While working with a data on sp500 I have encountered one problem concerning the interpretation of ac and pac graphs. The problem is that none of them shows a significant lag outside of confidence band. I do not know how to choose p and q in this case in order to build my ARIMA model. Any help would be highly appreciated. I am also attaching the graphs.
These functions inform us that there is no significant autoregressive component in your data, so
p = 0.
You don't need to take differences of master data as well since you do not see declining autogression from lag 1 to 40 (referring to your charts), existence of which would be an indication of long memory, artifact of having not stationary (trendy data). So,
d = 0.
Given that you cannot expect that your residuals contain any autoregressive dependency in the absence of any significant dependencies to model (and to produce residuals), the q component seems to be zero as well. So,
q = 0.
It looks like a good approximation of ARIMA parameters to your data.
Update: I just saw @Richard Hardy's comment while I was typing, so we came in simultaneously.