Peter Exterkate | University of Sydney 

Kernel ridge regression is a technique to perform ridge regression with a potentially infinite number of nonlinear transformation of the independent variables as regressors. This makes it a powerful forecasting tool, which is applicable in many different contexts. However, it is usually applied only to independent and identically distributed observations. This paper introduces a variant of kernel ridge regression for time series with stochastic volatility. The conditional mean and volatility are both modelled as nonlinear functions of observed variables. We set up the estimation problem in a Bayesian manner and derive a Gibbs sampler to obtain draws from the predictive distribution. A simulation study and an application to forecasting the distribution of returns on the S&P500 index are presented, and we find that our method outperforms most popular GARCH variants in terms of one-day-ahead predictive ability. Notably, most of this improvement comes from a more adequate approximation to the tails of the distribution.

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