Details

Autor(en) / Beteiligte

• Alexander, Carol
• Rauch, Johannes

Titel

A general property for time aggregation

Ist Teil von

• European journal of operational research, 2021-06, Vol.291 (2), p.536-548

Ort / Verlag

Elsevier B.V

Erscheinungsjahr

2021

Link zum Volltext

Quelle

Elsevier ScienceDirect Journals Complete

Beschreibungen/Notizen

• •Estimates from time-aggregating estimators are independent of data frequency.•Long-term estimates may be derived from high-frequency data.•Our general property encompasses previous as special cases.•Give unbiased and efficient estimators for nth-order moments of log returns.•Applications to long-term asset management and hedging financial instruments. 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.