Regularized Partially Functional Autoregressive Model

Abstract

Functional time series and high-dimensional scalar predictors frequently arise in a wide range of modern economic and business applications, which require statistical models that can simultaneously handle the temporal and causal dependence that are prevalent in large sets of mixed-type data. We propose a partially functional autoregressive model (pFAR) to describe the dynamic evolution of the serially correlated functional response on its own lagged values and the causal relation with a large amount of exogenous scalar predictors. Our estimation is conducted by facilitating the sieve method and a two-layer sparsity assumption that is imposed on groups and elements. In the high-dimensional setting, the sparse structure is completely unknown and it is identified entirely data-driven with a forward-looking criterion. In addition, asymptotic properties of the estimators are established. Extensive simulation studies show that the pFAR model accurately identifies the sparse structure with a convincing and stable predictive performance. The power of the pFAR model is further confirmed by real data analysis of day-ahead gas demand and supply curve predictions of multiple nodes in the German natural gas transmission network with different functions. Given the historical values of the daily curves and 85 scalar predictors, the model detects several essential categories of mixed-type predictors with insightful economic interpretation. It also provides appealing out-of-sample forecast accuracy when compared to a number of popular alternative models.