What GARCH Forecasts: Conditional Volatility Rather Than Returns
Summary
The discussion distinguishes forecasting the variance of returns from forecasting their expected direction. A conventional GARCH model updates conditional variance using past squared residuals and earlier variance estimates, making it a framework for modeling changing volatility and volatility clustering. The accepted response emphasizes that this structure alone does not produce a return forecast; predicting returns is described as more difficult.
A second answer qualifies that conclusion: a GARCH specification can be extended or interpreted to model conditional return expectations, depending on assumptions, but this is not its central purpose. It contrasts the squared-residual structure with ARMA models, which offer a more general way to represent serial dependence and can include signed terms. The exchange gives conceptual explanations and a book recommendation, but no empirical comparison, forecast results, or implementation guidance. Whether a return model is useful depends on the assumptions about return behavior and should not be inferred from volatility forecasts alone.
Key ideas
- Standard GARCH models describe conditional variance using past squared shocks and prior variance estimates.
- A volatility forecast does not by itself imply a forecast of the mean return.
- Return prediction is a distinct and generally harder modeling task.
- Extensions can model conditional return expectations, but that is not the primary role of GARCH.
- ARMA models provide a broader framework for signed serial dependence in returns.
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Full text
# Can I forecast stock returns using GARCH?
# Can I forecast stock returns using GARCH?
I know this is a rookie question, but I have seen some comments about using GARCH to forecast stock returns.
Is it something people do? Wasn't GARCH just for volatility?
Also, can you suggest any (simple) papers that could help me better understand this technique and how to apply it in Eviews or R?
## Answer by Yang Gao (score 3)
https://quant.stackexchange.com/a/34959
The GARCH(p, q) model (where p is the order of the GARCH terms ${\sigma^2}$ and q is the order of the ARCH terms ${\epsilon^2}$ ), following the notation of original paper is given by: $$ {\sigma_t^2}={\omega}+{\sum_{i=1}^q}{\alpha_i}{\epsilon_{t-i}^2}+{\sum_{i=1}^p}{\beta_i}{\sigma_{t-i}^2} $$
Obviously, the GARCH model is about volatility and variance of returns. It can only forecast volatility, but not returns.
Actually, It is much more difficult to forecast returns than to forecast volatility.
You could take this book to understand GARCH and apply it with R: An Introduction to Analysis of Financial Data with R.
## Answer by David Addison (score 1)
https://quant.stackexchange.com/a/34968
It depends on your beliefs about the nature of stock returns. Whether or not those beliefs reflect reality is a different matter. I think it's helpful to consider what is being modeled in GARCH by breaking down the term:
Generalized - i.e., can take a number of parameters in order to fit generic data types.
Autoregressive - i.e., terms tend to revert to their means, a-la a Ornstein-Uhlenbeck process (also, Brownian Motion under friction).
Conditional - i.e., future terms are dependent on past terms and/or best estimates of future terms are based on Bayesian inference; reflects stylized beliefs on absolute return/variance clustering.
Heteroskedasticity - i.e., literally, "differing variance"; parameters change over time.
While it is technically possible to use GARCH to model the conditional expectations of stock returns, GARCH models were not intended to model returns. Implicit in the name is its intent as skedasticity (i.e., volatility) metric in which terms are squared residuals of periodic returns.
Relaxing the squared error condition, however, results in a particular form of Autoregressive Moving Averages (ARMA). ARMAs are a more generic class of econometric model which allow for negative terms and which can conform to many stylized facts of security returns.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.