Recurrent Conditional Heteroskedasticity

Abstract

We propose a new class of financial volatility models, which we call the REcurrent Conditional Heteroskedastic (RECH) models, to improve both the in-sample analysis and out-of-sample forecast performance of the traditional conditional heteroskedastic models. In particular, we incorporate auxiliary deterministic processes, governed by recurrent neural networks, into the conditional variance of the traditional conditional heteroskedastic models, e.g. the GARCH-type models, to flexibly capture the dynamics of the underlying volatility. The RECH models can detect interesting effects in financial volatility overlooked by the existing conditional heteroskedastic models such as the GARCH (Bollerslev, 1986), GJR (Glosten et al., 1993) and EGARCH (Nelson, 1991). The new models often have good out-of-sample forecasts while still explain well the stylized facts of financial volatility by retaining the well-established structures of the econometric GARCH-type models. These properties are illustrated through simulation studies and applications to four real stock index datasets. An user-friendly software package together with the examples reported in the paper are available at https://github.com/vbayeslab.

A practical tutorial on Variational Bayes

“…Conditional heteroskedastic models, such as GARCH of Bollerslev (1986), represent σ 2 t as a deterministic function of the observations and conditional variances in the previous time steps. Nguyen et al (2020) recently propose a new class of conditional heteroskedastic models, namely the REcurrent Conditional Heteroskedastic (RECH) models, by combining recurrent neural networks (RNNs) and GARCH-type models, for flexible modelling of the volatility dynamics. The conditional variance in the RECH models is the sum of two components: the recurrent component modeled by an RNN, and the garch component modeled by a GARCH-type structure.…”

“…The distribution parameters must be stored in a Matlab 1D array. In this example, we use the same priors as suggested in Nguyen et al (2020) Similar to the other VB algorithm classes, the MGVB class stores the outputs in a Matlab structure which can be used as shown in the following code to visualize the density of variational distribution and smoothed lower bound. The following code defines a function that computes both h(θ) and ∇ θ h(θ) as in ( 27)-( 28 % Compute gradient of the h(theta) h func grad = llh grad + log prior grad; % h func grad must be a column h func grad = reshape(h func grad,length(h func grad),1); end There are some rules to define a proper function for calculating h(θ) and ∇h(θ) that it is compatible with the VB algorithm classes in the package.…”

Volatility-inspired $σ$-LSTM cell

“…Recently, several studies [11,12] have explored the heteroskedasticity of returns with recurrent NN architectures, but not by means of modified LSTM cell. In [11], authors have proposed the RECH model, where ω-constant of the GARCH process is modeled by a particular RNN model.…”