Hi all. I am taking a Financial Data Analytics class and am having trouble with a practice question. All data and questions are below. How do I perform this in R Studio. Thank you!

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

19970630 -0.005255 0.043453

19970731 0.016544 0.078123

19970829 -0.170886 -0.057446

19970930 0.066783 0.053154

19971031 -0.071721 -0.034478

19971128 0.106225 0.044587

19971231 0.067000 0.015732

19980130 -0.029053 0.010150

19980227 0.059846 0.070449

19980331 0.130601 0.049946

19980430 -0.020178 0.009076

19980529 0.032949 -0.018826

19980630 0.092823 0.039438

19980731 -0.058480 -0.011615

19980831 -0.190994 -0.145797

19980930 -0.112860 0.062396

19981030 0.172451 0.080294

19981130 0.039223 0.059126

19981231 -0.043711 0.056375

19990129 -0.025187 0.041009

19990226 -0.022010 -0.032283

19990331 -0.036634 0.038794

19990430 0.108961 0.037944

19990528 0.006428 -0.024970

19990630 -0.092555 0.054438

19990730 -0.023185 -0.032046

19990831 -0.012384 -0.006254

19990930 -0.190637 -0.028552

19991029 0.222798 0.062539

19991130 0.141483 0.019062

19991231 -0.133023 0.057844

20000131 -0.013948 -0.050904

20000229 -0.153428 -0.020108

20000331 -0.031208 0.096720

20000428 0.006658 -0.030796

20000531 0.129630 -0.021915

20000630 0.079297 0.023934

20000731 0.067465 -0.016341

20000831 -0.141692 0.060699

20000929 0.050736 -0.053483

20001031 0.095238 -0.004949

20001130 0.040083 -0.080069

20001229 -0.026946 0.004053

20010131 -0.048205 0.034637

20010228 -0.085690 -0.092291

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20010430 0.022808 0.076814

20010531 0.026196 0.005090

20010629 -0.046835 -0.025004

20010731 -0.008889 -0.010772

20010831 0.091256 -0.064108

20010928 -0.033696 -0.081723

20011031 0.021985 0.018099

20011130 -0.015455 0.075176

20011231 0.004046 0.007574

20020131 -0.072110 -0.015574

20020228 0.083200 -0.020766

20020328 0.106985 0.036739

20020430 0.062189 -0.061418

20020531 0.000901 -0.009081

20020628 0.011519 -0.072465

20020731 -0.108214 -0.078995

20020830 0.021225 0.004881

20020930 -0.055686 -0.110013

20021031 -0.030859 0.086436

20021129 -0.013769 0.057070

20021231 -0.039439 -0.060333

20030131 -0.077099 -0.027415

20030228 -0.005932 -0.017004

20030331 0.011934 0.008358

20030430 -0.001976 0.081044

20030530 0.127970 0.050899

20030630 0.023261 0.011322

20030731 -0.031028 0.016224

20030829 -0.032244 0.017873

20030930 -0.007813 -0.011944

20031031 0.080075 0.054962

20031128 0.006897 0.007129

20031231 0.091398 0.050765

20040130 -0.029754 0.017276

20040227 0.014622 0.012209

20040331 0.011809 -0.016359

20040430 0.005368 -0.016791

20040528 0.015424 0.012083

20040630 -0.012074 0.017989

20040730 -0.131141 -0.034291

20040831 0.019380 0.002287

20040930 -0.098636 0.009364

20041029 0.015231 0.014014

20041130 -0.027054 0.038595

20041231 0.059272 0.032458

20050131 -0.003602 -0.025290

20050228 0.031574 0.018903

20050331 -0.019860 -0.019118

20050429 0.042477 -0.020109

20050531 0.027394 0.029952

20050630 -0.058257 -0.000143

20050729 0.048144 0.035968

20050831 0.005484 -0.011222

20050930 -0.012045 0.006949

20051031 -0.009493 -0.017741

20051130 0.004441 0.035186

20051230 -0.055751 -0.000952

20060131 0.026544 0.025467

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