Calendar and Session Representations in Mixed-Calendar Multivariate Forecasting

Multivariate forecasting with variables observed on different temporal calendars requires a choice about how their histories are represented in a common input sequence. Prior work has largely treated mixed-calendar alignment as a preprocessing step or focused on modeling irregular observations, leaving direct comparisons of alternative temporal representations under identical forecast targets and evaluation dates less examined. This study compares a Calendar representation, which preserves the complete daily grid, with a Session representation, which retains only observed financial trading sessions. Epidemiological and financial data from Saudi Arabia and Germany are evaluated using identical forecast targets and target dates. Under fixed-duration matching, both representations use the same preceding 28 calendar days, whereas under fixed-sequence-length matching, Calendar uses 20 calendar days and Session uses the 20 most recent trading sessions. Ridge regression, a multilayer perceptron, and a gated recurrent unit are used to examine whether representation effects vary across model classes, while additional variants evaluate observation indicators and elapsed-time information. Ridge consistently favors Calendar across the evaluated empirical settings, MLP generally favors Calendar with variation across countries and matching rules, while GRU effects are smaller in magnitude and most 95% uncertainty intervals span zero. The choice between fixed-duration and fixed-sequence-length matching changes some representation effects, while adding observation indicators or elapsed-time information does not consistently improve performance. A target-specific naive baseline outperforms all core learned configurations, so the learned-model comparisons are interpreted primarily as analyses of representation sensitivity. In controlled simulation, representation differences are small under regular scheduled closures but become more Calendar-favoring when additional observation gaps are introduced. Overall, the results show that the effects of temporal representation vary with the model, the construction of the historical input, and the way observation gaps arise.

@article{Alzhrani2026,
  title     = {Calendar and Session Representations in Mixed-Calendar Multivariate Forecasting},
  journal   = {International Journal of Advanced Computer Science and Applications},
  volume    = {17},
  number    = {8},
  year      = {2026},
  publisher = {The Science and Information Organization},
  author    = {Khudran M. Alzhrani},
  doi       = {10.14569/IJACSA.2026.0170878},
  url       = {https://doi.org/10.14569/IJACSA.2026.0170878}
}