When to Model Financial Prices, Returns, or Stationary Spreads
Summary
The discussion challenges the idea that financial models should always use returns simply because price levels are often nonstationary. It notes that returns are a common starting point for time-series analysis and can represent price behavior indirectly, but returns themselves may also fail to be stationary. Stationarity must therefore be assessed rather than assumed.
The answers describe several cases where price levels or transformations of them matter directly: equity valuation, portfolio valuation for risk management, and pairs trading where a ratio or spread between two prices may be stationary. The exchange offers examples rather than a systematic modeling guide, and one answer makes an overly broad claim connecting stationarity, independent and identically distributed data, and maximum-likelihood fitting. Model choice depends on the question, the series’ properties, and the assumptions of the method being used.
Key ideas
- Returns are often used in time-series analysis, but they are not guaranteed to be stationary.
- Price levels can be modeled directly when the series and method support it.
- Cointegration analysis can examine price combinations whose spread is stationary.
- Portfolio valuation and equity valuation use prices directly or indirectly.
- Choose the modeled quantity based on the task and verify the relevant statistical assumptions.
Tags
Full text
# Modeling Financial Time Series # Modeling Financial Time Series 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 ? ## Answer by user12348 (score 2) https://quant.stackexchange.com/a/11426 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. ## Answer by Bob Jansen (score 0) https://quant.stackexchange.com/a/11422 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. ## Answer by Kumar (score 0) https://quant.stackexchange.com/a/11431 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.
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.