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Theory and Modern Applications

Table 2 Critical values for FI models intercept and trend included in integer Fourier function

From: Fractional unit-root tests allowing for a fractional frequency flexible Fourier form trend: predictability of Covid-19

T

100

250

500

1%

5%

10%

1%

5%

10%

1%

5%

10%

k = 1

0.1

−4.722

−4.110

−3.809

−4.649

−4.054

−3.765

−4.567

−4.003

−3.708

0.2

−4.505

−3.865

−3.511

−4.320

−3.722

−3.447

−4.257

−3.698

−3.397

0.3

−4.183

−3.524

−3.199

−4.089

−3.409

−3.087

−4.031

−3.394

−3.073

0.4

−3.931

−3.205

−2.883

−3.730

−3.107

−2.781

−3.723

−3.035

−2.717

0.5

−3.640

−2.951

−2.606

−3.515

−2.837

−2.484

−3.414

−2.732

−2.392

0.6

−3.367

−2.752

−2.382

−3.220

−2.536

−2.174

−3.127

−2.444

−2.079

0.7

−3.167

−2.502

−2.167

−3.044

−2.345

−1.987

−2.806

−2.202

−1.882

0.8

−2.985

−2.282

−1.933

−2.843

−2.143

−1.777

−2.733

−2.020

−1.671

0.9

−2.857

−2.170

−1.782

−2.720

−2.007

−1.620

−2.557

−1.916

−1.530

k = 2

0.1

−4.524

−3.869

−3.519

−4.402

−3.775

−3.458

−4.369

−3.764

−3.453

0.2

−4.253

−3.606

−3.261

−4.130

−3.541

−3.197

−4.099

−3.501

−3.178

0.3

−4.122

−3.343

−3.006

−3.887

−3.273

−2.941

−3.883

−3.223

−2.878

0.4

−3.764

−3.147

−2.766

−3.599

−2.955

−2.633

−3.570

−2.924

−2.591

0.5

−3.548

−2.868

−2.510

−3.360

−2.712

−2.342

−3.349

−2.636

−2.288

0.6

−3.353

−2.689

−2.316

−3.159

−2.453

−2.122

−3.063

−2.410

−2.056

0.7

−3.051

−2.422

−2.062

−2.903

−2.233

−1.900

−2.905

−2.192

−1.818

0.8

−2.969

−2.234

−1.884

−2.753

−2.116

−1.730

−2.685

−2.005

−1.643

0.9

−2.755

−2.084

−1.724

−2.593

−1.961

−1.596

−2.598

−1.866

−1.524

k = 3

0.1

−4.318

−3.649

−3.310

−4.209

−3.602

−3.273

−4.189

−3.561

−3.258

0.2

−4.055

−3.445

−3.093

−4.031

−3.392

−3.053

−3.919

−3.337

−2.998

0.3

−3.899

−3.231

−2.885

−3.822

−3.115

−2.791

−3.771

−3.097

−2.768

0.4

−3.650

−3.026

−2.680

−3.476

−2.870

−2.527

−3.504

−2.832

−2.491

0.5

−3.478

−2.791

−2.446

−3.324

−2.677

−2.327

−3.262

−2.588

−2.246

0.6

−3.311

−2.569

−2.212

−3.112

−2.473

−2.092

−3.019

−2.344

−1.978

0.7

−3.084

−2.407

−2.038

−2.843

−2.209

−1.858

−2.824

−2.177

−1.821

0.8

−2.947

−2.240

−1.884

−2.811

−2.084

−1.727

−2.656

−1.986

−1.636

0.9

−2.863

−2.142

−1.763

−2.660

−1.977

−1.608

−2.543

−1.870

−1.496

k = 4

0.1

−4.157

−3.508

−3.167

−4.141

−3.487

−3.166

−4.145

−3.495

−3.146

0.2

−4.025

−3.344

−2.962

−3.912

−3.269

−2.946

−3.911

−3.240

−2.932

0.3

−3.903

−3.178

−2.816

−3.778

−3.088

−2.754

−3.704

−3.013

−2.692

0.4

−3.727

−2.941

−2.604

−3.519

−2.858

−2.505

−3.408

−2.819

−2.479

0.5

−3.411

−2.761

−2.392

−3.290

−2.639

−2.286

−3.160

−2.543

−2.203

0.6

−3.201

−2.525

−2.173

−3.151

−2.399

−2.053

−2.996

−2.328

−1.970

0.7

−3.031

−2.368

−1.998

−2.847

−2.211

−1.879

−2.837

−2.126

−1.762

0.8

−2.856

−2.209

−1.854

−2.714

−2.078

−1.724

−2.691

−2.002

−1.639

0.9

−2.853

−2.113

−1.741

−2.708

−1.973

−1.610

−2.497

−1.863

−1.513

k = 5

0.1

−4.212

−3.454

−3.111

−4.021

−3.411

−3.113

−4.052

−3.405

−3.077

0.2

−3.994

−3.302

−2.939

−3.874

−3.231

−2.903

−3.787

−3.202

−2.894

0.3

−3.816

−3.114

−2.758

−3.626

−3.006

−2.663

−3.602

−2.988

−2.672

0.4

−3.522

−2.895

−2.552

−3.429

−2.783

−2.466

−3.427

−2.740

−2.430

0.5

−3.458

−2.683

−2.318

−3.267

−2.605

−2.260

−3.173

−2.532

−2.188

0.6

−3.270

−2.544

−2.177

−3.012

−2.368

−2.027

−3.032

−2.342

−1.965

0.7

−3.100

−2.390

−2.001

−2.872

−2.231

−1.896

−2.840

−2.121

−1.735

0.8

−2.887

−2.241

−1.869

−2.801

−2.093

−1.726

−2.727

−1.991

−1.612

0.9

−2.734

−2.101

−1.745

−2.693

−1.968

−1.617

−2.596

−1.865

−1.490