Essays in time series analysis

Abstract

I have three chapters in my dissertation. The first chapter is about the estimation and inference for DSGE model; the second chapter is about testing financial contagion among stock markets, and in the last chapter, I propose a new econometrics method to forecast inflation interval. This first chapter studies proper inference and asymptotically accurate structural break tests for parameters in Dynamic Stochastic General Equilibrium (DSGE) models in a maximum likelihood framework. Two empirically relevant issues may invalidate the conventional inference procedures and structural break tests for parameters in DSGE models: (i) weak identification and (ii) moderate parameter instability. DSGE literatures focus on dealing with weak identification issue, but ignore the impact of moderate parameter instability. This paper contributes to the literature via considering the joint impact of two issues in DSGE framework. The main results are: in a weakly identified DSGE model, (i) moderate instability from weakly identified parameters would not affect the validity of standard inference procedures or structural break tests; (ii) however, if strongly identified parameters are featured with moderate time-variation, the asymptotic distributions of test statistics would deviate from standard ones and would no longer be nuisance parameter free, which renders standard inference procedures and structural break tests invalid and provides practitioners misleading inference results; (iii) as long as I concentrate out strongly identified parameters, the instability impact of them would disappear as the sample size goes to infinity, which recovers the power of conventional inference procedure and structural break tests for weakly identified parameters. To illustrate my results, I simulate and estimate a modified version of the Hansen (1985) Real Business Cycle model and find that my theoretical results provide reasonable guidance for finite sample inference of the parameters in the model. I show that confidence intervals that incorporate weak identification and moderate parameter instability reduce the biases of confidence intervals that ignore those effects. While I focus on DSGE models in this paper, all of my theoretical results could be applied to any linear dynamic models or nonlinear GMM models. The second chapter, regarding the asymmetric and leptokurtic behavior of financial data, we propose a new contagion test in the quantile regression framework that is robust to model misspecification. Unlike conventional correlation-based tests, the proposed quantile contagion test allows us to investigate the stock market contagion at various quantiles, not only at the mean. We show that the quantile contagion test can detect a contagion effect that is possibly ignored by correlation-based tests. A wide range of simulation studies show that the proposed test is superior to the correlation-based tests in terms of size and power. We compare our test with correlation-based tests using three real data sets: the 1994 Tequila crisis, the 1997 Asia crisis, and the 2001 Argentina crisis. Empirical results show substantial differences between two types of tests. In the third chapter, I use Quantile Bayesian Approach-- to do the interval forecast for inflation in the semi-parametric framework. This new method introduces Bayesian solution to the quantile framework for two reasons: 1. It enables us to get more efficient quantile estimates when the informative prior is used (He and Yang (2012)); 2. We use Markov Chain Monte Carlo (MCMC) algorithm to generate samples of the posterior distribution for unknown parameters and take the mean or mode as the estimates. This MCMC estimator takes advantage of numerical integration over the standard numerical differentiation based optimization, especially when the likelihood function is complicated and multi-modal. Simulation results find better interval forecasting performance of Quantile Bayesian Approach than commonly used parametric approach.