Bootstrapping high frequency data

We develop in this thesis bootstrap methods for high frequency financial data. The first two chapters focalise on bootstrap methods for the "pre-averaging" approach, which is robust to the presence of market microstructure effects. The main idea underlying this approach is that we can reduce the impact of the noise by pre-averaging high frequency returns that are possibly contaminated with market microstructure noise before applying a realized volatility-like statistic. Based on this approach, we develop several bootstrap methods, which preserve the dependence structure and the heterogeneity in the mean of the original data. The third chapter shows how and to what extent the local Gaussian- ity assumption can be explored to generate a bootstrap approximation for covolatility measures. The first chapter is entitled "Bootstrap inference for pre-averaged realized volatility based on non-overlapping returns". The main contribution of this chapter is to propose bootstrap methods for realized volatility-like estimators defined on pre-averaged returns. In particular, we focus on the pre-averaged realized volatility estimator proposed by Podolskij and Vetter (2009). This statistic can be written (up to a bias correction term) as the (scaled) sum of squared pre-averaged returns, where the pre-averaging is done over all possible non-overlapping blocks of consecutive observations. Pre-averaging reduces the influence of the noise and allows for realized volatility estimation on the pre-averaged returns. The non-overlapping nature of the pre-averaged returns implies that these are asymptotically independent, but possibly heteroskedastic. This motivates the application of the wild bootstrap in this context. We provide a proof of the first order asymptotic validity of this method for percentile and percentile-t intervals. Our Monte Carlo simulations show that the wild bootstrap can improve the finite sample properties of the existing first order asymptotic theory provided we choose the external random variable appropriately. The second chapter is entitled "Bootstrapping pre-averaged realized volatility under market microstructure noise ". In this chapter we propose a bootstrap method for inference on integrated volatility based on the pre-averaging approach of Jacod et al. (2009), where the pre-averaging is done over all possible overlapping blocks of consecutive observations. The overlapping nature of the pre-averaged returns implies that these are m-dependent with m growing slowly with the sample size n. This motivates the application of a blockwise bootstrap method. We show that the “blocks of blocks” bootstrap method suggested by Politis and Romano (1992) (and further studied by Bühlmann and Künsch (1995)) is valid only when volatility is constant. The failure of the blocks of blocks bootstrap is due to the heterogeneity of the squared pre-averaged returns when volatility is stochastic. To preserve both the dependence and the heterogeneity of squared pre-averaged returns, we propose a novel procedure that combines the wild bootstrap with the blocks of blocks bootstrap. We provide a proof of the first order asymptotic validity of this method for percentile intervals. Our Monte Carlo simulations show that the wild blocks of blocks bootstrap improves the finite sample properties of the existing first order asymptotic theory. The third chapter is entitled "Bootstrapping realized volatility and realized beta under a local Gaussianity assumption". The financial econometric of high frequency data litera- ture often assumed a local constancy of volatility and the Gaussianity properties of high frequency returns in order to carry out inference. In this chapter, we show how and to what extent the local Gaussianity assumption can be explored to generate a bootstrap approximation. We show the first-order asymptotic validity of the new wild bootstrap method, which uses the conditional local normality properties of financial high frequency returns. In addition to that we use Edgeworth expansions and Monte Carlo simulations to compare the accuracy of the bootstrap with other existing approaches. It is shown that at second order, the new wild bootstrap matches the cumulants of realized betas-based t-statistics, whereas it provides a third-order asymptotic refinement for realized volatility. Monte Carlo simulations suggest that our new wild bootstrap methods improve upon the first-order asymptotic theory in finite samples and outperform the existing bootstrap methods for realized covolatility measures. We use empirical work to illustrate its uses in practice.

Keyphrases: Bootstrap, Expansions d’Edgeworth, Realized betas, High frequency data, Realized volatility, Market microstructure noise, Pre-averaging, Edgeworth expansions