Best linear forecast of volatility in financial time series

TL;DR

This paper introduces an analytical method for forecasting financial volatility by modeling autocorrelation with exponential superpositions, accounting for leverage and clustering, and compares it to ARCH models.

Contribution

It presents a new explicit analytical approach for optimal linear volatility forecasting in financial time series, incorporating leverage and clustering effects.

Findings

Effective volatility prediction for Dow Jones 30

Explicit analytical solution derived for stationary processes

Connections established with ARCH models

Abstract

The autocorrelation function of volatility in financial time series is fitted well by a superposition of several exponents. Such a case admits an explicit analytical solution of the problem of constructing the best linear forecast of a stationary stochastic process. We describe and apply the proposed analytical method for forecasting volatility. The leverage effect and volatility clustering are taken into account. Parameters of the predictor function are determined numerically for the Dow Jones 30 Industrial Average. Connection of the proposed method to the popular ARCH models is discussed.