Two essays on applications of mixture models in finance

Mixture models are of intensive interest for researchers over the last decade. Their importance is due to the fact that they provide natural representations for unobserved heterogeneity in the population. In addition to medical statistics, econometrics and survival analysis, the mixture models has also been used in the field of finance. This dissertation presents two such applications in finance. In the first application, a common-factor mixture model is developed to investigate relationships of security returns, return volatility and trading volume. The model generalizes and outperforms the standard mixture of distribution hypothesis (MDH) model (Tauchen and Pitts, 1983) by capturing possible interactions among securities. The model implies: first, common factor structures stem from information effects; second, cross-firm variations rely both on common factors and information flows; finally, common factor structures and information flows both have explanatory power beyond information flows in the positive relationship between volatility and volume. The model is fitted for intraday data of Dow Jones 30 stocks using the EM algorithm. The results show 3-factor structures in both return and trading volume series. The second application uses a bivariate mixture transition distribution (BMTD) time series model (Hassan, 1999) to test the theoretical predictions on the dynamic relationship between time duration between transactions and price volatility. A negative interactive time-varying association between time durations and price volatility is embedded in the specifications of the model. The BMTD model is different from those models developed in previous studies in two ways: First, the model relaxes the assumption of exogenous time durations, which suggests that prices may have impacts on time durations. The model also implies that the impact of prices on time durations changes over time. Second, the model suggests a Pareto distribution instead of exponential family distributions for time durations. The empirical results support the specifications of the Pareto model. Besides, the proposed unvariate mixture transition distribution models for time durations and price volatility tend to outperform the autoregressive conditional duration (ACD) model and generalized autoregressive conditional heteroskedasticity (GARCH) model, which are used by other researchers to examine the same issue