Mixed membership nearest neighbor model with feature difference

The nearest neighbor model has been a popular model for spatial data. This model assumes a distance‐based neighborhood structure among a set of entities that define the observations in a dataset. Values of a dependent variable are a function of the corresponding values of its neighbors and values of its own explanatory variables. In this paper, we extend the concept of “spatial neighbors” to a more general network dependency where the nearest neighbor is not necessarily distance‐based. As each entity can belong to multiple groups, observations can be related by multiple networks. By exploring the overlapping information that are exhibited by an entity and its neighbors, we modify the traditional spatial autoregressive model with autoregressive disturbances (SARAR) in three ways. First, multiple networks are allowed. Second, differences between the explanatory variables and their corresponding neighboring averages are applied. Third, apart from independent innovations, we investigate the case where the innovations are also multiple‐network dependent. Statistical inference of the model parameters is achieved via maximizing the profile log‐likelihood function. The standard errors of the profile maximum likelihood estimators are calculated by the inverse Fisher information matrix. Four variations of the multiple network autoregressive models are applied to predict changes in stock prices of 555 companies listed in the Hong Kong Stock Exchange. The model with attribute differencing and dependent innovations produces a smaller out‐of‐sample mean prediction error sum of squares than that of the other models.