Testing the correct specification of a system of spatial dependence models for stock returns

This paper provides two specification tests for the system of spatial autoregressive model of order m. We derive the theoretical limit distributions and show in a detailed Monte Carlo simulation study that the tests result in reasonable sized testing procedures with large power. In the empirical application, we analyze Euro Stoxx 50 returns in two different time spans, looking for insights how well models with different specifications of the spatial weighting matrices (local, country, industry and country-industry specific dependencies including interaction effects) fit to the data. The analyzes also demonstrate the ability of the tests to detect inaccurate Value-at-Risk forecasts.