Break Point Estimation and Variable Selection in Quantile Regressions PDF Download

Author: Ming Zhong
Publisher:
ISBN: 9781267666772
Category :
Languages : en
Pages :

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Book Description
In both statistics and econometrics, there is a large amount of research literature on issues related to structural breaks. Since checking model stability is a long-standing problem in regression (or autoregression) models, it is desirable to develop methodsto test the presence of break points, and estimate their locations if they exist. By doing so a data series may be segmented into several subseries, which are commonly assumed to have the same functional form but dierent parameters. Another important issue in multiple regressions involves determining which covariates are to be included in the final model. In practice, it is often the case that many covariates are collected and a large parametric model is built at the initial stage. However, the inclusion of irrelevant variables may reduce model performance and stability, aggravate computational burden, and make the resultant model difficult to interpret. Thus, how to efficiently select a subset of significant covariates upon which the response variable depends is of key importance when building multiple regressionmodels. The goal of our research focuses on the above-mentioned two questions: break point detection and variable selection. In Chapter 2, we jointly address both issues in a quantile regression setting. We then elaborate on the problem of break point detection for nonstationary time series in Chapter 3. For both investigations, we emphasize the importance of utilizing quantile related models, and develop methodologies based on them. In Chapter 1, we first introduce the quantile regression model. Distinct from classical regressions in which parameter estimates are derived based on the conditional mean of the response variable given certain values of the predictor variables, quantile regressions aim at estimating either at the conditional median or other quantiles of the response variable. As time series counterpart, the quantile autoregression model is then presented, and shown to be a member of the class of random coefficient autoregressions, often used in time series analysis. We further introduce the problem of break point detection and variable selection in detail, and conduct a literature review on these two topics. As the goal is to nd the best model (either with correctly identified break points, or with appropriately selected variables, or both), the estimation criterion (based on the Minimum Description Length Principle) and the optimization algorithm (based on a Genetic Algorithm) are illustrated. In the second chapter, we propose a new procedure for simultaneously estimating the number and locations of structural breaks and conducting variable selection at conditional quantile(s). In particular, with piecewise quantile regression structure, the estimated segments with selected variables are expected to minimize a convex objective function, and a genetic algorithm is implemented to solve this optimization problem. To incorporate possibly skewed and heavy-tailed innovations into the model building process, we propose the use of Asymmetric Laplace innovations as a substitute of Gaussian innovations. We develop large sample properties and theoretical justifications for the consistency of this method. Numerical results from simulations and data applications show that the proposed approach turns out to be competitive with and often superior to a number of existing methods. The third chapter presents the approach for estimating the number and locations of break points in nonstationary time series via quantile autoregression models. The methodology and its implementation details are linked to those in Chapter 2. Asymptotic properties and theoretical justifications for the consistency of this method are derived, and several simulations as well as data applications are employed to illustrate that our method consistently estimates the number and locations of the breaks.