# Browsing by Subject "time change"

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Item Essays in Financial Econometrics(2010-01-14) Jeong, Dae HeeShow more I consider continuous time asset pricing models with stochastic differential utility incorporating decision makers' concern with ambiguity on true probability measure. In order to identify and estimate key parameters in the models, I use a novel econometric methodology developed recently by Park (2008) for the statistical inference on continuous time conditional mean models. The methodology only imposes the condition that the pricing error is a continuous martingale to achieve identification, and obtain consistent and asymptotically normal estimates of the unknown parameters. Under a representative agent setting, I empirically evaluate alternative preference specifications including a multiple-prior recursive utility. My empirical findings are summarized as follows: Relative risk aversion is estimated around 1.5-5.5 with ambiguity aversion and 6-14 without ambiguity aversion. Related, the estimated ambiguity aversion is both economically and statistically significant and including the ambiguity aversion clearly lowers relative risk aversion. The elasticity of intertemporal substitution (EIS) is higher than 1, around 1.3-22 with ambiguity aversion, and quite high without ambiguity aversion. The identification of EIS appears to be fairly weak, as observed by many previous authors, though other aspects of my empirical results seem 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 wide class 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 continuous semimartingale reduces to Brownian motion if and only if it is a continuous martingale. This follows immediately from the celebrated theorem by Dambis, Dubins and Schwarz. For the test of martingale, I may therefore see if the given process becomes Brownian motion after the time change. I use several existing tests for multivariate normality to test whether the time changed process is indeed Brownian motion. I provide asymptotic theories for my test statistics, on the assumption that the sampling interval decreases, as well as the time horizon expands. The stationarity of the underlying process is not assumed, so that my results are applicable also to nonstationary processes. A Monte-Carlo study shows that our tests perform very well for a wide range of realistic alternatives and have superior power than other discrete time tests.Show more Item Essays on the Predictability and Volatility of Asset Returns(2010-10-12) Jacewitz, Stefan A.Show more This dissertation collects two papers regarding the econometric and economic theory and testing of the predictability of asset returns. It is widely accepted that stock returns are not only predictable but highly so. This belief is due to an abundance of existing empirical literature fi nding often overwhelming evidence in favor of predictability. The common regressors used to test predictability (e.g., the dividend-price ratio for stock returns) are very persistent and their innovations are highly correlated with returns. Persistence when combined with a correlation between innovations in the regressor and asset returns can cause substantial over-rejection of a true null hypothesis. This result is both well documented and well known. On the other hand, stochastic volatility is both broadly accepted as a part of return time series and largely ignored by the existing econometric literature on the predictability of returns. The severe e ffect that stochastic volatility can have on standard tests are demonstrated here. These deleterious e ffects render standard tests invalid. However, this problem can be easily corrected using a simple change of chronometer. When a return time series is read in the usual way, at regular intervals of time (e.g., daily observations), then the distribution of returns is highly non-normal and displays marked time heterogeneity. If the return time series is, instead, read according to a clock based on regular intervals of volatility, then returns will be independent and identically normally distributed. This powerful result is utilized in a unique way in each chapter of this dissertation. This time-deformation technique is combined with the Cauchy t-test and the newly introduced martingale estimation technique. This dissertation nds no evidence of predictability in stock returns. Moreover, using martingale estimation, the cause of the Forward Premium Anomaly may be more easily discerned.Show more