EJOR_2020.pdf (1.09 MB)
A general property for time aggregation
journal contribution
posted on 2023-06-09, 20:07 authored by Carol AlexanderCarol Alexander, Johannes RauchWe 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.
History
Publication status
- Published
File Version
- Accepted version
Journal
European Journal of Operational ResearchISSN
0377-2217Publisher
ElsevierExternal DOI
Issue
2Volume
291Page range
536-548Department affiliated with
- Accounting and Finance Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2020-01-07First Open Access (FOA) Date
2022-01-12First Compliant Deposit (FCD) Date
2020-01-07Usage metrics
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