Fourier instantaneous estimators and the Epps effect

Abstract

We compare the Malliavin-Mancino and Cuchiero-Teichmann Fourier instantaneous estimators to investigate the impact of the Epps effect arising from asynchrony in the instantaneous estimates. We demonstrate the instantaneous Epps effect under a simulation setting and provide a simple method to ameliorate the effect. We find that using the previous tick interpolation in the Cuchiero-Teichmann estimator results in unstable estimates when dealing with asynchrony, while the ability to bypass the time domain with the Malliavin-Mancino estimator allows it to produce stable estimates and is therefore better suited for ultra-high frequency finance. An empirical analysis using Trade and Quote data from the Johannesburg Stock Exchange illustrates the instantaneous Epps effect and how the intraday correlation dynamics can vary between days for the same equity pair.

The Epps effect under alternative sampling schemes

“…Third, because it can deal with asynchrony, it uses the same fixed observations when investigating different time scales. This leads to more stable estimates at different time scales [6]. On the other hand, observations are dropped when sampling at different time scales for the RV estimator, therefore the time series changes slightly each time through the loss in resolution.…”

“…On the other hand, observations are dropped when sampling at different time scales for the RV estimator, therefore the time series changes slightly each time through the loss in resolution. These changes cause larger changes to the correlation estimate at each time scale, making the estimates less stable [6].…”

“…Although the transactions were in the correct order, without an exact millisecond or nanosecond time stamp means that we cannot correctly order the events for event time sampling. 6 Therefore, we process the data by aggregating transactions (for each security) with the same time stamp using a volume weighted average.…”

“…The Epps effect is pervasive and has been observed in stock markets and foreign exchange markets (see Mastromatteo et al [24] and references therein). More recently, as an extension to Mattiussi and Iori [25], Chang [6] also demonstrated the Epps effect on instantaneous correlation estimates. There is an abundance of literature investigating the causes (see [24,26,30,35,36]) and corrections (see [4,11,19,27,38]).…”

“…M the reconstruction frequency. Here, because we are using integrated estimates we do not need to concern ourselves with issues pertaining to the choice of M [6]. Many estimation methods do not allow the precise extraction of the correlations as a direct function of the sampling frequency independent of assumption relating to the underlying stochastic processes.…”