Essays in Financial Econometrics

I consider continuous time asset pricing models with stochastic differential utilityincorporating decision makers' concern with ambiguity on true probability measure.In order to identify and estimate key parameters in the models, I use a novel econometricmethodology developed recently by Park (2008) for the statistical inference oncontinuous time conditional mean models. The methodology only imposes the conditionthat the pricing error is a continuous martingale to achieve identification, andobtain consistent and asymptotically normal estimates of the unknown parameters.Under a representative agent setting, I empirically evaluate alternative preferencespecifications including a multiple-prior recursive utility. My empirical findings aresummarized as follows: Relative risk aversion is estimated around 1.5-5.5 with ambiguityaversion and 6-14 without ambiguity aversion. Related, the estimated ambiguityaversion is both economically and statistically significant and including the ambiguityaversion clearly lowers relative risk aversion. The elasticity of intertemporal substitution(EIS) is higher than 1, around 1.3-22 with ambiguity aversion, and quite highwithout ambiguity aversion. The identification of EIS appears to be fairly weak, asobserved by many previous authors, though other aspects of my empirical resultsseem quite robust.Next, I develop an approach to test for martingale in a continuous time framework.The approach yields various test statistics that are consistent against a wideclass of nonmartingale semimartingales. A novel aspect of my approach is to use a time change defined by the inverse of the quadratic variation of a semimartingale,which is to be tested for the martingale hypothesis. With the time change, a continuoussemimartingale reduces to Brownian motion if and only if it is a continuousmartingale. This follows immediately from the celebrated theorem by Dambis, Dubinsand Schwarz. For the test of martingale, I may therefore see if the given processbecomes Brownian motion after the time change. I use several existing tests formultivariate normality to test whether the time changed process is indeed Brownianmotion. I provide asymptotic theories for my test statistics, on the assumption thatthe sampling interval decreases, as well as the time horizon expands. The stationarityof the underlying process is not assumed, so that my results are applicable also tononstationary processes. A Monte-Carlo study shows that our tests perform very wellfor a wide range of realistic alternatives and have superior power than other discretetime tests.