Table 3.

The results of asymmetric Fourier causality test for COVID-19 cases

Null hypothesis	lnCases ↛ lnPM2.5			lnCases+ ↛ lnPM2.5 –			lnCases+ ↛ lnPM2.5+
Cities	Test statistics	p	k	Test statistics	p	k	Test statistics	p	k
New York	7.837	9	1	7.676	12	3	4.971	7	3
Los Angeles	18.720	12	1	28.949*	12	3	17.133	10	1
Chicago	21.032***	12	3	22.533**	12	1	17.436	12	1
Phoenix	18.074	12	1	24.059**	10	1	6.712	8	1
Philadelphia	13.337	8	1	19.378**	10	2	8.805	10	2
San Antonio	11.571	11	1	25.552**	11	2	9.318	12	2
San Diego	4.057	9	1	5.206	10	2	4.650	10	1
San Jose	8.677	12	1	23.261**	12	2	6.760	10	1

Optimal lag lengths and frequencies are selected by AIC. The maximum lag length set at 12 using the Schwert’s (1989) approach (${\mathrm{k}}_{\max }=12\times {\left(\frac{111}{100}\right)}^{1/4}=12$)

*, **, and ***statistical significance at 1%, 5%, and 10% levels, respectively)