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Theory and Modern Applications

Table 1 Critical values for FI models only intercept included in integer frequency 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

−4.297

−3.635

−3.295

−4.210

−3.565

−3.227

−4.175

−3.580

−3.262

0.2

−4.035

−3.377

−3.026

−3.858

−3.295

−2.970

−3.969

−3.330

−3.001

0.3

−3.777

−3.099

−2.762

−3.625

−3.011

−2.672

−3.675

−3.009

−2.676

0.4

−3.506

−2.868

−2.510

−3.386

−2.732

−2.398

−3.444

−2.780

−2.419

0.5

−3.275

−2.604

−2.260

−3.155

−2.506

−2.142

−3.212

−2.500

−2.159

0.6

−3.060

−2.406

−2.048

−2.851

−2.233

−1.898

−2.995

−2.290

−1.941

0.7

−2.860

−2.217

−1.875

−2.790

−2.077

−1.727

−2.812

−2.102

−1.745

0.8

−2.777

−2.094

−1.729

−2.706

−1.999

−1.618

−2.613

−1.935

−1.600

0.9

−2.667

−1.963

−1.604

−2.522

−1.839

−1.499

−2.583

−1.870

−1.512

k = 2

0.1

−3.804

−3.172

−2.809

−3.851

−3.163

−2.804

−3.809

−3.119

−2.781

0.2

−3.737

−3.015

−2.655

−3.632

−2.963

−2.625

−3.628

−2.968

−2.629

0.3

−3.571

−2.854

−2.470

−3.431

−2.771

−2.428

−3.431

−2.755

−2.415

0.4

−3.305

−2.656

−2.292

−3.229

−2.579

−2.232

−3.271

−2.613

−2.239

0.5

−3.170

−2.473

−2.111

−3.029

−2.406

−2.051

−3.124

−2.399

−2.032

0.6

−3.058

−2.326

−1.953

−2.912

−2.170

−1.819

−2.882

−2.192

−1.838

0.7

−2.944

−2.182

−1.818

−2.759

−2.068

−1.700

−2.809

−2.069

−1.695

0.8

−2.648

−1.995

−1.661

−2.594

−1.902

−1.554

−2.594

−1.890

−1.540

0.9

−2.586

−1.926

−1.554

−2.480

−1.825

−1.461

−2.523

−1.837

−1.483

k = 3

0.1

−3.636

−2.964

−2.616

−3.614

−2.989

−2.657

−3.510

−2.941

−2.589

0.2

−3.505

−2.847

−2.514

−3.492

−2.830

−2.485

−3.420

−2.810

−2.491

0.3

−3.311

−2.698

−2.344

−3.364

−2.668

−2.323

−3.304

−2.657

−2.315

0.4

−3.246

−2.549

−2.213

−3.222

−2.509

−2.157

−3.191

−2.485

−2.142

0.5

−3.072

−2.430

−2.050

−2.968

−2.326

−1.974

−3.044

−2.306

−1.959

0.6

−2.944

−2.269

−1.878

−2.819

−2.171

−1.817

−2.857

−2.205

−1.848

0.7

−2.867

−2.123

−1.761

−2.755

−2.054

−1.666

−2.737

−2.012

−1.628

0.8

−2.775

−2.006

−1.661

−2.644

−1.937

−1.546

−2.611

−1.941

−1.578

0.9

−2.577

−1.905

−1.554

−2.480

−1.827

−1.474

−2.498

−1.807

−1.453

k = 4

0.1

−3.579

−2.926

−2.563

−3.526

−2.909

−2.564

−3.563

−2.880

−2.561

0.2

−3.466

−2.758

−2.425

−3.399

−2.758

−2.435

−3.415

−2.756

−2.402

0.3

−3.355

−2.670

−2.283

−3.246

−2.588

−2.248

−3.233

−2.623

−2.281

0.4

−3.206

−2.528

−2.144

−3.087

−2.408

−2.065

−3.185

−2.441

−2.108

0.5

−3.099

−2.347

−2.009

−2.962

−2.294

−1.945

−2.994

−2.331

−1.942

0.6

−3.011

−2.270

−1.899

−2.821

−2.130

−1.786

−2.820

−2.136

−1.788

0.7

−2.829

−2.094

−1.724

−2.706

−2.030

−1.672

−2.680

−1.988

−1.623

0.8

−2.670

−1.994

−1.628

−2.510

−1.919

−1.558

−2.617

−1.888

−1.525

0.9

−2.634

−1.897

−1.536

−2.488

−1.821

−1.439

−2.552

−1.892

−1.492

k = 5

0.1

−3.555

−2.861

−2.525

−3.445

−2.866

−2.540

−3.484

−2.801

−2.494

0.2

−3.431

−2.724

−2.391

−3.383

−2.726

−2.368

−3.345

−2.694

−2.374

0.3

−3.333

−2.578

−2.246

−3.269

−2.568

−2.241

−3.290

−2.576

−2.234

0.4

−3.136

−2.465

−2.131

−3.034

−2.420

−2.088

−3.058

−2.413

−2.064

0.5

−2.975

−2.334

−1.969

−2.955

−2.299

−1.932

−2.945

−2.291

−1.930

0.6

−2.961

−2.187

−1.810

−2.797

−2.095

−1.742

−2.838

−2.140

−1.801

0.7

−2.808

−2.092

−1.708

−2.713

−2.001

−1.642

−2.655

−1.987

−1.642

0.8

−2.684

−2.009

−1.640

−2.609

−1.917

−1.546

−2.599

−1.909

−1.550

0.9

−2.650

−1.909

−1.537

−2.571

−1.874

−1.484

−2.509

−1.813

−1.444