AIC, BIC and log likelihood which more important? I am currently searching for the best ARMA(p,q) model for my conditional mean.
When comparing the AIC, BIC and LL, I see that some model perform better in AIC, some in BIC and some in LL. The AC and PAC only showed significance in lag 1. The bitcoin log returns have been taken as variable. Can someone help me which to choose for the conditional mean?


You can use the log-likelihood to compare models of different size, under one condition. (Though you might still prefer to use AIC as recommended by @Christian Henning.)
While it's true that bigger models fit the data better, if the two models you want to compare are nested, you can use a likelihood ratio test (LRT) to decide whether it's (statistically) justified to include the additional parameters. Two models are nested if we can simplify the bigger model into the smaller model by imposing constraints on the parameters, eg. by setting some parameters to 0.
The LRT statistic is
$$
2\big\{ \ell(\text{bigger model}) - \ell(\text{smaller model}) \big\} \sim \chi^2_p
$$
where $\ell$ is the maximized log-likelihood, p is the number of extra parameters in the bigger model and $\chi^2_p$ is the chi-squared distribution with p degrees of freedom. Intuitively, we have a distribution for how much better the bigger model fits the data if its extra p parameters explain noise by chance.
Two models ARMA(p1,q1) and ARMA(p2,q2) are nested are long as p1 ≤ p2 and q1 ≤ q2.
So let's use a likelihood ratio test to compare the biggest and smallest model in your list, ARMA(0,0) and ARMA(2,2).
pchisq(2 * (2633.6256 - 2629.7241), df = 4, lower.tail = FALSE)
#> [1] 0.099

The p-value is 0.1, so your data doesn't need either an AR or a MA component. The ARMA(0,0) has the smallest AIC as well.
