Choosing Time-Series and Cross-Sectional Models for Return Forecasting
Summary
The document surveys approaches to forecasting asset returns, including time-series, cross-sectional, and panel models. Time-series examples include autoregressive models, moving averages, and ARIMA; the discussion says lag choice should be guided by diagnostics such as partial autocorrelation, seasonality, and heteroskedasticity. It distinguishes mean-reverting price behavior, where an autoregressive model may be suitable, from volatility dynamics, for which ARCH and GARCH models are more relevant.
Cross-sectional regressions can relate returns to security characteristics or factor exposures, while panel methods combine time and cross-section. The answer offers no empirical comparison or forecast results. Instead, it emphasizes that a model encodes assumptions about how the data are generated, and recommends beginning with empirical investigation and a theory of returns. The scope is a high-level orientation: model suitability depends on the asset and data, and the text does not provide a full procedure for selecting or validating a forecasting strategy.
Key ideas
- Time-series, cross-sectional, and panel models offer distinct frameworks for return forecasting.
- Autoregressive models may suit mean-reverting prices, while lag selection requires diagnostic analysis.
- ARCH and GARCH models are presented primarily as tools for modeling volatility dynamics.
- Factor regressions can explain cross-sectional return differences using security characteristics or exposures.
- Model choice should reflect an empirically studied theory of the return-generating process.
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Full text
# What methods do I need to learn in order forecast asset price movements? # What methods do I need to learn in order forecast asset price movements? What are the standard models used to forecast asset price movements? For example, if I were to trade an option, what model would I use in conjunction with option pricing models to forecast the stock price? Should I use GARCH or one of its variants? ## Answer by Ram Ahluwalia (score 13) https://quant.stackexchange.com/a/1545 You can forecast stock prices thru time-series models, cross-sectional, or panel models. There is considerable variation within these categories. In time-series models you would use an auto-regressive model such as an AR(1) where the independent variable is the dependent variable lagged by one period. Naturally, an AR(2) would consist of 2 lags and so on. AR(1) models are best when the stock price exhibits mean reversion and does not have a unit root. You would have to perform an analysis to determine the appropriate # of lags (partial auto-correlation coefficient, checks for seasaonlity, heteroskedasticity, etc.) and so forth. Other time-series models include the Moving Average MA(1), or combination models such as ARIMA. These models have different properties from AR(1) models. For example, the auto-correlation function of the residuals for a MA(1) collapses to zero after one lag. GARCH and ARCH models are also worth exploring, particularly for volatility modeling, however this specification is not used for modeling returns because returns do not have clustering and memory in the same way that volatility does. I would recommend Ruey Tsay's text to learn more about time-series models. Cross-sectional models use multiple regression to predict returns based on a security's characteristics or exposures to factors. In this case you may elect to explain security returns in terms of a factor model. Other models might consist of panel models (i.e. time series and cross-sectional) such as random effects or mixed effects. In any modeling choice, however, you are making a claim as to the structure of the data generating process. I would argue that you begin with empirical study, develop a theory that describes returns, and then formulate your ideas on the best approach to model the series. Some popular theories are covered in John Cochrane's asset pricing text.
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