Recent Developments in Factor Models and Time Series Analysis
Saturday, Jan. 6, 2018 10:15 AM - 12:15 PM
- Chair: Junsoo Lee, University of Alabama
Factor-driven Two-regime Regression
AbstractWe propose a novel two-regime regression model, where the switching between the regimes is
driven by either observable or unobservable factors or by both. When the factors are not directly observable, we estimate them by the PCA of a much larger data set. This approach is attractive because the factors represent the economy-wide shocks and thus factor-driven regime switching is more appealing than the settings that have been widely used in practice such as where the regime is determined by a single observable variable or by an exogenous markov process. The estimation of this model is challenging both computationally and theoretically because both the estimated factors and multiple parameters are subject to a discontinuous transformation. Therefore, we show that our optimization problem can be reformulated as an iterative mixed integer optimization. The resulting algorithm can successfully handle the computational issue caused by multi-dimensional discontinuity. Furthermore, we derive the asymptotic distributions of the resulting estimator under the shrinking delta scheme. In particular, not only we establish the conditions on the factor estimation for the oracle property, which are different from those for smooth factor augmented models, but also we analyze a non-oracle case and show how the estimation error affects the asymptotic distribution of the regime-determining parameters. They are non-standard and non-pivotal, leading us to propose a bootstrap. Finally, we illustrate our methods using an economic application.
Efficient Estimation of Panel Data Model with Interactive Effects Using High Dimensional Covariance Matrix
AbstractWe consider the efficient estimation of panel data models with interactive effects, which relies on a high-dimensional inverse covariance matrix estimator. By using a consistent estimator of the inverse idiosyncratic covariance matrix, we can take into account both cross-sectional correlations and heteroskedasticity. In the presence of cross-sectional correlations, the proposed estimator eliminates the cross-sectional correlation bias, and is more efficient than the existing methods. The rate of convergence can also be improved. In addition, we find that when the statistical inference involves estimating a high-dimensional inverse covariance matrix, the minimax convergence rate on large covariance estimations is not sufficient for inferences. To address this issue, a new “doubly weighted convergence” result is developed. The proposed method is applied to the US divorce rate data. We find that our more efficient estimator identifies the significant effects of divorce-law reforms on the divorce rate, and provides tighter confidence intervals than existing methods.
Constrained Factor Models for High-dimensional Matrix-variate Time Series
AbstractIn many scientific fields, including finance and meteorology, high-dimensional matrix-variate data are routinely collected over time. Matrix-variate factor models are an effective dimension reduction method for analyzing such data, because they incorporate the structural interrelations between columns and rows. Exploitation of natural structure in the loading matrices can further improve the efficiency in estimation and enhance interpretations of the estimated common factors. In this paper, we propose constrained and partially constrained factor models for matrix-variate time series. For estimation, we employ spectral decomposition of certain semi-positive definite matrices constructed from the cross-covariance matrices at nonzero lags. We establish asymptotic properties of the estimators when the dimension of the data and the dimensions of constrained row and column loading spaces go to infinity with the sample size. We show that the rates of convergence of the constrained matrix-variate factor loading matrices are much faster than those of the conventional matrix-variate factor analysis. We use simulation to demonstrate performance of the proposed method and the associated asymptotic properties. We then apply the proposed analysis to Fame-French 10-by-10 portfolio return series and corporate financial 16-by-200 by matrix-variate time series.
Large-N and Large-T Properties of Dynamic Panel GMM Estimators When Data Are Not Mean Stationary
AbstractFor the dynamic panel data models with a large number of cross-sectional units (N) repeatedly observed over a short time period (T), the dependent variables are often assumed to be stationary in mean. This is because implementing in GMM the moment conditions relevant under the mean stationarity assumption often substantially improves the finite-sample properties of the resulting estimator. We refer to the GMM estimator using some of the moment conditions implied by the mean stationarity condition as “MS” estimator. This paper addresses four issues related to the large-N and large-T properties of the MS estimators for dynamic panel models. The first issue is whether the MS estimators are consistent and asymptotically normal even if data are not mean stationary. The second is whether use of the MS moment conditions leads to a substantial efficiency gain. The third issue is how we would test the mean stationarity hypothesis, especially when data are generated by nearly unit root processes. The fourth is how the MS estimators can be used to test unit roots.
- C2 - Single Equation Models; Single Variables
- C4 - Econometric and Statistical Methods: Special Topics