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Theory and Modern Applications

Table 4 The results of the FFFFF-FI-ADF (FFFFF-FI-ADF)

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

FFFFF-FI-ADF

Brazil

Chile

France

Germany

Italy

AG

d = 0.402

d = 0.633

d = 0.256

d = 0.405

d = 0.539

−6.688 (0.000)

−5.343 (0.000)

−5.617 (0.000)

−3.313 (0.007)

−2.257 (0.054)

New method.

d = 0.401

d = 0.006

d = 0.170

d = 0.013

d = 0.378

−6.695 (0.000)

−3.709 (0.000)

−4.520 (0.000)

−3.382 (0.007)

−2.453 (0.034)

GPH

d = 0.393

d = 0.621

d = 0.321

d = 0.522

d>1.000

−6.713 (0.000)

−5.350 (0.000)

−5.671 (0.000)

−3.252 (0.003)

 

RE

d = 0.185

d = 0.325

d = 0.296

d = 0.583

d = 0.766

−7.225 (0.000)

−5.404 (0.000)

−5.652 (0.000)

−3.213 (0.003)

−1.986 (0.045)

Frac. Fre.

0.4

0.1

1.1

1.1

1.0

FFFFF-FI-ADF

Russia

Spain

Turkey

UK

US

AG

d = 0.183

d = 0.654

d = 0.904

d = 0.147

d>1.000

−1.299 (0.679)

−1.903 (0.065)

−3.122 (0.001)

−4.614 (0.003)

 

New method.

d>0.7

d = 0.556

d = 0.151

d = 0.139

d = 0.133

 

−1.955 (0.083)

−2.893 (0.065)

−5.339 (0.000)

−3.208 (0.057)

GPH

d = 0.289

d = 0.684

d = 0.922

d>1.000

d>1.000

−0.972 (0.687)

−1.888 (0.064)

−3.129 (0.002)

  

RE

d = 0.876

d = 0.753

d = 0.817

d = 0.317

d = 0.608

0.232 (0.690)

−1.856 (0.054)

−3.087 (0.003)

−5.549 (0.000)

−3.076 (0.006)

Frac. Fre.

0.8

1.1

1.3

0.1

1.0

  1. Note: Andrews and Guggenberger (2003) (AG), Robinson (1994) (RE) and Geweke and Porter-Hudak (1983) (GPH). For fractional frequency, we have used the simplex methodology. The values in the parentheses are p-values for related test.