Cholesky–ANN models for predicting multivariate realized volatility

• Date: 01 September 2020
• Author: Andrea Bucci
• DOI: http://doi.org/10.1002/for.2664
• Published date: 01 September 2020

Received: 12 August 2019 Accepted: 12 January 2020

DOI: 10.1002/for.2664

RESEARCH ARTICLE

Cholesky–ANN models for predicting multivariate realized

volatility

Andrea Bucci1,2

1Department of Economics and Social

Sciences, Università Politecnica delle

Marche, Ancona, Italy

2Department of Biomedical Sciences and

Public Health, Università Politecnica delle

Marche, Ancona, Italy

Correspondence

Andrea Bucci, Department of Economics

and Social Sciences, Università Politecnica

delle Marche, 60121 Ancona, Italy.

Email: a.bucci@univpm.it

Abstract

Accurately forecasting multivariatevolatility 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 us to specify nonlinear

relations without any particular distributional assumption. Out-of-sample com-

parisons reveal that artificial neural networksare not able to strongly outperform

the competing models. However, long-memory detecting networks, like non-

linear autoregressive model process with exogenous input and long short-term

memory, show improved forecastaccuracy with respect to existing econometric

models.

KEYWORDS

Cholesky decomposition, Neural networks, Realized covariances

1INTRODUCTION

Forecasting the volatility of a portfolio has assumed a cru-

cial role in the financial markets, holding the attention of

a stream of econometric literature.

This paper draws closely on the contributions made to

volatility models and artificial neural networks (ANNs).

In particular, a strand of literature (e.g., Anderson, Nam,

& Vahid, 1999; Maheu & McCurdy, 2002) has demon-

strated that volatility asymmetrically responds to unex-

pected news and that linear methods may not be adequate

to model it. A first attempt to model nonlinearities in mul-

tivariate conditional volatility has been provided by Kwan,

Li, and Ng (2005), which relies on a multivariate threshold

generalized autoregressive conditional heteroskedasticity

(GARCH) model. Recently,the introduction of a nonpara-

metric measure, like realized volatility, has allowed the

implementation of different multivariate models, such as

the vector smooth transition autoregressive model (Bucci,

Palomba, & Rossi, 2019) and ANNs with multiple target

variables.

The attention of this paper is focused on the use of neu-

ral networks (NNs) in finance. ANNs have been widely

applied in economics and finance, since they are capa-

ble of detecting nonlinear dependencies and long-term

persistence without any assumption on the distribution

of the target variables. However, despite the large num-

ber of papers that refer to the application of ANNs for

financial time series forecasting (e.g., Khan, 2011; White,

1988), only a few works focus specifically on their appli-

cation to forecasting conditional volatility. The majority of

these studies foresee the combination of a GARCH model

with an NN architecture (e.g., Donaldson & Kamstra,1997;

Hu & Tsoukalas, 1999), with few exceptions (e.g., Bucci,

2019; Fernandes, Medeiros, & Scharth, 2014; Vortelinos,

2017). None of these works is designed for the multivariate

context.

Extending the above-mentioned literature, this study

seeks to understand whether ANNs provide more accurate

forecasts than existing models in a multivariate frame-

work. In doing so, the analysis relies on both feedfor-

ward (FNNs) and recurrent neural networks (RNNs).

Journal of Forecasting. 2020;39:865–876. wileyonlinelibrary.com/journal/for © 2020 John Wiley & Sons, Ltd. 865