What is the null hypothesis of the Mcleod and Li test? 
I did the Mcleod and Li test.
There are some critical cases $\text{lag} = 5, 6, \dots, 11$ but not at all. First four cases are located above red line $p=0.05$.
I'm so confused. 
What does this figure mean? Are there ARCH effects or not?
 A: The null hypothesis of the McLeod and Li test is that there is no autoregressive conditional heteroskedasticity (ARCH) among the lags considered. That is, there are no ARCH effects between lag $1$ and lag $k$ (considering all $k$ lags together), where $k$ is on the horizontal axis in the figure.
Your figure displays test results for a number of different lags $k$. Considering each of them individually, you can 


*

*either reject the null hypothesis in favour of the alternative (which is that ARCH effects are present) -- when the observed $p$-value is below the horizontal red line;

*or fail to reject the null hypothesis (i.e. fail to find enough evidence against the null) -- when the observed $p$-value is above the horizontal red line.


Taking the test results for different lags together, you have a multiple testing problem. Given a confidence level of 95%, about 5% of the $p$-values should be below the horizontal red line under the null (i.e. when ARCH effects are truly absent). In your case, 7 out of 20 cases are below the line, which is 35% -- way more than 5% -- so the null hypothesis is not likely to hold.
In summary, you have an indication that there are ARCH effects at some higher lags, so the data is not likely to have been generated by an ARCH-free process.
