A Multivariate Spatial and Spatiotemporal ARCH Model

TL;DR

This paper develops a multivariate spatiotemporal ARCH model incorporating spatial spill-over effects in variance, with a novel estimation method, and demonstrates its application to real estate data revealing dominant temporal volatility patterns.

Contribution

It introduces a new multivariate spatiotemporal ARCH model with explicit spatial and cross-variable effects, along with a consistent QMLE estimation approach.

Findings

Weak spatial interactions in real estate volatility

Temporal autoregressive effects dominate market risk

Interactions between property types are mainly lagged

Abstract

This paper introduces a multivariate spatiotemporal autoregressive conditional heteroscedasticity (ARCH) model based on a vec-representation. The model includes instantaneous spatial autoregressive spill-over effects in the conditional variance, as they are usually present in spatial econometric applications. Furthermore, spatial and temporal cross-variable effects are explicitly modelled. We transform the model to a multivariate spatiotemporal autoregressive model using a log-squared transformation and derive a consistent quasi-maximum-likelihood estimator (QMLE). For finite samples and different error distributions, the performance of the QMLE is analysed in a series of Monte-Carlo simulations. In addition, we illustrate the practical usage of the new model with a real-world example. We analyse the monthly real-estate price returns for three different property types in Berlin from 2002 to 2014. We find weak (instantaneous) spatial interactions, while the temporal autoregressive structure in the market risks is of higher importance. Interactions between the different property types only occur in the temporally lagged variables. Thus, we see mainly temporal volatility clusters and weak spatial volatility spill-overs.