Regularized Vector Autoregressive Model for time series data with multiple covariates

Abstract

This study develops a Regularized Vector Autoregressive (VAR) model to address challenges like high dimensionality, multicollinearity, and overfitting in time series forecasting with external covariates. Traditional VAR models often struggle with scalability and stability in high-dimensional contexts. By incorporating Ridge, Lasso, and Elastic Net regularization techniques, the model enhances forecasting accuracy and model interpretability. Using a real-world dataset of Walmart sales, including weekly sales alongside economic and environmental covariates, the methodology applies preprocessing, regularized model formulation, and cross-validation for parameter tuning. Performance is evaluated using metrics like Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE), comparing traditional and regularized VAR models. The findings demonstrate the utility of regularized VAR models in handling complex time series data influenced by external covariates, with implications for broader applications in fields such as finance, healthcare, and environmental science.

KEYWORDS: Regularized VAR model, Time Series Forecasting, Multiple Covariates, High Dimensionality, Overfitting.