Multivariate time-series forecasting is subject to certain difficulties, including intricate inter-variable dependency, non-stationary behavior, and temporal dynamics. This paper introduces a new statistical learning model that incorporates decomposed-based pre-processing and adaptive learning of graphs for predictive analytics. The framework utilizes a multi-layered approach that includes three main stages: decomposition of the data into the components such as trend, seasonality, and residual parts; learning the graphs for each of the components based on inter-variable dependency; and, finally, a combination of statistical and neural forecasting methods. Results obtained from benchmark experiments show significant improvement of performance of the proposed framework in comparison with state-of-the-art baseline models. In particular, component-based modeling with learned dependency graphs outperforms other methods consistently for all forecasting horizons in the presence of correlations between channels and seasonality effects.