Three Essays on the Econometric Analysis of High Frequency Financial Data

This thesis is motivated by the observation that the time series properties of financial security prices can vary fundamentally with their sampling frequency. Econometric models developed for low frequency data may thus be unsuitable for high frequency data and vice versa. For instance, while daily or weekly returns are generally well described by a martingale difference sequence, the dynamics of intra-daily, say, minute by minute, returns can be substantially more complex. Despite this apparent conflict between the behavior of high and low frequency data, it is clear that the two are intimately related and that high frequency data carries a wealth of information regarding the properties of the process, also at low frequency. The objective of this thesis is to deepen our understanding of the way in which high frequency data can be used in financial econometrics. In particular, we focus on (i) how to model high frequency security prices, and (ii) how to use high frequency data to estimate latent variables such as return volatility. One finding throughout the thesis is that the choice of sampling frequency is of fundamental importance as it determines both the dynamics and the information content of the data. A more detailed description of the chapters follows below. Chapter one examines the impact of serial correlation in high frequency returns on the realized variance measure. In particular, it is shown that the realized variance measure yields a biased estimate of the conditional return variance when returns are serially correlated. Using 10 years of FTSE-100 minute by minute data we demonstrate that a careful choice of sampling frequency is crucial in avoiding substantial biases. Moreover, we find that the autocovariance structure (magnitude and rate of decay) of FTSE-100 returns at different sampling frequencies is consistent with that of an ARMA process under temporal aggregation. A simple autocovariance function based method is proposed for choosing the “optimal” sampling frequency, that is, the highest available frequency at which the serial correlation of returns has a negligible impact on the realized variance measure. We find that the logarithmic realized variance series of the FTSE-100 index, constructed using an optimal sampling frequency of 25 minutes, can be modelled as an ARFIMA process. Exogenous variables such as lagged returns and contemporaneous trading volume appear to be highly significant regressors and are able to explain a large portion of the variation in daily realized variance. Chapter two (based on joint work with George Jiang) proposes an unbiased estimator of the latent variables within the Affine Jump Diffusion model. The estimator is model consistent, can be implemented based on high Oomen, Roel C.A. (2003), Three Essays on the Econometric Analysis of High Frequency Financial Data European University Institute DOI: 10.2870/23324 frequency observations of the state variable, and we derive conditions under which it has minimum variance. In a simulation experiment we illustrate the performance of our estimator and show that its properties compare favorably to commonly used alternatives. Because our approach can, in principle, be applied to any latent variable model in the general Affine Jump Diffusion framework, it covers a wide range of models frequently studied in the finance literature including the stochastic volatility model. Based on the proposed estimator of latent variables, we outline a flexible GMM estimation procedure that relies on the matching of conditional moments or cumulants of both the observed and the unobserved state variables. Chapter three studies two extensions of the compound Poisson process with iid Gaussian innovations which are able to characterize important features of high frequency security prices. The first model explicitly accounts for the presence of the bid/ask spread encountered in price-driven markets. This model can be viewed as a mixture of the compound Poisson process model by Press and the bid/ask bounce model by Roll. The second model generalizes the compound Poisson process to allow for an arbitrary dependence structure in its innovations so as to account for more complicated types of market microstructure. Based on the characteristic function, we provide a detailed analysis of the static and dynamic properties of the price process. Comparison with actual high frequency data suggests that the proposed models are sufficiently flexible to capture a number of salient features of financial return data including a skewed and fat tailed marginal distribution, serial correlation at high frequency, time variation in market activity both at high and low frequency. The current framework also allows for a comprehensive investigation of the “market-microstructure-induced bias” in the realized variance measure and we find that, for realistic parameter values, this bias can be substantial. We analyze the impact of the sampling frequency on the bias and find that for non-constant trade intensity, “business” time sampling maximizes the bias but achieves the lowest overall MSE. Oomen, Roel C.A. (2003), Three Essays on the Econometric Analysis of High Frequency Financial Data European University Institute DOI: 10.2870/23324 JOINT RESEARCH STATEMENT CHAPTER 2