A Generalized Space-Time ARMA Model with an Application to Regional Unemployment Analysis in Italy

The STARMA (space-time autoregressive moving average) model class was introduced in the mid-1970s as a spatio-temporal extension to the ARMA time series model class. To enhance the model’s ability in dealing with spatial dependence and heterogeneity of observations, the article extends the STARMA model specification by augmenting the set of explanatory variables with simultaneous spatial lags of the observed process and unobservable shocks and by letting model parameters vary with location in space. Having introduced the extended specification,the space time impulse response function is subsequently presented as a useful tool in addressing structural issues. The article then deals with maximum likelihood estimation and hypothesis testing; in particular, Lagrange multiplier tests are proposed for spatial heterogeneity in the intercept, conditional variance and ARMA coefficients. The article closes with an application to the analysis of the series of the regional unemployment rate in Italy, aimed at evaluating the extent of the spatial propagation of regional specific shocks to unemployment and the degree of spatial heterogeneity in the process parameters.