Connectedness between Gold and Cryptocurrencies in COVID-19 Pandemic: A Frequency-Dependent Asymmetric and Causality Analysis

Table 9

Stationarity of quantile residuals.

Quantiles	ADF	PP
0.05	−2.2296	−26.0020^∗∗
0.10	−2.3779	−28.7460^∗∗∗
0.15	−2.5097	−30.1900^∗∗∗
0.20	−2.6914	−30.4550^∗∗∗
0.25	3.3159^∗	−36.1560^∗∗∗
0.30	−3.7425^∗∗	−41.6150^∗∗∗
0.35	−3.7850^∗∗	−40.8460^∗∗∗
0.40	−3.7998^∗∗	−39.484^∗∗∗
0.45	−3.6681^∗∗	−36.1860^∗∗∗
0.50	−3.7431^∗∗	−37.4810^∗∗∗
0.55	−3.9178^∗∗	−39.6880^∗∗∗
0.60	−3.9746^∗∗	−40.7780^∗∗∗
0.65	−4.0389^∗∗∗	−40.8560^∗∗∗
0.70	−4.0383	−40.8860^∗∗∗
0.75	−4.1474^∗∗∗	−42.4200^∗∗∗
0.80	−4.1967	−42.532^∗∗∗
0.85	−4.2204^∗∗∗	−42.8520
0.90	−4.2582^∗∗∗	−42.0080^∗∗∗
0.95	−4.2435^∗∗∗	−38.9630^∗∗∗

NB: ^∗∗∗, ^∗∗, and ^∗denote significance at 1%, 5%, and 10%, respectively. The residuals stationarity outcome presented in Table 9 at all quantiles are similar for the signal and all the decomposed series. This is not surprising because each of the VMFs has a cosine function wave shape, and that is sparsely varying, positive envelopes, and an instantaneous frequency that fluctuates sluggishly. The outcome for PP depicts that all the quantiles are stationary, whereas ADF test indicates that all but four lower quantiles are stationary.