Analyzing the Role of Statistical Learning in Improving Forecast Accuracy Across Multivariate Time Series Data

Posted: Jan 15, 2020

• Sarah Miller
• Scarlett Jones
• John Jones

Abstract

Multivariate time series forecasting represents a critical challenge in numerous domains including finance, healthcare, environmental science, and industrial applications. Traditional approaches to multivariate forecasting have largely relied on statistical methods such as vector autoregression (VAR) and its extensions, which model linear relationships between multiple time series. While these methods provide interpretable results and well-understood statistical properties, they often struggle with complex non-linear dependencies and high-dimensional settings. More recently, machine learning approaches including recurrent neural networks and gradient boosting have demonstrated impressive performance in capturing non-linear patterns but may lack the statistical rigor and interpretability of traditional methods. This research addresses the fundamental gap between traditional statistical methods and modern statistical learning techniques by developing an integrated framework that leverages the strengths of both approaches. Our work is motivated by the observation that different statistical learning methods excel in different temporal contexts and data regimes. Rather than proposing yet another standalone algorithm, we introduce a meta-framework that dynamically selects and combines forecasting methods based on the characteristics of the multivariate time series at hand. The primary contribution of this research lies in the development of a novel feature representation for multivariate time series that captures both linear dependencies and non-linear interactions across series. This representation enables our framework to make informed decisions about which statistical learning techniques to apply and how to combine their predictions. Additionally, we introduce an adaptive weighting mechanism that adjusts the contribution of different forecasting methods based on their recent performance and the current temporal context.