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A general property for time aggregation

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  • Alexander, Carol
  • Rauch, Johannes

Abstract

We classify all functions of multivariate stochastic processes having time-series estimates that are independent of data frequency. Such an estimator applied to high-frequency data may be used to infer properties of estimates relating to low-frequency data. Our property encompasses two previously-proposed time-aggregation properties (with limited solutions) as different special cases. Our general time-aggregating functions satisfy a pair of coupled second-order partial differential equations. We derive analytic solutions for arbitrary-dimensional martingales and log-martingales. The time-aggregation property of a time-series model is similar – indeed time-aggregating functions always correspond to point estimators based on expected values – but we do not propose a specific new forecasting model. However, we do derive time-aggregating unbiased and efficient estimators for nth-order moments of log returns, applying these results to problems facing portfolio managers who re-optimise portfolios or hedge their risks at lower frequencies than the frequency at which their risk premia are monitored.

Suggested Citation

  • Alexander, Carol & Rauch, Johannes, 2021. "A general property for time aggregation," European Journal of Operational Research, Elsevier, vol. 291(2), pages 536-548.
    • Handle: RePEc:eee:ejores:v:291:y:2021:i:2:p:536-548
    DOI: 10.1016/j.ejor.2019.12.045
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