Search

Platform businesses operate on a digital core and their decision making requires high-dimensional accurate forecast streams at different levels of cross-sectional (e.g., geographical regions) and temporal aggregation (e.g., minutes to days). It also necessitates coherent forecasts across all levels of the hierarchy to ensure aligned decision making across different planning units such as pricing, product, controlling and strategy. Given that platform data streams feature complex characteristics and interdependencies, we introduce a non-linear hierarchical forecast reconciliation method that produces cross-temporal reconciled forecasts in a direct and automated way through the use of popular machine learning methods. The method is sufficiently fast to allow forecast-based high-frequency decision making that platforms require. We empirically test our framework on unique, large-scale streaming datasets from a leading on-demand delivery platform in Europe and a bicycle sharing system in New York City.

Reverse Unrestricted MIxed DAta Sampling (RU-MIDAS) regressions are used to model high-frequency responses by means of low-frequency variables. However, due to the periodic structure of RU-MIDAS regressions, the dimensionality grows quickly if the frequency mismatch between the high- and low-frequency variables is large. Additionally the number of high-frequency observations available for estimation decreases. We propose to counteract this reduction in sample size by pooling the high-frequency coefficients and further reduce the dimensionality through a sparsity-inducing convex regularizer that accounts for the temporal ordering among the different lags. To this end, the regularizer prioritizes the inclusion of lagged coefficients according to the recency of the information they contain. We demonstrate the proposed method on an empirical application for daily realized volatility forecasting where we explore whether modeling high-frequency volatility data in terms of low-frequency macroeconomic data pays off.

Mixed-frequency Vector AutoRegressions (MF-VAR) model the dynamics between variables recorded at different frequencies. However, as the number of series and high-frequency observations per low-frequency period grow, MF-VARs suffer from the "curse of dimensionality". We curb this curse through a regularizer that permits hierarchical sparsity patterns by prioritizing the inclusion of coefficients according to the recency of the information they contain. Additionally, we investigate the presence of nowcasting relations by sparsely estimating the MF-VAR error covariance matrix. We study predictive Granger causality relations in a MF-VAR for the U.S. economy and construct a coincident indicator of GDP growth. Supplementary Materials for this article are available online., Comment: Forthcoming in Journal of Computational and Graphical Statistics