This dissertation is composed of two essays on time series analysis and applied macroeconomics. 

The first essay extends the Zero-Information-Limit Condition (ZILC) theory to the Generalized ZILC, and shows how the Generalized ZILC applies in the GARCH(1,1) model theoretically and empirically. In the theoretical part, under the Generalized ZILC theory proposed in the essay, the estimated information of the GARCH coefficient in the GARCH(1,1) model is overestimated; the estimated variance and estimated standard error of the GARCH coefficient is too small relative to the true value. Therefore, the actual size of the t-statistics of the GARCH estimate is too large. When sample size increases, this problem still exists. Because of the underestimated variance, it would be too often to reject the true null hypotheses. This essay proposes an empirical application strategy, by constructing the ZILC zone and safe zone for the GARCH(1,1) model. In the application part, this paper uses Value-at-Risk analysis in the risk management, to show that, if we fail to pay attention to the Generalized ZILC issue, the risk calculated by Value-at-Risk methodology using the GARCH(1,1) model, would be underestimated. At last, this paper proposes a Parametric Bootstrapping strategy, to generate a ratio and correct the underestimated variance of the GARCH coefficient in the GARCH(1,1) model.  

In the second essay, I estimate the extent to which shocks to ``animal spirits" can have an effect on real economic outcomes at business cycle frequencies.  Recent advances in rational expectations models that formalize a role for animal spirits shocks (or ``sentiments" shocks) motivate an empirical examination of this question. I use monthly data on consumer confidence and coincident economic activity indexes at the level of U.S. states in a structural Vector AutoRegression (SVAR) model with long run restrictions to identify shocks to animal spirits and to economic fundamentals (which we refer to as ``news" shocks). Specifically, I assume that animal spirits shocks cannot have an effect on the level of output in the long run. I find that, although most variation in the level of output (in the short run and in the long run) can be explained by innovations in news, animal spirits do have statistically and economically significant effects at business cycle frequencies. Two years after a positive innovation in animal spirits, the level of output is about three percent higher than it was before the shock. Significant effects can also be observed on retail sales, non-farm payrolls, the unemployment rate, and aggregate wages and salaries.