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A general property for time aggregation
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DOI：10.1016/j.ejor.2019.12.045.png)
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Abstract
En 中文
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. Crown Copyright (c) 2020 Published by Elsevier B.V. All rights reserved.
Keywords:
Aggregation property
Higher moments
Risk premia
Time aggregation
Unbiased and efficient estimators
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