Linear Forecast Reconciliation: From Hierarchical Time Series to Traffic Anomaly Detection

Forecasting many related time series often involves hierarchical or grouped structures, where forecasts must be both accurate and coherent with respect to aggregation constraints. Traditional approaches fit separate univariate models such as ETS or ARIMA for each series and then apply a reconciliation step, but this can be computationally heavy at scale. In this talk, I will present linear model based approaches to fast forecast reconciliation. First, I introduce a linear modeling framework that performs forecasting and reconciliation in a single step for hierarchical and grouped time series. This approach substantially reduces computational cost while maintaining forecast accuracy and supports flexible inclusion of covariates and handling of missing data. I demonstrate its performance using examples such as Australian domestic tourism. I then focus on a case study of Taiwanese highway traffic during consecutive holidays, where reconciled ordinary least squares (OLS) forecasts combined with bootstrap prediction intervals form the basis of a prediction based anomaly detection method. By encoding seasonal patterns with Fourier terms and representing spatial structure through a traffic hierarchy, our simple OLS models effectively capture complex traffic dynamics and highlight regions and directions with atypical flows. Together, these results show how linear models and forecast reconciliation provide a scalable and interpretable toolkit for hierarchical time series forecasting, with practical implications for traffic management and beyond.

ASA Cincinnati Chapter Spring Seminar

Virtual (Online)