Local Parametric Estimation in High Frequency Data

In this paper, we give a general time-varying parameter model, where the multidimensional parameter possibly includes jumps. The quantity of interest is defined as the integrated value over time of the parameter process $\Theta = T^{-1} \int_0^T \theta_t^* dt$. We provide a local parametric estimator (LPE) of $\Theta$ and conditions under which we can show the central limit theorem. Roughly speaking those conditions correspond to some uniform limit theory in the parametric version of the problem. The framework is restricted to the specific convergence rate $n^{1/2}$. Several examples of LPE are studied: estimation of volatility, powers of volatility, volatility when incorporating trading information and time-varying MA(1).Comment: 67 pages, 4 figure

ANOVA for diffusions and It\^{o} processes

It\^{o} processes are the most common form of continuous semimartingales, and include diffusion processes. This paper is concerned with the nonparametric regression relationship between two such It\^{o} processes. We are interested in the quadratic variation (integrated volatility) of the residual in this regression, over a unit of time (such as a day). A main conceptual finding is that this quadratic variation can be estimated almost as if the residual process were observed, the difference being that there is also a bias which is of the same asymptotic order as the mixed normal error term. The proposed methodology, ``ANOVA for diffusions and It\^{o} processes,'' can be used to measure the statistical quality of a parametric model and, nonparametrically, the appropriateness of a one-regressor model in general. On the other hand, it also helps quantify and characterize the trading (hedging) error in the case of financial applications.Comment: Published at http://dx.doi.org/10.1214/009053606000000452 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise

Classical statistics suggest that for inference purposes one should always use as much data as is available. We study how the presence of market microstructure noise in high-frequency financial data can change that result. We show that the optimal sampling frequency at which to estimate the parameters of a discretely sampled continuous-time model can be finite when the observations are contaminated by market microstructure effects. We then address the question of what to do about the presence of the noise. We show that modelling the noise term explicitly restores the first order statistical effect that sampling as often as possible is optimal. But, more surprisingly, we also demonstrate that this is true even if one misspecifies the assumed distribution of the noise term. Not only is it still optimal to sample as often as possible, but the estimator has the same variance as if the noise distribution had been correctly specified, implying that attempts to incorporate the noise into the analysis cannot do more harm than good. Finally, we study the same questions when the observations are sampled at random time intervals, which are an essential feature of transaction-level data.

Edgeworth Expansions for Realized Volatility and Related Estimators

This paper shows that the asymptotic normal approximation is often insufficiently accurate for volatility estimators based on high frequency data. To remedy this, we compute Edgeworth expansions for such estimators. Unlike the usual expansions, we have found that in order to obtain meaningful terms, one needs to let the size of the noise to go zero asymptotically. The results have application to Cornish-Fisher inversion and bootstrapping.

A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High Frequency Data

It is a common practice in finance to estimate volatility from the sum of frequently-sampled squared returns. However market microstructure poses challenges to this estimation approach, as evidenced by recent empirical studies in finance. This work attempts to lay out theoretical grounds that reconcile continuous-time modeling and discrete-time samples. We propose an estimation approach that takes advantage of the rich sources in tick-by-tick data while preserving the continuous-time assumption on the underlying returns. Under our framework, it becomes clear why and where the usual' volatility estimator fails when the returns are sampled at the highest frequency.

Combating Withholding Tax Reclaim Schemes in Europe : An event study examining the effect of policies aimed at combating fraudulent withholding tax reclaim schemes

In the last decade, numerous tax scandals have been exposed to the public. Among the largest of these is the so-called CumEx scandal, which revealed how billions of euros have been fraudulently acquired from European treasuries through trading schemes taking advantage of loopholes in the dividend tax legislation. These schemes are the center of this thesis. The first scheme, referred to as cum-ex, allows investors to obtain numerous tax reimbursements for a single dividend withholding tax payment. The second scheme, known as cum-cum, is a tax arbitrage strategy that exploits differences in dividend taxation rates between domestic and foreign investors, thereby lowering the effective tax liabilities of the participants. This thesis contains an explanation of the inner workings of the schemes, an examination of their prevalence in various European countries, and an analysis of the effects of policy changes implemented to prevent the schemes from being executed. To assess the extent and development of the schemes we utilize daily transaction volume data of shares to detect abnormal trading activity around the ex-dividend date. Such abnormal activity is potentially indicative of the presence of cum-cum and cum-ex schemes. We assess the impact of policy changes taken to combat the schemes by comparing trading patterns around the ex-dividend date before and after the implementation of said changes. We analyze nine separate reforms in seven countries aimed at combating cum-cum and cumex schemes. We find evidence of significant abnormal share trading around the ex-date in five out of seven countries, indicative of dividend tax schemes being present. We find that policy changes implemented in four out of nine reforms, in Germany (two separate reforms), France, and Finland, have led to a significant decline in abnormal trading correlating with that of known tax schemes. In the latter four countries, Austria, Belgium, Denmark, and Norway, the implemented policy changes had no significant impact on trading patterns, indicative of policy changes being ineffective in combating the cum-cum and cum-ex schemes.nhhma

Ultra high frequency volatility estimation with dependent microstructure noise

We analyze the impact of time series dependence in market microstructure noise on the properties of estimators of the integrated volatility of an asset price based on data sampled at frequencies high enough for that noise to be a dominant consideration. We show that combining two time scales for that purpose will work even when the noise exhibits time series dependence, analyze in that context a refinement of this approach based on multiple time scales, and compare empirically our different estimators to the standard realized volatility. --Market microstructure,Serial dependence,High frequency data,Realized volatility,Subsampling,Two Scales Realized Volatility