Modelling high-dimensional time series efficiently by means of constrained spatio--temporal models

Abstract

Many econometric analyses involve spatio--temporal data. A considerable amount of literature has addressed spatio--temporal models, with Spatial Dynamic Panel Data (SDPD) being widely investigated and applied. In real data applications, checking the validity of the theoretical assumptions underlying the SDPD models is essential but sometimes difficult. At other times, the assumptions are clearly violated. For example, the spatial matrix is assumed to be known but it may actually be unknown and needs to be estimated. In such cases, the performance of the SDPD model's estimator is generally affected. Motivated by such considerations, we propose a new model (called stationary SDPD) and a new estimation procedure based on simple and clear assumptions that can be easily checked with real data. The new model is highly adaptive, and the estimation procedure has a rate of convergence that is not affected by the dimension of the time series (under general assumptions), notwithstanding the relatively high number of parameters to be estimated. The new model may be used to represent a wide class of multivariate time series, not necessarily spatio-temporal. So, it can be used as a valid alternative to vector autoregressive (VAR) models with two immediate advantages: i) a faster rate of convergence of the estimation procedure and ii) the possibility of estimating the model even when the dimension is higher than the time series length, overcoming the curse of dimensionality typical of the VAR models. The simulation study shows that the new estimation procedure performs well compared with the classic alternative procedure, even when the spatial matrix is unknown and therefore estimated.