Price time series are not stationary. So we difference them and get the return time series, which are stationary. Does this mean, it is always a good idea to model only the return series of financial assets.
Alternatively, do we not need to model prices ever ?
Not sure of the context of your question. I can think of the following instances. 1. If you are doing stationarity test on a time series, normally you start out with returns series. The difference you take there is to determine the lag that gives you the stationary time series, used in cointegration. 2. Prices are not stationary so are the returns many times. 3. I have seen some do pair trading based on ratio of prices of stocks, it works when they find a pair that has a spread that is stationary. 4. Risk management uses prices in a more direct way by valuing portfolio for VaR etc.
Sometimes prices are directly modeled, for example equity valuation. In Time Series analysis you're right that prices are not directly modeled but I wouldn't say are not modeled ever. They are modeled indirectly using the returns. Since often it's the price of an asset you're interested in.
Nobody stops you from modelling prices if your price series were stationary.
Modelling needs stationarity assumption because distributions cannot be fit to non-iid random variables. Non-iid random variables cannot use maximum-likelihood to fit parameters.
