Econometric estimation and testing for high-dimensional time series and panel data

Abstract

High-dimensional time series analysis has become an active area of research, because of its increasing prevalence in applications as well as the unique challenges it presents. This thesis first explores a range of questions in this area, related to how high dimensionality invalidates conventional statistical methods. It seeks to find out how to extend the existing models to cope with increasing dimensionality; how to develop a reliable as well as efficient estimation approach under the complex structure of high-dimensional datasets; and how to gain some benefits from the current information explosion. We have addressed these problems through a theoretical study using M−estimation for high-dimensional time series linear models. One advantage of M−estimation is that it can act as a robust alternative for some classical statistical methods that are sensitive to outliers or distributional deviations. Furthermore, M−estimation features generality by covering a variety of estimation approaches, for example, the least squares estimation and quantile regression. Hence, the first objective of this thesis is to study the asymptotic properties of the M−estimator for analysing high-dimensional time series data. We also evaluate the finite sample performance of the proposed M−estimator by conducting a series of Monte Carlo experiments. Compared with the least squares estimator, the M−estimator has been found to perform much better, with high resistance to the presence of non-normal errors. Another central issue discussed in this thesis lies in panel data analysis. The increasing availability of panel datasets makes this an intriguing area to investigate. The advantage of panel datasets over univariate time series or cross-sectional data enables researchers to study the comprehensive interactions within socioeconomic networks. One remarkable feature of panel data is that cross-sectional units are likely to be correlated with each other, arising from spatial spillover, unobservable common factors and economic interactions among them. In the literature of late, econometricians have paid considerable attention to propose new methodologies for modelling the cross-sectional dependence, for instance, the multifactor error structure. However, the assumptions in the existing literature are overly restrictive (see, for example Bai 2009). Consequently, the second objective of this thesis is to develop the least squares estimator for a large panel data model with a multifactor error structure under a relaxed assumption framework. The estimator is shown to be consistent and asymptotic normal while its asymptotic distribution is non-centred. Hence, the closed expressions of the estimators for the asymptotic bias are given. Monte Carlo simulations not only investigate the small-sample performance of our estimator, but also show how well our bias estimators can centre the asymptotic distributions under different sample sizes and various strengths of dependence. In addition to large panels, short panels have also become pervasive in empirical studies, of which the cross-sectional dimension is relatively large compared with its temporal dimension. However, for the yearly data, fixed time periods can still span a rather long time span. The assumption of parameter stability becomes questionable due to the dramatically changing economic environment. A distance type estimator is introduced in this thesis for a short panel data model with a multifactor error structure, of which the asymptotic properties have been discussed. Monte Carlo simulations show that: (1) this structural break detection method performs well in terms of size and power; (2) it can also locate the break successfully; and (3) its setup incorporates the short panel data models with fixed effects as a special case. The proposed method, which uses a dataset consisting of more than 4,000 US financial institutions, has been further employed to provide empirical evidence of the well-known Gibrat’s ‘Law’.