A scalar dynamic conditional correlation model: Structure and estimation

Abstract

The dynamic conditional correlation (DCC) model has been widely used for modeling the conditional correlation of multivariate time series by Engle (2002). However, the stationarity conditions have been established only recently and the asymptotic theory of parameter estimation for the DCC model has not yet to be fully discussed. In this paper, we propose an alternative model, namely the scalar dynamic conditional correlation (SDCC) model. Sufficient and easily-checked conditions for stationarity, geometric ergodicity, and β-mixing with exponential-decay rates are provided. We then show the strong consistency and asymptotic normality of the quasi-maximum-likelihood estimator (QMLE) of the model parameters under regular conditions. The asymptotic results are illustrated by Monte Carlo experiments. As a real-data example, the proposed SDCC model is applied to analyzing the daily returns of the FSTE (financial times and stock exchange) 100 index and FSTE 100 futures. Our model improves the performance of the DCC model in the sense that the Li-McLeod statistic of the SDCC model is much smaller and the hedging efficiency is higher.