Survey_HOR_2014

Abstract

Our major focus is on time series models where the number of parameters relative to the number of observations is high and thus it is computationally challenging or virtually impossible to optimize the entire log-likelihood in one step. The algorithm and corresponding asymptotic theory, however, can also be applied to other estimation and inference problems. The asymptotic distribution of the iterative estimation procedure in dependence of the exact number of iterations is particularly useful since researchers limit the latter in realistic applications. As illustrated in the paper, these results can be used, among others, to easily establish the asymptotic efficiency of the feasible generalized least squares (FGLS) estimator. Closest to our approach is the procedure proposed by Song, Fan, and Kalbfleisch (2005) who suggest decomposing the log-likelihood into a so-called (simple) working and a (complicated) error part. Our approach, however, differs in two important respects: Firstly, our algorithm relies onthe decomposition of the parameter space into G sub-spaces and thus is more flexible if ? is large. Secondly, we do not require the analytical first-order derivative which makes it more tractable if the underlying model is complex. The small-sample performance of the procedure is illustrated in two comprehensive simulation studies. The first one investigates the properties of ?hn for a 5-dimensional VARMA model including 24 parameters based on 50 observations. In the second simulation study, we analyze the performance of our estimator for a 15-dimensional VMEM containing 375 parameters based on a sample size of 500. We illustrate that our proposed procedure significantly simplifies the underlying estimation problem and performs sufficiently well even in these inherently high-dimensional settings. Finally, we apply our approach to measure volatility connections between 30 companies by extending the connectedness measure introduced by Diebold and Yilmaz (2014) to a high-dimensional and non-Gaussian setting.