I have the time series of the prices of two securities, A and B, over the same period of time and sampled at the same frequency. I would like to test whether there is any statistically significant difference over time between the two prices (my null hypothesis would be that the difference is null). Specifically, I am using price differences as a proxy for market efficiency. Imagine A and B are a security and its synthetic equivalent (i.e. both are claims to exactly the same cash flows). If the market is efficient, both should have the exact same price (barring different transaction costs, etc.), or a zero price difference. This is what I would like to test for. What is the best way to do so?
I might have intuitively run a two-sided t-test on the "difference" time series, i.e. on the A-B time series, and tested for $\mu_0$=0. However, I have the suspicion that there might be more robust tests, that take into account things like potential homoskedastic errors or the presence of outliers. In general, are there things to watch out for when working with the prices of securities?