A scalar dynamic conditional correlation model: structure and estimation

The dynamic conditional correlation (DCC) model has been popularly used for modeling conditional correlation of multivariate time series since Engle (2002). However, the stationarity conditions are established only most recently and the asymptotic theory of parameter estimation for the DCC model has not been discussed fully. In this paper, we propose an alternative model, namely the scalar dynamic conditional correlation (SDCC) model. Sufficient and easy-checking 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 analysing the daily returns of the FSTE 100 index and FSTE 100 futures. Our model improves the performance of the DCC model in the sense that the LiMcleod statistic of the SDCC model is much smaller and the hedging efficiency is higher.