I am currently taking a time series econometrics class, and we have been building models to predict the change in a variable (such as the change in the price of a stock, or interest rates).

Up until now we have been using ordinary/conditional least squares to predict the parameter coefficients. However recently, the professor changed our method to the maximum likelihood estimator because he said the regressors were stochastic and would result in biased estimates. Can anyone explain what this means and how the maximum likelihood estimation method solves the problem?

The models we have been building are Autoregressive and Moving Average models, which use lagged values of the dependent variable and shocks from the past to predict the current change in the variable.