Assessing efficiency in prices and trading volumes of cryptocurrencies before and during the COVID-19 pandemic with fractal, chaos, and randomness: evidence from a large dataset

Financial Innovation

Table 3 Results of one-sided F-test when applied to price time series

Statistical tests	Null hypothesis	p-value
F-test	Variance of CD prior pandemic is larger (lower) to variance of CD during pandemic	0.9984 (0.0016)
F-test	Variance of LE prior pandemic is larger (lower) to variance of LE during pandemic	0.0173 (0.9827)
F-test	Variance of AE prior pandemic is larger (lower) to variance of AE during pandemic	2.7267 × 10^–04 (0.9997)

CD denotes correlation dimension, LE denotes Lyapunov exponent, and AE denotes approximate entropy. We performed one-sided (right) tests and one-sided (left) tests. All statistical tests are performed at 5% significance level. A p-value less than 5% significance level implies rejection of the null hypothesis. Therefore, during the pandemic period, the variance of correlation dimension decreased whilst the variance of Lyapunov exponent and the variance of approximate entropy increased