A general property for time aggregation

Alexander, Carol and Rauch, Johannes (2021) A general property for time aggregation. European Journal of Operational Research, 291 (2). pp. 536-548. ISSN 0377-2217

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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.

Item Type: Article
Keywords: Aggregation Property, Higher Moments, Risk Premia, Time Aggregation, Unbiased and Efficient Estimators
Schools and Departments: University of Sussex Business School > Accounting and Finance
Subjects: H Social Sciences > HA Statistics > HA154 Statistical data
H Social Sciences > HG Finance > HG0101 Theory. Method. Relation to other subjects
H Social Sciences > HG Finance > HG0101 Theory. Method. Relation to other subjects > HG0106 Mathematical models
Depositing User: Carol Alexander
Date Deposited: 07 Jan 2020 08:17
Last Modified: 12 Jan 2022 02:00
URI: http://sro.sussex.ac.uk/id/eprint/89186

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