Table 14 Time–frequency multi-beta-AR-EGARCH estimates

\(\beta_{m} = Market Beta\); \({ }\beta_{o} = Oil Beta ;\) \(\beta_{g} = Gold Beta\); \(Beta\) \(\beta_{SMB} = SMB Beta ;\)\(\beta_{HML} = HML Beta\)

Pf1D1

1.0128

1.8260

− 0.0147

− 4.0513

− 0.0271

− 4.1888

0.0137

1.3197

0.0111

0.9067

0.9198

5054.1431

770.8507

10.6967

Pf1D2

1.0293

4.6444

− 0.0272

− 10.7529

− 0.0463

− 7.2919

0.0710

5.6888

0.0850

5.9507

0.9049

1318.0062

1376.3509

11.7707

Pf1D3

1.0420

5.5350

− 0.0264

− 6.7614

− 0.0429

− 5.6053

0.0971

7.6941

0.1141

6.1202

0.9627

632.0573

1847.2088

323.9638

Pf1D4

1.0647

9.4863

− 0.0514

− 17.7020

− 0.0187

− 5.2777

0.0092

1.7401

0.1505

14.9950

0.9890

108.3324

1989.3269

5.3578

Pf1D5

1.0397

8.0482

− 0.0313

− 13.5745

− 0.0945

− 22.9679

0.1586

21.5679

0.1510

16.6384

0.9967

1025.6481

3557.1430

15.1779

Pf1D6

1.0733

22.3863

− 0.0766

− 38.7805

− 0.1362

− 52.3561

0.2349

39.7099

0.1661

34.5741

0.9994

388.6896

4842.1533

2.8870

Pf2D1

0.9885

− 1.7824

− 0.0016

− 0.4237

− 0.0065

− 0.8588

0.0343

2.2726

0.0483

2.8409

0.9152

1982.3226

766.0051

7.0794

Pf2D2

0.9934

− 1.0095

− 0.0141

− 3.2003

0.0003

0.0343

0.0589

3.7068

0.0820

4.1472

0.8843

1268.8381

1361.8681

24.5851

Pf2D3

0.9944

− 0.9029

− 0.0141

− 4.2682

0.0021

0.4989

0.1075

10.2505

0.0089

0.9911

0.9524

526.5796

2018.7980

468.0411

Pf2D4

0.9873

− 2.2911

− 0.0066

− 3.0118

− 0.0170

− 8.0105

0.0982

11.3004

0.0187

2.3086

0.9880

273.3564

1924.1235

6.0320

Pf2D5

1.0446

10.7182

− 0.0349

− 16.8265

0.0191

6.0452

0.0430

4.5824

− 0.0143

− 1.3943

0.9966

18.2804

3385.2359

7.2749

Pf2D6

1.0543

32.7148

− 0.0253

− 17.4259

0.0110

5.4796

0.2653

47.2160

0.0509

11.1970

0.9994

105.4132

4948.7422

26.5995

pf3D1

0.9007

− 6.8954

0.0841

10.3003

0.0814

5.9320

− 0.0160

− 0.5192

0.0718

2.3146

0.7624

1267.2178

831.7440

9.0860

pf3D2

0.8970

− 7.9242

0.1280

16.2711

0.0864

6.5131

− 0.0293

− 1.4324

0.0391

1.3449

0.6929

628.2041

1304.3842

26.3066

pf3D3

0.8950

− 7.1751

0.1728

20.6186

0.0418

2.8580

0.0514

1.4915

0.0833

2.7162

0.8740

702.2852

1925.7050

386.8339

pf3D4

0.9037

− 5.9604

0.2112

30.6337

0.0900

6.6366

0.1715

5.3644

− 0.1186

− 4.9075

0.9639

478.0363

2058.4045

11.0169

pf3D5

0.9480

− 7.6244

0.1289

14.2375

0.1681

34.6976

− 0.0005

− 0.0286

− 0.1963

− 11.5581

0.9884

250.9343

3574.9310

2.9612

pf3D6

0.8555

− 11.2671

0.2942

27.2611

0.0317

4.9733

− 0.3159

− 15.0591

0.1596

22.7156

0.9975

12,005.5624

4593.1584

0.0498

pf4D1

1.1218

14.2701

− 0.0145

− 5.1229

− 0.0594

− 7.9133

0.0049

0.3654

0.0812

6.0728

0.8945

3912.0928

759.5884

3.6846

pf4D2

1.1128

12.9494

− 0.0205

− 4.1248

− 0.0717

− 8.5750

0.0492

2.7191

0.1634

9.1622

0.8675

2389.9123

1372.2471

10.6827

pf4D3

1.1200

12.0426

− 0.0116

− 2.3942

− 0.0821

− 7.1891

0.0491

2.6198

0.2383

11.6878

0.9472

2718.4934

1877.9496

302.0437

pf4D4

1.1252

20.6822

− 0.0386

− 17.6717

− 0.0900

− 17.8351

− 0.0489

− 4.6542

0.2568

20.0316

0.9824

417.7878

1927.0607

4.9735

pf4D5

1.1236

24.9265

− 0.0547

− 32.5790

− 0.0614

− 19.0736

0.0899

18.6292

0.1965

24.3080

0.9948

1046.7269

3292.5984

12.6606

pf4D6

1.0841

5.3668

− 0.0737

− 40.5908

− 0.1897

− 21.1726

0.0319

8.0065

0.1994

37.2976

0.9989

1774.3733

4833.1435

0.0679

pf5D1

0.9590

− 5.9736

− 0.0170

− 5.4061

0.0028

0.4165

0.0355

2.5711

− 0.0127

− 0.7911

0.9234

1928.9845

792.0324

7.3002

pf5D2

0.9819

− 2.9366

− 0.0299

− 9.4215

− 0.0042

− 0.6262

0.0534

3.9681

− 0.0151

− 0.9699

0.9051

1114.3730

1316.5605

10.3169

pf5D3

1.0034

0.5089

− 0.0195

− 6.0161

− 0.0112

− 1.7126

0.0162

1.2892

− 0.0138

− 0.9361

0.9587

540.7671

1859.9520

344.4924

pf5D4

0.9909

− 1.9855

− 0.0232

− 11.0116

0.0186

4.3092

0.0467

4.1252

− 0.0022

− 0.2312

0.9856

1053.9387

1902.7966

3.3969

pf5D5

1.0405

9.7558

− 0.0478

− 23.5468

0.0735

27.1366

0.1658

25.7960

− 0.0968

− 12.5002

0.9969

147.0312

3290.8140

8.1607

pf5D6

0.9506

− 15.2984

− 0.0004

− 0.1757

0.0366

15.2212

0.2996

49.8728

− 0.1889

− 26.8280

0.9991

15,758.1129

4587.7523

0.0094

pf6D1

0.8737

− 17.1138

0.0187

3.7732

0.0281

4.6470

− 0.0305

− 2.5606

0.0286

1.9040

0.9150

728.3765

786.3586

1.7048

pf6D2

0.8878

− 15.6270

0.0268

8.0587

0.0598

11.5432

0.0167

1.8168

0.0454

4.3768

0.8871

478.9190

1332.8522

11.8096

pf6D3

0.8766

− 17.6389

0.0432

16.1826

0.0446

6.7467

0.0704

4.8289

− 0.0348

− 3.5503

0.9438

3435.1631

1921.9218

339.6454

pf6D4

0.8704

− 20.6654

0.0406

12.9371

0.0554

9.1593

0.0990

7.5633

− 0.0644

− 3.4686

0.9820

1720.4819

2118.0799

2.1100

pf6D5

0.9172

− 13.7235

0.0238

8.1041

0.0427

9.4687

0.0207

1.8452

− 0.0078

− 1.1847

0.9949

1025.5750

3580.5899

9.3538

pf6D6

0.9040

− 51.2927

0.0826

56.5789

0.0914

48.7542

− 0.0105

− 2.5330

− 0.0724

− 23.2545

0.9988

1021.3129

5128.3632

34.9478

Pf7D1

1.0379

4.8018

− 0.0093

− 2.2685

− 0.0036

− 0.6998

0.0221

1.2601

0.0335

2.2809

0.9125

1549.7345

746.1414

3.7055

Pf7D2

1.0327

4.8484

− 0.0157

− 3.9411

− 0.0019

− 0.6123

0.0557

4.8466

0.0352

4.7899

0.8854

747.5027

1305.3457

20.3845

Pf7D3

1.0351

3.9255

− 0.0322

− 12.6129

0.0011

0.5556

− 0.0112

− 0.7803

− 0.0142

− 0.9359

0.9428

271.1022

1956.2690

380.4895

Pf7D4

1.0493

7.2107

− 0.0262

− 9.8505

− 0.0096

− 2.4314

− 0.0128

− 1.4769

− 0.0828

− 9.2075

0.9858

335.6903

1860.5534

5.8824

Pf7D5

0.9905

− 1.8724

− 0.0324

− 9.0003

− 0.0170

− 3.3819

0.1034

7.9933

0.1163

8.4322

0.9958

30.6748

3573.5427

4.0842

Pf7D6

0.8777

− 43.8547

− 0.0322

− 14.3253

− 0.0040

− 1.8821

− 0.0196

− 9.3017

− 0.0251

− 5.8013

0.9988

1820.0950

4921.4491

4.5020

pf8D1

0.9905

− 0.9161

− 0.0113

− 1.8357

0.0165

1.4676

0.0122

0.5680

0.0521

2.3787

0.8592

876.7466

825.9724

7.5587

pf8D2

0.9980

− 0.1947

− 0.0110

− 2.1039

0.0071

1.2473

0.0558

2.0518

0.0773

2.8974

0.8202

562.8547

1298.3455

18.0321

pf8D3

1.0520

5.4799

− 0.0175

− 3.0904

− 0.0202

− 1.8986

0.0096

0.4702

− 0.0050

− 0.2193

0.9220

1379.8857

1842.5713

302.5731

pf8D4

1.0544

5.6999

− 0.0545

− 11.7887

− 0.0002

− 0.0090

0.0437

1.6324

0.0799

3.4195

0.9749

233.1310

1969.8363

4.0433

pf8D5

1.0579

9.5613

− 0.0492

− 13.5931

0.0389

6.1059

0.1166

8.0279

− 0.0528

− 4.8712

0.9926

150.7068

3524.0528

16.8286

pf8D6

0.9568

− 3.4414

− 0.0144

− 7.1454

− 0.0880

− 16.4707

0.1087

4.4857

0.3633

42.1324

0.9987

33.3478

4913.5588

35.2440