Comparison of Classical and Dynamic Network Models Efficiency in the Application of Generalized Network Autoregressive Models

One of the most challenging issues in forecasting economic variables is the lack of sufficient data or  the missing data in time series. In this paper, the time series of the GDP growth rate from 1980 to 2019 for 18 Middle East and North African countries is modeled via a generalized network autoregressive model. Of the total observations, 13.42% were missed. In the proposed model, a random network is applied to the data for which nodes represent countries or related time series. Then, an autoregressive model of each node was constructed based on all the data of its multi-stage neighboring nodes. Some parameters of the model may depend on the node (local model) or can be considered the same for all network nodes (global model). The missing data are modeled by changing the weights of the network edges. Finally, the time series was predicted based on the constructed model. Because the network structure affects the model and ultimately the forecast, and on the other hand it is difficult to examine all possible networks, ten thousand un-directional random networks and 16 models including 8 local models and 8 global models on each network are considered. Out of 160,000 models, the network and the model with the least prediction error are selected as the best network and model that are used for the main prediction. The lowest in-sample predictive error was obtained at a local network, which has 64 edges and the number of corresponding model parameters is 4. Finally, the model is compared with the classical models such as AR and VAR. The results indicate the superiority of the proposed method in significantly reducing the prediction error over the AR and VAR models.