Factor models are highly common in the financial literature. Recent
advances allow to relax the constancy of slope coefficients (the so-called be-
tas) by considering conditional regressions. The theory on the estimation
of these dynamic conditional betas however usually relies on short memory
volatility models, which can be restrictive in empirical applications. More-
over, exogenous variables have proven useful in recent studies on volatility
modeling. In this paper, we introduce a multivariate framework allowing for
time-varying betas in which covolatilities can exhibit higher persistence than
the standard exponential decay. Covariates are included in the dynamics of
both conditional variances and betas. We establish stationarity conditions
for the proposed model and prove the consistency and asymptotic normality
of the QML estimator. Monte Carlo experiments are conducted to assess
the performance of the estimation procedure in finite sample. Finally, we
discuss the choice of potential relevant exogenous variables and illustrate the
pertinence of the model on real data applications.