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

Omay, Tolga; Baleanu, Dumitru

doi:10.1186/s13662-021-03317-9

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table B3 Critical values for FI models intercept and trend included in fractional frequency Fourier function \(d = (0.1, 0.5)\)

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

T	100			250			500
T	1%	5%	10%	1%	5%	10%	1%	5%	10%
k = 1.1
0.1	−4.813	−4.163	−3.830	−4.667	−4.078	−3.772	−4.587	−4.012	−3.733
0.2	−4.474	−3.866	−3.557	−4.353	−3.772	−3.436	−4.343	−3.728	−3.443
0.3	−4.261	−3.566	−3.234	−4.060	−3.434	−3.106	−3.958	−3.390	−3.067
0.4	−3.904	−3.253	−2.909	−3.718	−3.116	−2.783	−3.673	−3.035	−2.715
0.5	−3.656	−2.988	−2.636	−3.488	−2.827	−2.468	−3.376	−2.734	−2.411
k = 1.2
0.1	−4.737	−4.146	−3.811	−4.622	−4.018	−3.730	−4.530	−4.012	−3.729
0.2	−4.497	−3.853	−3.533	−4.367	−3.753	−3.429	−4.252	−3.712	−3.409
0.3	−4.185	−3.524	−3.200	−4.012	−3.407	−3.105	−3.954	−3.339	−3.036
0.4	−3.918	−3.251	−2.906	−3.706	−3.108	−2.786	−3.623	−3.037	−2.695
0.5	−3.639	−2.997	−2.616	−3.515	−2.811	−2.483	−3.350	−2.759	−2.393
k = 1.3
0.1	−4.720	−4.141	−3.821	−4.625	−4.072	−3.755	−4.565	−3.982	−3.708
0.2	−4.463	−3.859	−3.538	−4.316	−3.765	−3.455	−4.263	−3.686	−3.384
0.3	−4.168	−3.548	−3.213	−4.023	−3.417	−3.084	−3.993	−3.366	−3.032
0.4	−3.874	−3.223	−2.905	−3.695	−3.061	−2.750	−3.630	−3.036	−2.698
0.5	−3.610	−2.962	−2.615	−3.437	−2.815	−2.462	−3.310	−2.735	−2.404
k = 1.4
0.1	−4.720	−4.134	−3.814	−4.685	−4.012	−3.711	−4.570	−3.992	−3.683
0.2	−4.364	−3.785	−3.467	−4.258	−3.678	−3.375	−4.222	−3.669	−3.379
0.3	−4.172	−3.514	−3.189	−3.957	−3.373	−3.062	−3.906	−3.320	−2.992
0.4	−3.931	−3.228	−2.890	−3.685	−3.055	−2.717	−3.651	−3.015	−2.681
0.5	−3.618	−2.957	−2.591	−3.410	−2.781	−2.463	−3.298	−2.674	−2.375
k = 1.5
0.1	−4.638	−4.086	−3.750	−4.552	−3.986	−3.675	−4.509	−3.950	−3.631
0.2	−4.389	−3.769	−3.442	−4.223	−3.676	−3.348	−4.213	−3.654	−3.338
0.3	−4.116	−3.485	−3.161	−4.018	−3.364	−3.022	−3.906	−3.320	−3.001
0.4	−3.843	−3.206	−2.852	−3.704	−3.044	−2.726	−3.665	−3.036	−2.680
0.5	−3.626	−2.949	−2.587	−3.386	−2.764	−2.429	−3.309	−2.652	−2.307
k = 1.6
0.1	−4.739	−4.055	−3.749	−4.557	−3.965	−3.672	−4.476	−3.928	−3.624
0.2	−4.422	−3.736	−3.423	−4.207	−3.638	−3.312	−4.195	−3.599	−3.292
0.3	−4.157	−3.477	−3.134	−3.954	−3.361	−3.032	−3.893	−3.292	−2.954
0.4	−3.885	−3.147	−2.808	−3.710	−3.045	−2.699	−3.571	−2.973	−2.640
0.5	−3.594	−2.897	−2.559	−3.380	−2.764	−2.405	−3.367	−2.692	−2.335
k = 1.7
0.1	−4.651	−3.990	−3.653	−4.493	−3.905	−3.584	−4.447	−3.854	−3.560
0.2	−4.374	−3.776	−3.401	−4.323	−3.642	−3.313	−4.249	−3.557	−3.264
0.3	−4.078	−3.428	−3.088	−3.940	−3.319	−3.000	−3.858	−3.269	−2.975
0.4	−3.800	−3.159	−2.815	−3.694	−3.064	−2.687	−3.583	−2.987	−2.630
0.5	−3.480	−2.861	−2.523	−3.419	−2.754	−2.398	−3.297	−2.660	−2.317
k = 1.8
0.1	−4.580	−3.944	−3.633	−4.484	−3.890	−3.568	−4.469	−3.877	−3.555
0.2	−4.327	−3.710	−3.372	−4.225	−3.582	−3.296	−4.153	−3.561	−3.253
0.3	−4.037	−3.411	−3.068	−3.922	−3.279	−2.971	−3.846	−3.247	−2.929
0.4	−3.756	−3.161	−2.814	−3.643	−3.013	−2.670	−3.628	−2.955	−2.631
0.5	−3.595	−2.892	−2.547	−3.440	−2.754	−2.399	−3.326	−2.659	−2.315
k = 1.9
0.1	−4.644	−3.926	−3.587	−4.448	−3.811	−3.471	−4.367	−3.796	−3.490
0.2	−4.263	−3.670	−3.333	−4.071	−3.506	−3.226	−4.167	−3.520	−3.203
0.3	−4.079	−3.395	−3.067	−3.898	−3.275	−2.934	−3.838	−3.234	−2.900
0.4	−3.793	−3.105	−2.769	−3.663	−3.028	−2.679	−3.535	−2.916	−2.586
0.5	−3.635	−2.871	−2.517	−3.402	−2.741	−2.415	−3.305	−2.648	−2.308
k = 2.0
0.1	−4.537	−3.880	−3.531	−4.398	−3.815	−3.458	−4.318	−3.719	−3.429
0.2	−4.257	−3.632	−3.283	−4.210	−3.568	−3.235	−4.128	−3.463	−3.157
0.3	−4.055	−3.368	−3.003	−3.869	−3.261	−2.936	−3.776	−3.171	−2.841
0.4	−3.757	−3.086	−2.750	−3.573	−2.977	−2.652	−3.575	−2.914	−2.583
0.5	−3.512	−2.875	−2.499	−3.326	−2.706	−2.354	−3.259	−2.638	−2.313

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