Modeling Skewness and Kurtosis in Daily Equity Returns

Summary

The document asks whether daily return skewness and kurtosis can be forecast in a manner similar to variance models such as GARCH, using only daily S&P return data. It raises the presence of fat tails and negative skewness as motivations for studying higher moments, and points to historical discussions of S&P 500 skewness. The accepted answer states that skewness and kurtosis can be modeled with approaches analogous to GARCH and its variants.

The answer provides no model specification, estimation procedure, data requirements, or empirical results, and refers generally to a paper for further detail. It therefore establishes a modeling direction rather than demonstrating a forecast or its usefulness. The question's claims about investor preferences and relationships between variance, skewness, and kurtosis are not substantiated in the supplied material. Readers would need additional sources to assess model performance and whether these conditional moments are predictable at a daily horizon.

Key ideas

• The document asks whether daily return skewness and kurtosis can be forecast alongside variance.
• The answer says GARCH-like models can be used for skewness and kurtosis.
• No model details, estimates, or predictive evidence are provided.
• Claims about investor preferences and relationships among higher moments remain unsupported here.

Tags

# how to compute daily skewness of S&P daily return timeseries under no other more high - frequency time series?


# how to compute daily skewness of S&P daily return timeseries under no other more high - frequency time series?












As we all know , return time series marked features: fat tail or negative skewness and peakedness. For a similar problem of variance computation, we can compute variance by garch model and other derivatives.In other words,Does we predict skewnenss like predicting variance by garch model and other derivatives ? does the existing model for skewness exist ? According to modern fiancial theory(investors like high return ,high skewness or positive skewness ,dislike variance ,kurtosis),we can deduce$\frac{ \partial {\text{variance}}}{\partial{\text{skewness}}}<0$ and$\frac{ \partial {\text{variance}}}{\partial{\text{kurtosis}}}>0$.and kurtosis ? Two seeming useful links:

- http://www.portfolioprobe.com/2012/01/16/a-slice-of-sp-500-skewness-history/

- http://blog.datapunks.com/2011/10/market-skewness/

Any comments are appreciated

## Answer by Jacky Zhang (score 0, accepted)

https://quant.stackexchange.com/a/11442

skewness and kurtosis can both be predicted by models similar to garch and its derivatives. For more details: a new published paper here

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.