Nonlinear Time Series Models with Applications in Macroeconomics and Finance.

Summary The following three chapters examine: 1) whether Southeast Asian real exchange rates are nonlinear, 2) Bayesian inference on nonlinear time series model with applications to the real exchange rate, and 3) cyclicality and rebound effect in the stock market.Since the late 1990s, theoretical and empirical analyses devoted to the real exchange rate suggest that the dynamics could be well estimated by nonlinear models. The first chapter examines this possibility using monthly ASEAN-5 data, and extends existing research in two directions. First, we use recently developed unit root tests which will allow for more flexibility in stationary nonlinear models as an alternative to the commonly used SETAR or ESTAR model. Second, although different nonlinear models survive mis-specification tests, a Monte Carlo experiment using generalized impulse response functions is used to compare their relative adequacy. Our results i) support the nonlinear mean-reversion hypothesis, and thus purchasing power parity, in half of the cases and ii) indicate MRLSTAR and ESTAR as the most likely processes generating real exchange rates.The second chapter analyzes ACR model. We propose a full Bayesian approach to inference and particular attention is paid to the parameters of the threshold variables. We discuss the choice of a priori distributions and propose a Markov chain Monte Carlo algorithm to estimate the parameters and latent variables. A simulation study and application to real exchange rate data illustrate the analysis.The third chapter explores that different forms of overlaps in financial markets can present in a Markov Switching model. It builds on the rebound effects first analyzed by Kim, Morley and Piger [2005] in the business cycle and generalized by Bec, Bouabdallah and Ferrara [2011] to allow for a more flexible rebound type.Our results i) show that the rebound effect is statistically significant and important in all cases, but Germany where the evidence is less clear and ii) the permanent negative impact of bear markets on the index is significantly reduced when the rebound is explicitly taken into account.