We propose a new class of models specifically tailored for spatio-temporal data analysis. To this end, we generalize the spatial autoregressive model with autoregressive and heteroskedastic disturbances, i.e., SARAR(1,1), by exploiting the recent advancements in Score Driven (SD) models typically used in timeseries econometrics. In particular, we allow for time-varying spatial autoregressive coefficients as well as time-varying regressor coefficients and cross-sectional standard deviations. We report an extensive Monte Carlo simulation study in order to investigate the finite sample properties of the Maximum Likelihood estimator for the new class of models as well as its flexibility in explaining a misspecified dynamic spatial dependence process. The new proposed class of models are found to be economically preferred by rational investors through an application to portfolio optimization.Modeling spatio-temporal data has recently received an increasing amount of attention, with applications that span from time geography to spatial panel data econometrics (see An et al., 2015).Specifically to the econometric field, researchers were focused on how to manage the raising availability of panel data by proposing a new class of dynamic spatial autoregressive models able to deal with: (i) serial dependence between the observations on each spatial unit over time, (ii) spatial dependence between the observations at each point in time, (iii) unobservable spatial and/or time-period-specific effects, (iv) endogeneity of one or more of the regressors other than dependent variables lagged in space and/or time (see Elhorst, 2012). According to the type of restriction that we impose, one may obtain several dynamic spatial sub-models. For instance, a time-space dynamic model can be obtained if we impose restrictions on the spatio-temporal evolution of the regressors, or a time-space recursive model if we ignore spatial autocorrelation but we account for time/space-lagged dependent variable and eventually for spatiallylagged regressors (see Elhorst, 2010;LeSage and Pace, 2009). As Anselin et al. (2008) stressed, however, the sub-general time-space dynamic model still may suffer from identification problems 1 , which led to the