Intra-day periodicity, temporal aggregation and time-to-maturity in FTSE-100 index futures volatility

Intra-day periodicity has been widely observed in financial data. Recent research examining intra-day foreign exchange rate volatility dynamics reports that failure to account for this periodicity results in inconsistent GARCH parameter estimates in relationship to theoretical predictions on temporal aggregation. This article seeks to appraise the generality of this conclusion to the FTSE-100 index futures market. The nature of periodicity is first examined. Subsequent empirical results concerning the temporal aggregation of GARCH models show that the use of returns that are not adjusted for such periodicity are misleading. However, adjustment using a sine-cosine wave method or standardization by mean absolute returns provide more consistent results, the latter method dominating in out-of-sample forecasting of the volatility of successive individual futures contracts. The potential time-to-maturity effects of single contracts are also considered, but are statistically rejected for both forms of periodicity-adjusted data.