Applications of Higher-Order Optimal Newton Secant Iterative Methods in Ocean Acidification and Investigation of Long-Run Implications of CO_𝟐 Emissions on Alkalinity of Seawater

Table 3

Unit root tests.

Series	ADF		DF-GLS
	With constant and; without trend	With constant and; with trend	With constant and; without trend	With constant and; with trend
log10pH	3.412[0]	−1.800[0]	−0.121[4]	−0.147[1]
log10CO2	3.266[0]	−1.894[0]	−0.130[4]	−0.188[1]
Δlog10pH	−2.291[3]	−6.104[1]^∗	−2.352[2]^∗∗	−4.486[1]^∗
Δlog10CO2	−2.347[3]	−6.101[1]^∗	−2.423[2]^∗∗	−6.241[1]^∗

Note: to select the order of lag, we start with a maximum lag length of 4 and pare it down as per the Akaike information criterion (AIC). There is no general rule on how to choose the maximum lag to start with. The bandwidth and maximum lag length are chosen according to the Bartlett kernel which is equal to 4(𝑇/100)^2/9≈4, where 𝑇=54. The optimal lag length is given in square brackets. The MacKinnon critical values [10] for the ADF unit root tests with a constant and without a time are −3.59, −2.94, and −2.60 at 1%, 5%, and 10% significance level,respectively, while those with a constant and a time trend are −4.17, −3.51, and −3.19, respectively. DF-GLS critical values without trend at 1%, 5%, and 10% levels are −2.62, −2.26, and −1.95 and with a trend are −3.76, −3.17, and −2.87, respectively. The optimal lag is chosen according to the Akaike information criterion (AIC) and Schwarz Bayesian criterion for the ADF and DF-GLS tests, respectively. * and ** denote 1% and 5% significance level correspondingly.