Essays on time series econometrics and financial econometrics

My DPhil thesis includes three essays on time series econometrics and financial econometrics, preceded by a brief introduction. The first essay proposes a new class of multivariate volatility models utilizing realized measures of asset volatility and covolatility extracted from high-frequency data. Dimension reduction for estimation of large covariance matrices is achieved by imposing a factor structure with time-varying conditional factor loadings. The models are applied to modeling the conditional covariance data of large U.S. financial institutions during the financial crisis, where empirical results show that the new models have both superior in- and out-of-sample properties. We show that the superior performance applies to a wide range of quantities of interest, including volatilities, covolatilities, betas and scenario-based risk measures. Time-varying volatility is common in macroeconomic data and has been incorporated into macroeconomic models in recent work. The second essay estimates dynamic panel data models with stochastic volatility by maximizing an approximate likelihood obtained via Rao–Blackwellized particle filters. Monte Carlo studies reveal the good and stable performance of our particle filter-based estimator. When the volatility of volatility is high, or when regressors are absent but stochastic volatility exists, our approach can be better than the maximum likelihood estimator which neglects stochastic volatility and GMM estimators. In the third essay, we test for the stable factor structure against considerable time variation in the factor loadings in the form of martingales. We obtain the asymptotic distribution of the test statistic by deriving the conditions under which the estimation error of the common factors is asymptotically negligible for the test statistic. Monte Carlo simulations show that the proposed test performs well. We apply the test to a panel of macroeconomic and financial variables in the UK and find the evidence of unstable factor structure during the recent financial crisis.