Essays on the Estimation of Time Series Models.
详细信息
文摘
This work focuses on estimation of time series models. First, we use the non-Gaussian quasi maximum likelihood estimator QMLE) to estimate the GARCH model. Such method usually suffers inconsistency. We identify an unknown scale parameter that is critical to consistent estimation, and propose a two-step non-Gaussian QMLE 2SNG-QMLE) for estimation of the scale parameter and GARCH parameters. This novel approach is consistent and asymptotically normal, and it has higher efficiency than the Gaussian QMLE particularly when errors have heavy tails. We next examine the properties of penalized least-squares PLS) with time series data. Such high-dimensional variable selection method has gained considerable importance in several areas of economics and finance. Assuming that the errors follow a sub-exponential strong mixing process, we show that show that PLS achieves model selection consistency with oracle properties even for dimensionality of Non-polynomial NP) of sample size. The results apply to a range of folded-concave penalty functions, and we explain the advantages of using a strictly fold-concave penalty over the L 1 penalty. We apply PLS to estimate and forecast U.S. home prices at county level using a high-dimensional vector autoregression VAR). PLS is used to select the correlating counties and estimate coefficients. We conduct out-of-sample tests, and the sparse VAR model shows improved forecasting power. We notice that using error correlation information may improve estimation accuracy, and design routines and conduct simulation studies to compare penalized pairwise likelihood estimation with equation-by-equation PLS. The final part of this work surveys recent development of screening methods in ultra high dimensional variable sections, and presents an algorithm to enhance the speed of iterative two-scale methods.