Well, I cannot give you a perfect answer, since your question lacks some informations which would be necessary to know what you are pointing at.
First of all, I think you are talking about stock market returns, because for those models metioned you need stationarity and that will most likely be the case in returns. So your Y represent the stock returns, e.g. for each day. The prices in general won't be modelled by these models.
Most likely there will be no autocorrleation in stock market returns, because then you could trade on it and make money (simplified). So in most cases the AR(1) term will be non-significant or just weak significant and the value itself very small. If you use a rolling estimation and plot the AR(1) coefficient over time, you will see that it will be very small all the time and in most market situations it will be non-significant. What reasons should there for using a MA(1) model? I don't know it.
Your first AR(1) model is the so-called "random walk" model (without drift): it assumes that, from one period to the next, the original time series merely takes a random "step" away from its last recorded position.
So in case of random walk you do not know anything about the behaviour, maybe that fits it best?