Essays on state-space and regime-switching models in a high-dimensional setting
OA Version
Citation
Abstract
This dissertation consists of three chapters on high-dimensional Markov regime-switching and linear Gaussian state-space models.
The first chapter (coauthored with Zhongjun Qu) presents a modeling framework and estimation methods for detecting regime switching in high-dimensional data. Given that the maximum likelihood estimator fails to converge due to the high dimensionality of the parameter space, we develop an effective Gibbs sampling algorithm for estimation and inference. As an empirical application, we consider a dataset consisting of four groups of US aggregate macroeconomic variables and their disaggregate counterparts: industrial production, capacity utilization, nonfarm payroll employees, and hours worked. Our model produces smaller mean-squared forecasting errors than the corresponding aggregate model in most cases. It also provides forecasts for sub-series, which the aggregate model can not offer. Moreover, we find that our model's inference on probabilities of recessions is very close to the NBER's business cycle dating.
The second chapter examines several econometric issues related to data aggregation for linear Gaussian state-space models. It generalizes the aggregation results from autoregressive moving average (ARMA) models to linear Gaussian state-space models. Also, it provides new theoretical results for inference on state variables, highlighting the channels through which the disaggregate model achieves better estimates than the aggregate model. Monte Carlo simulations confirm the theoretical results. An empirical application to aggregate and disaggregate unemployment data reveals the extent of the information loss caused by aggregation.
The third chapter generalizes the first chapter's framework to allow mixed sampling frequencies. We propose a data-driven model and estimate it using the Gibbs sampler. From simulations, we demonstrate that the mixed-frequency model outperforms the model with only high-frequency processes when estimating the state variable. As an empirical application, we consider a dataset with monthly employment and quarterly industrial production, quarterly capacity utilization, and quarterly hours worked. We find that our mixed-frequency Markov regime-switching model outperforms the classic single-frequency Markov regime-switching model to estimate the US monthly business cycles at the aggregate level.