Gaussian Process-Mixture Conditional Heteroscedasticity

Abstract

Generalized autoregressive conditional heteroscedasticity (GARCH) models have long been considered as one of the most successful families of approaches for volatility modeling in financial return series. In this paper, we propose an alternative approach based on methodologies widely used in the field of statistical machine learning. Specifically, we propose a novel nonparametric Bayesian mixture of Gaussian process regression models, each component of which models the noise variance process that contaminates the observed data as a separate latent Gaussian process driven by the observed data. This way, we essentially obtain a Gaussian process-mixture conditional heteroscedasticity (GPMCH) model for volatility modeling in financial return series. We impose a nonparametric prior with power-law nature over the distribution of the model mixture components, namely the Pitman-Yor process prior, to allow for better capturing modeled data distributions with heavy tails and skewness. Finally, we provide a copula-based approach for obtaining a predictive posterior for the covariances over the asset returns modeled by means of a postulated GPMCH model. We evaluate the efficacy of our approach in a number of benchmark scenarios, and compare its performance to state-of-the-art methodologies.

Deep learning with t -exponential Bayesian kitchen sinks

“…One direction for further research concerns postulating nonelliptical latent variable densities, which can account for skewness in a fashion similar, e.g., to (Partaourides and Chatzis, 2017;Chatzis, 2010). Introduction of a solid means of capturing conditional heteroscedasticity in modeled sequential data, in a fashion similar, e.g., to (Platanios and Chatzis, 2014), is also a challenge of immense interest. On a different vein, we must emphasize that our approach is not capable of modeling spatial dynamics and dependencies the way, e.g., convolutional networks do.…”

Remaining Useful Life Prediction for Lithium-Ion Batteries Based on Gaussian Processes Mixture

“…According to the way in which the dataset is generated, GPM model can be classified into the discriminative model where inputs are fixed [15–17] and the generative model where the inputs are random vectors [18–20]. The gating function, defined as the distribution of the partition of the samples, can be fixed mixing proportions [15, 18], Dirichlet Process [19, 20], Pitman-Yor Process [16], etc. Besides, in some GPM models, various priors can be imposed onto the model parameters.…”

Forecasting Value at Risk and Expected Shortfall of Foreign Exchange Rate Volatility of Major African Currencies via GARCH and Dynamic Conditional Correlation Analysis

“…Most popular models for financial volatility are based on the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) class of models. GARCH and related class of models have a long history and have received wide range of applications in economics and similar areas [See Engle ( 1982 ), Bollerslev ( 1986 ), Hentschel ( 1995 ), Lanne and Saikkonen ( 2005 ), Platanios and Chatzis ( 2014 ) and Otto et al ( 2018 )]. In particular, foreign exchange rates data have received attention based on the GARCH class of models.…”