QuoteOriginally posted by: exotiqHere's a general question for the ARCH gurus: do these models stop at variance, or can they be generalized to handle higher moments, such as time varying skew and kurtosis of a time series?Yes the first generalisation was made by Bruce Hansen (1994), he proposes what he calls the conditional density model, this model is GARCH like and has conditonal variance, skewness and kurtosis. The code (in Gauss) is even available from Bruce's homepage http://www.ssc.wisc.edu/~bhansen/progs/ier_94.html
. Other models with time varying conditonal skewness and/or kurtosis are Brännäs and Nordman (2003a,b), Níguez and Perote (2004) as well as Lanne and Saikkonen (2005) among others. A general problem with these models are that they require several thousand observations to estimate the parameters with any precision. On the other hand you may not have to be so worried from a practical perspective of non-stationarity in the data since you have a time-varying distribution.Complete references Brännäs, K., and N. Nordman. An alternative conditional asymmetry specification for stock returns. Applied Financial Economics, 13 (2003a), 537-541.Brännäs, K., and N. Nordman. Conditional skewness modeling for stock returns. Applied Economics Letters, 10 (2003b), 725-728.Hansen, B. Autoregressive conditional density estimation. International Economic Review, 35 (1994), 705-730.Lanne, M., and Saikkonen, P. Modeling conditional skewness in stock returns. Unpublished Working paper, European University Institute Working Paper ECO No. 2005/14. (2005).Ñíguez, T., and J. Perote. Forecasting the Density of Asset Returns. Unpubl. working paper. London School of Economics and Political Science, London. (2004).