A Simple Long Memory Model of Realized Volatility

Abstract

In the present work we propose a new realized volatility model to directly model and forecast the time series behavior of volatility. The purpose is to obtain a conditional volatility model based on realized volatility which is able to reproduce the memory persistence observed in the data but, at the same time, remains parsimonious and easy to estimate. Inspired by the Heterogeneous Market Hypothesis and the asymmetric propagation of volatility between long and short time horizons, we propose an additive cascade of different volatility components generated by the actions of different types of market participants. This additive volatility cascade leads to a simple AR-type model in the realized volatility with the feature of considering volatilities realized over different time horizons. We term this model, Heterogeneous Autoregressive model of the Realized Volatility (HAR-RV). In spite of the simplicity of its structure, simulation results seem to confirm that the HAR-RV model successfully achieves the purpose of reproducing the main empirical features of financial data (long memory, fat tail, self-similarity) in a very simple and parsimonious way. Preliminary results on the estimation and forecast of the HAR-RV model on USD/CHF data, show remarkably good out of sample forecasting performance which steadily and substantially outperforms those of standard models.