0.014093 -0.007405

19770331 -0.018091 -0.002212 0.00753 0.007848 0.006871

19770429 -0.003659 0.017994 0.02488 0.008339 0.01409

19770531 -0.015803 -0.006419 -0.010268 -0.009083 -0.00149

19770630 0.047698 0.050767 0.074823 0.074592 0.074829

19770729 -0.013255 -0.021676 -0.015669 -0.003122 0.005767

19770831 -0.011677 -0.022938 -0.005422 -0.016348 -0.02019

19770930 -0.001951 -0.000995 0.004098 0.014111 0.017767

19771031 -0.043407 -0.036093 -0.025475 -0.021759 -0.031608

19771130 0.031112 0.047278 0.0728 0.103846 0.089596

19771230 0.004479 0.006829 0.011408 0.013388 0.014722

19780131 -0.062186 -0.057471 -0.048303 -0.020631 0.00478

19780228 -0.016074 -0.01782 0.00597 0.027277 0.032579

19780331 0.019256 0.039867 0.071432 0.078042 0.092997

19780428 0.090255 0.075704 0.075307 0.087632 0.08516

19780531 0.006843 0.02675 0.039228 0.068662 0.081704

19780630 -0.018249 -0.015104 -0.001869 0.00163 0.001854

19780731 0.055644 0.049352 0.04901 0.05679 0.052701

19780831 0.02979 0.035443 0.079789 0.072012 0.121905

19780929 -0.005209 -0.006671 -0.021603 -0.011056 -0.002263

19781031 -0.076646 -0.125223 -0.167718 -0.241447 -0.239397

19781130 0.030149 0.034387 0.049843 0.069869 0.073003

19781229 0.020203 0.000248 0.011552 0.010811 -0.00079

19790131 0.035101 0.052476 0.080652 0.114372 0.12059

19790228 -0.027509 -0.031935 -0.030942 -0.025555 -0.02517

19790330 0.0493 0.073203 0.094027 0.105335 0.094505

19790430 0.003393 -0.00127 0.013453 0.018507 0.02909

19790531 -0.018502 -0.003652 -0.013396 -0.005546 -0.007959

19790629 0.03538 0.062144 0.051754 0.054039 0.04903

19790731 0.004935 0.027496 0.039476 0.021246 0.019436

19790831 0.056733 0.060304 0.065842 0.08945 0.08157

19790928 0.002751 0.000984 -0.005583 -0.01117 -0.014482

19791031 -0.055801 -0.079816 -0.085178 -0.119663 -0.108689

19791130 0.051129 0.066653 0.078359 0.094154 0.063935

19791231 0.01199 0.04052 0.035288 0.074767 0.073014

19800131 0.061682 0.066161 0.064476 0.10014 0.114047

19800229 0.016553 -0.025146 -0.025717 -0.027364 -0.027541

19800331 -0.096744 -0.116833 -0.152582 -0.18918 -0.192455

19800430 0.042414 0.057822 0.066272 0.065893 0.056609

19800530 0.047808 0.069866 0.078134 0.06655 0.071021

19800630 0.02848 0.04234 0.051288 0.039126 0.040632

19800731 0.054632 0.080625 0.099021 0.137272 0.108809

19800829 0.013449 0.025002 0.036217 0.072781 0.082943

19800930 0.024628 0.035898 0.030845 0.027316 0.028708

19801031 0.020754 0.014414 0.022143 0.04132 0.032605

19801128 0.129188 0.085953 0.064253 0.069025 0.027352

19801231 -0.039689 -0.017899 -0.027319 -0.033371 -0.031815

19810130 -0.057169 -0.033817 0.004821 0.01674 0.034188

19810227 0.01774 0.008944 0.020025 0.014133 0.00991

19810331 0.019261 0.077539 0.082778 0.095843 0.093096

19810430 -0.029966 -0.008781 0.014869 0.032499 0.038398

19810529 -0.001835 0.022585 0.018178 0.028022 0.034391

19810630 -0.000546 -0.014301 -0.006593 -0.009901 0.009558

19810731 0.008963 -0.010012 -0.023071 -0.037194 -0.025912

19810831 -0.052426 -0.058096 -0.065328 -0.080668 -0.080764

19810930 -0.051993 -0.051525 -0.055591 -0.078797 -0.086296

19811030 0.0505 0.072269 0.057032 0.090751 0.081734

19811130 0.051194 0.033292 0.033991 0.025897 0.020277

19811231 -0.032349 -0.02186 -0.023564 -0.003065 -0.028879

19820129 -0.01427 -0.03119 -0.020485 -0.021786 -0.006772

19820226 -0.054569 -0.050299 -0.029741 -0.044828 -0.041014

19820331 -0.008096 -0.009509 0.007547 -0.001101 -0.006003

19820430 0.036001 0.051338 0.044274 0.040044 0.038886

19820528 -0.021587 -0.038903 -0.026785 -0.027917 -0.019453

19820630 -0.015556 -0.02943 -0.009362 -0.029271 -0.031733

19820730 -0.018898 -0.035237 -0.023592 -0.023055 -0.01294

19820831 0.12792 0.123537 0.117993 0.083156 0.064037

19820930 0.008445 0.014075 0.022656 0.029422 0.027618

19821029 0.104797 0.12518 0.133246 0.147729 0.151446

19821130 0.039396 0.047456 0.074682 0.073883 0.099093

19821231 0.01213 0.014769 -0.002352 0.02517 0.007787

19830131 0.039064 0.028275 0.04872 0.076123 0.107242

19830228 0.025498 0.028056 0.032826 0.050677 0.051508

19830331 0.031406 0.027774 0.032043 0.041157 0.058068

19830429 0.078297 0.061569 0.06854 0.081621 0.071337

19830531 -0.020074 0.022277 0.044888 0.082803 0.123791

19830630 0.038691 0.025471 0.034526 0.027798 0.039943

19830729 -0.03524 -0.035805 -0.029033 -0.017412 -0.019394

19830831 0.020524 -0.001009 -0.020653 -0.024283 -0.03861

19830930 0.011382 0.020705 0.036339 0.00232 -0.004633

19831031 -0.009432 -0.02314 -0.040539 -0.063904 -0.070552

19831130 0.017569 0.019818 0.052854 0.05045 0.047765

19831230 -0.004081 -0.013227 -0.017695 -0.019377 -0.028683

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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

Top of Form

A

Suppose that the asset return rt follows the model

Does the unconditional variance of rt exist? Why?

B

The file assignment_4.txt contains monthly stock returns for S&P500 index (sp) and Coca-Cola Company (ko). Note they are simple returns and you need to convert the simple returns to log returns. Answer following questions for both sp and ko:

(a) Is the expected monthly log return zero? Is there any serial correlation in the log returns? Is there any ARCH effect in the log returns?

(b) Build a Gaussian GARCH model for the log returns. Perform model checking and write down the fitted model.

(c) Build a GARCH model with Student t innovations for the log returns. Perform model checking and write down the fitted model.

date ko sp

19610131 0.009331 0.063156

19610228 0.103236 0.026870

19610330 0.012291 0.025536

19610428 -0.050000 0.003843

19610531 0.087719 0.019139

19610630 -0.058065 -0.028846

19610731 0.008621 0.032797

19610831 0.022792 0.019623

19610929 0.034540 -0.019686

19611031 0.005420 0.028323

19611130 0.125067 0.039347

19611229 -0.002410 0.003225

19620131 -0.099034 -0.037876

19620228 -0.016086 0.016270

19620330 0.041962 -0.005860

19620430 -0.026316 -0.061970

19620531 -0.091892 -0.085990

19620629 -0.082143 -0.081838

19620731 0.120915 0.063562

19620831 -0.007289 0.015284

19620928 -0.070778 -0.048207

19621031 0.012739 0.004443

19621130 0.092453 0.101557

19621231 -0.011594 0.013492

19630131 0.058651 0.049128

19630228 -0.002770 -0.028852

19630329 0.046389 0.035464

19630430 -0.010695 0.048520

19630531 0.005405 0.014327

19630628 0.015323 -0.020198

19630731 0.018667 -0.003460

19630830 0.070681 0.048749

19630930 0.004156 -0.011034

19631031 0.014706 0.032218

19631129 0.019807 -0.010539

19631231 0.102503 0.024444

19640131 0.021622 0.026926

19640228 0.003175 0.009865

19640331 0.067511 0.015167

19640430 0.005964 0.006077

19640528 0.009881 0.011452

19640630 0.034247 0.016424

19640731 0.050428 0.018240

19640831 -0.009058 -0.016230

19640930 -0.007313 0.028718

19641030 -0.033333 0.008078

19641130 0.032567 -0.005185

19641231 0.050373 0.003909

19650129 0.094139 0.033156

19650226 0.022727 -0.001485

19650331 -0.062857 -0.014526

19650430 0.074957 0.034239

19650528 -0.001585 -0.007743

19650630 -0.018413 -0.048632

19650730 0.001626 0.013433

19650831 0.019481 0.022522

19650930 0.005414 0.032006

19651029 -0.015924 0.027345

19651130 0.057282 -0.008764

19651231 0.058462 0.008951

19660131 -0.002907 0.004869

19660228 -0.072886 -0.017873

19660331 0.062579 -0.021815

19660429 -0.071429 0.020509

19660531 0.016026 -0.054140

19660630 -0.049211 -0.016138

19660729 0.030050 -0.013453

19660831 -0.027553 -0.077751

19660930 -0.000333 -0.007004

19661031 0.105705 0.047544

19661130 0.049772 0.003117

19661230 0.042151 -0.001492

19670131 0.059972 0.078178

19670228 0.057895 0.001963

19670331 0.032587 0.039410

19670428 0.096852 0.042239

19670531 -0.004415 -0.052441

19670630 0.097783 0.017512

19670731 0.035497 0.045344

19670831 -0.061704 -0.011715

19670929 0.037787 0.032785

19671031 0.000000 -0.029056

19671130 0.119394 0.001065

19671229 -0.039855 0.026277

19680131 -0.049057 -0.043848

19680229 0.011905 -0.031223

19680329 0.051176 0.009400

19680430 0.097378 0.081929

19680531 0.006826 0.011169

19680628 0.000678 0.009120

19680730 -0.047619 -0.018478

19680830 0.046429 0.011459

19680930 -0.018089 0.038539

19681031 -0.001745 0.007208

19681129 0.044406 0.047964

19681231 -0.038655 -0.041617

19690131 0.003497 -0.008184

19690228 -0.047038 -0.047374

19690328 0.039561 0.034444

19690430 0.019435 0.021476

19690529 0.039861 -0.002218

19690630 -0.068933 -0.055577

19690731 -0.023381 -0.060178

19690829 0.075506 0.040074

19690930 0.064452 -0.025024

19691031 0.080775 0.044244

19691128 -0.063318 -0.035274

19691231 0.054487 -0.018655

19700130 -0.036474 -0.076472

19700227 0.045741 0.052693

19700331 -0.027330 0.001453

19700430 -0.080997 -0.090483

19700529 -0.035593 -0.060967

19700630 -0.019543 -0.050033

19700731 0.048649 0.073295

19700831 -0.013746 0.044459

19700930 0.043345 0.032998

19701030 0.057047 -0.011400

19701130 0.068063 0.047447

19701231 0.011940 0.056766

19710129 0.026549 0.040477

19710226 0.001437 0.009074

19710331 0.086313 0.036796

19710430 0.019894 0.036288

19710528 0.046814 -0.041558

19710630 0.023801 0.000703

19710730 -0.026797 -0.041324

19710831 0.091364 0.036095

19710930 -0.000963 -0.006968

19711029 0.004608 -0.041794

19711130 -0.003257 -0.002547

19711231 0.127021 0.086179

19720131 -0.018443 0.018121

19720229 0.042797 0.025303

19720330 0.012292 0.005912

19720428 0.034722 0.004384

19720531 0.019175 0.017275

19720630 0.007789 -0.021821

19720731 0.063670 0.002333

19720831 -0.005282 0.034454

19720929 0.001133 -0.004861

19721031 0.019504 0.009317

19721130 -0.005843 0.045617

19721229 0.042105 0.011828

19730131 -0.018519 -0.017111

19730228 -0.037736 -0.037490

19730330 -0.000535 -0.001433

19730430 -0.012522 -0.040800

19730531 0.019928 -0.018884

19730629 0.019893 -0.006575

19730731 0.006114 0.037982

19730831 -0.021701 -0.036685

19730928 0.041526 0.040096

19731031 -0.024786 -0.001291

19731130 -0.086941 -0.113861

19731231 -0.025048 0.016569

19740131 -0.071146 -0.010046

19740228 -0.021277 -0.003624

19740329 -0.037978 -0.023280

19740430 -0.041998 -0.039051

19740531 0.015403 -0.033551

19740628 0.012905 -0.014665

19740731 -0.211806 -0.077791

19740830 -0.145374 -0.090279

19740930 -0.288213 -0.119335

19741031 0.229268 0.163047

19741129 -0.134405 -0.053180

19741231 -0.018519 -0.020151

19750131 0.257075 0.122812

19750228 0.048780 0.059886

19750331 0.138819 0.021694

19750430 0.014241 0.047265

19750530 0.120125 0.044101

19750630 0.016156 0.044323

19750731 -0.120000 -0.067654

19750829 -0.034483 -0.021070

19750930 -0.073701 -0.034645

19751031 0.148410 0.061643

19751128 0.084000 0.024708

19751231 -0.060000 -0.011508

19760130 0.127660 0.118306

19760227 -0.088949 -0.011402

19760331 0.047781 0.030689

19760430 -0.061166 -0.010995

19760528 -0.015152 -0.014364

19760630 0.043538 0.040926

19760730 0.031204 -0.008055

19760831 -0.004323 -0.005124

19760930 0.001881 0.022641

19761029 -0.042213 -0.022235

19761130 -0.029939 -0.007775

19761231 -0.001580 0.052498

19770131 -0.053797 -0.050530

19770228 0.025084 -0.021660

19770331 0.013312 -0.014025

19770429 -0.037398 0.000203

19770531 -0.028716 -0.023568

19770630 0.047235 0.045360

19770729 0.050336 -0.016222

19770831 0.015974 -0.021042

19770930 0.006541 -0.002480

19771031 -0.056782 -0.043406

19771130 0.023679 0.026966

19771230 -0.016502 0.002847

19780131 -0.040268 -0.061514

19780228 0.003497 -0.024762

19780331 0.067875 0.024931

19780428 0.115512 0.085416

19780531 0.008876 0.004234

19780630 -0.010323 -0.017585

19780731 0.020958 0.053910

19780831 0.055718 0.025924

19780929 -0.012556 -0.007261

19781031 -0.071023 -0.091574

19781130 0.019817 0.016640

19781229 0.063636 0.014889

19790131 -0.002849 0.039746

19790228 -0.037143 -0.036526

19790330 -0.009139 0.055152

19790430 -0.033333 0.001673

19790531 -0.015674 -0.026336

19790629 -0.012994 0.038656

19790731 0.026144 0.008746

19790831 0.019108 0.053078

19790928 -0.072125 0.000000

19791031 -0.061433 -0.068606

19791130 -0.007564 0.042624

19791231 0.026022 0.016767

19800131 0.018116 0.057625

19800229 -0.064057 -0.004380

19800331 -0.025399 -0.101795

19800430 0.055556 0.041140

19800530 0.015038 0.046571

19800630 -0.006222 0.026969

19800731 0.121212 0.065039

19800829 -0.040541 0.005835

19800930 -0.076338 0.025168

19801031 -0.050388 0.016021

19801128 0.009469 0.102377

19801231 0.098765 -0.033874

19810130 0.007491 -0.045742

19810227 0.066914 0.013277

19810331 0.044042 0.036033

19810430 -0.061017 -0.023456

19810529 0.079422 -0.001657

19810630 -0.054716 -0.010408

19810731 -0.021583 -0.002210

19810831 -0.036765 -0.062099

19810930 0.048244 -0.053832

19811030 0.092593 0.049148

19811130 -0.018169 0.036590

19811231 -0.024561 -0.030075

19820129 -0.061151 -0.017544

19820226 -0.072797 -0.060548

19820331 0.103140 -0.010167

19820430 0.041985 0.040014

19820528 -0.044103 -0.039162

19820630 0.054688 -0.020290

19820730 0.085185 -0.022991

19820831 0.075085 0.115977

19820930 0.050667 0.007614

19821029 0.073620 0.110364

19821130 0.145600 0.036123

19821231 0.050505 0.015158

19830131 -0.033654 0.033134

19830228 -0.009950 0.018995

19830331 0.088844 0.033095

19830429 0.039720 0.074922

19830531 -0.067416 -0.012346

19830630 -0.025639 0.035224

19830729 -0.072682 -0.033014

19830831 0.113514 0.011319

19830930 0.000874 0.010158

19831031 0.024570 -0.015174

19831130 0.072806 0.017426

19831230 -0.031674 -0.008834

19840131 -0.051402 -0.009216

19840229 0.022167 -0.038859

19840330 0.071133 0.013498

19840430 0.000000 0.005466

19840531 0.002278 -0.059356

19840629 0.060273 0.017469

19840731 0.032538 -0.016451

19840831 0.039916 0.106332

19840928 0.023273 -0.003480

19841031 0.037924 -0.000060

19841130 -0.037462 -0.015112

19841231 0.008081 0.022374

19850131 -0.038076 0.074085

19850228 0.058333 0.008685

19850329 0.114016 -0.002925

19850430 -0.021429 -0.004594

19850531 -0.009124 0.054051

19850628 0.033002 0.012134

19850731 0.041441 -0.004848

19850830 -0.008651 -0.011995

19850930 -0.015846 -0.034724

19851031 0.026882 0.042509

19851129 0.172635 0.065062

19851231 0.015015 0.045061

19860131 -0.007396 0.002367

19860228 0.147541 0.071489

19860331 0.101610 0.052794

19860430 0.059382 -0.014148

19860530 0.040359 0.050229

19860630 0.088621 0.014110

19860731 -0.064741 -0.058683

19860829 -0.031949 0.071193

19860930 -0.098746 -0.085439

19861031 0.081181 0.054729

19861128 0.003686 0.021477

19861231 0.034247 -0.028288

19870130 0.129139 0.131767

19870227 0.052786 0.036924

19870331 0.025738 0.026390

19870430 -0.068306 -0.011450

19870529 0.005865 0.006034

19870630 0.044431 0.047915

19870731 0.070225 0.048224

19870831 0.062992 0.034959

19870930 -0.038914 -0.024166

19871030 -0.147287 -0.217630

19871130 -0.096242 -0.085349

19871231 0.030405 0.072861

19880129 0.005763 0.040432

19880229 -0.006645 0.041817

19880331 0.031438 -0.033343

19880429 0.000000 0.009425

19880531 -0.006536 0.003176

19880630 0.034211 0.043256

19880729 -0.016026 -0.005411

19880831 0.042345 -0.038600

19880930 0.101250 0.039729

19881031 -0.014286 0.025964

19881130 0.012754 -0.018891

19881230 0.028818 0.014688

19890131 0.047619 0.071115

19890228 0.021390 -0.028944

19890331 0.080419 0.020806

19890428 0.058537 0.050090

19890531 0.064516 0.035138

19890630 -0.017922 -0.007925

19890731 0.206208 0.088370

19890831 -0.022059 0.015517

19890929 0.012632 -0.006544

19891031 0.080224 -0.025175

19891130 0.072055 0.016541

19891229 0.000000 0.021417

19900131 -0.108414 -0.068817

19900228 0.023593 0.008539

19900330 0.065957 0.024255

19900430 0.020067 -0.026887

19900531 0.183607 0.091989

19900629 -0.012188 -0.008886

19900731 0.022535 -0.005223

19900831 -0.068871 -0.094314

19900928 -0.060355 -0.051184

19901031 0.136076 -0.006698

19901130 0.035097 0.059934

19901231 0.005405 0.024828

19910131 0.048387 0.041518

19910228 0.074359 0.067281

19910328 0.040382 0.022203

19910430 -0.027650 0.000346

19910531 0.085308 0.038577

19910628 -0.043843 -0.047893

19910731 0.103211 0.044859

19910830 0.093555 0.019649

19910930 -0.015361 -0.019144

19911031 0.032946 0.011860

19911129 0.044878 -0.043928

19911231 0.156757 0.111588

19920131 -0.034268 -0.019900

19920228 0.054839 0.009565

19920331 0.003425 -0.021832

19920430 0.015291 0.027893

19920529 0.060241 0.000964

19920630 -0.087727 -0.017359

19920731 0.046875 0.039374

19920831 0.026866 -0.023998

19920930 -0.054884 0.009106

19921030 0.003086 0.002106

19921130 -0.018092 0.030262

19921231 0.053459 0.010108

19930129 0.011940 0.007046

19930226 0.000000 0.010484

19930331 0.009912 0.018697

19930430 -0.076246 -0.025417

19930528 0.053968 0.022717

19930630 0.040241 0.000755

19930730 0.005814 -0.005327

19930831 0.002890 0.034432

19930930 -0.022017 -0.009988

19931029 0.026627 0.019393

19931130 -0.027781 -0.012911

19931231 0.062500 0.010091

19940131 -0.084034 0.032501

19940228 0.042813 -0.030045

19940331 -0.042346 -0.045746

19940429 0.027692 0.011531

19940531 -0.035928 0.012419

19940630 0.014161 -0.026812

19940729 0.092308 0.031467

19940831 0.036620 0.037643

19940930 0.061304 -0.026898

19941031 0.035990 0.020834

19941130 0.018759 -0.039505

19941230 0.007335 0.012299

19950131 0.019417 0.024278

19950228 0.047619 0.036074

19950331 0.029000 0.027329

19950428 0.031042 0.027960

19950531 0.060215 0.036312

19950630 0.038053 0.021279

19950731 0.029412 0.031776

19950831 -0.020952 -0.000320

19950929 0.077354 0.040098

19951031 0.041667 -0.004979

19951130 0.056974 0.041049

19951229 -0.019802 0.017444

19960131 0.015152 0.032617

19960229 0.071310 0.006934

19960329 0.027864 0.007917

19960430 -0.015106 0.013431

19960531 0.128834 0.022853

19960628 0.067935 0.002257

19960731 -0.043367 -0.045748

19960830 0.072000 0.018814

19960930 0.014925 0.054173

19961031 -0.007371 0.026131

19961129 0.014851 0.073376

19961231 0.029340 -0.021505

19970131 0.099762 0.061317

19970228 0.053996 0.005928

19970331 -0.083770 -0.042614

19970430 0.141256 0.058406

19970530 0.076621 0.058577

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What is the "Unit-root" and how to test it ?

Bottom of Form

Why the order of MA model can be determined by ACF while the AR model couldn't do so?

For the T-bill case, the first regression model (eq 2.46) generates very high R2 (96.5%), but why this model is still a bad one?

After reading the T-bill case, what is the best model do you think? Why?