Cholesky–ANN models for predicting multivariate realized volatility

Abstract

Accurately forecasting multivariate volatility plays a crucial role for the financial industry. The Cholesky-Artificial Neural Networks specification here presented provides a twofold advantage for this topic. On the one hand, the use of the Cholesky decomposition ensures positive definite forecasts. On the other hand, the implementation of artificial neural networks allows to specify nonlinear relations without any particular distributional assumption. Out-of-sample comparisons reveal that Artificial neural networks are not able to strongly outperform the competing models. However, long-memory detecting networks, like Nonlinear Autoregressive model process with eXogenous input and long shortterm memory, show improved forecast accuracy respect to existing econometric models.

Predicting stock market volatility based on textual sentiment: A nonlinear analysis

“…For example, it is used as a required input value when calculating value at risk (Gospodinov et al, 2006). Traditionally, econometric models, such as generalized autoregressive conditional heteroskedasticity (GARCH) family (Bollerslev, 1986) and HAR family (Corsi, 2009), are the first choice to model volatility, whereas, they are used on very strict terms although they are concise and intuitionistic; on the other hand are the recurrent neural networks (RNNs), which are widely used in time series predicting problems because it can detect long‐term persistence and nonlinear dependencies without any assumption on the distribution of the target variables (Bucci, 2020). As a type of RNNs, the long–short‐term memory (LSTM) model is one of the most advanced ML architectures for sequence learning tasks (Fischer & Krauss, 2018).…”

“…Finally, our study explains that the textual sentiment can improve stock volatility prediction by using a nonlinear regression model, and this improvement is significant and makes economic sense. A large number of empirical studies show that the ML method performs far better than the econometric methods in volatility prediction (see, for example, Bucci, 2020; Liu, 2019). The nonlinear models especially the deep learning techniques are more suitable to the complex and chaotic financial system.…”

Multivariate Realized Volatility Forecasting with Graph Neural Network

“…The aforementioned literatures adopt a univariate approach in this task, which means that the model only considers one outcome for one stock at the same time, instead of jointly considering the situations of all stocks, although the asset returns on the financial markets can be highly correlated (Campbell et al, 1993). Andersen et al (2005) propose linear multivariate volatility forecasting methods based on daily price data to take into account this correlation, while Bucci (2020) further uses neural networks to forecast realized volatility covariance matrix non-linearly. Bollerslev et al (2019) first propose a parametric multivariate model based on LOB data using covolatility and covariance matrices.…”

Forecasting High-Dimensional Covariance Matrices of Asset Returns with Hybrid GARCH-LSTMs

“…While there have already been a number of papers trying to predict the volatility of one asset using neural networks, the study of their application to the case of the conditional covariance matrix of asset returns remains almost non-existent. To our knowledge, only Cai et al (2013) and Bucci (2019) have addressed this issue so far. Cai et al (2013) relied on the use of a Conditionally Restricted Boltzmann Machine (CRBM) to predict the Cholesky factorization of the one-step-ahead conditional covariance matrix for a sample of forty assets, and found that their model produced similar results to those of a CCC.…”

“…Cai et al (2013) relied on the use of a Conditionally Restricted Boltzmann Machine (CRBM) to predict the Cholesky factorization of the one-step-ahead conditional covariance matrix for a sample of forty assets, and found that their model produced similar results to those of a CCC. Bucci (2019) also relied on the use of a Cholesky decomposition to ensure the positive definiteness of the predicted matrix, but with different types of ANNs and on a sample of only three assets. He found in particular that nonlinear autoregressive networks with exogenous inputs (NARX) and LSTMs allowed for a slight increase in precision compared to a DCC.…”