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

Nonparametric Density Estimation for Positive Time Series

The Gaussian kernel density estimator is known to have substantial problems for bounded random variables with high density at the boundaries. For i.i.d. data several solutions have been put forward to solve this boundary problem. In this paper we propose the gamma kernel estimator as density estimator for positive data from a stationary ?-mixing process. We derive the mean integrated squared error, almost sure convergence and asymptotic normality. In a Monte Carlo study, where we generate data from an autoregressive conditional duration model and a stochastic volatility model, we find that the gamma kernel outperforms the local linear density estimator. An application to data from financial transaction durations, realized volatility and electricity price data is provided.Gamma kernel, nonparametric density estimation, mixing process, transaction durations, realised volatility.

A No-Arbitrage Approach to Range-Based Estimation of Return Covariances and Correlations

We extend the important idea of range-based volatility estimation to the multivariate case. In particular, we propose a range-based covariance estimator that is motivated by financial economic considerations (the absence of arbitrage), in addition to statistical considerations. We show that, unlike other univariate and multivariate volatility estimators, the range-based estimator is highly efficient yet robust to market microstructure noise arising from bid-ask bounce and asynchronous trading. Finally, we provide an empirical example illustrating the value of the high-frequency sample path information contained in the range-based estimates in a multivariate GARCH framework.Range-based estimation, volatility, covariance, correlation, absence of arbitrage, exchange rates, stock returns, bond returns, bid-ask bounce, asynchronous trading

Combining long memory and level shifts in modeling and forecasting the volatility of asset returns

We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean- and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in high-frequency measures of volatility whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes, and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons

Combining long memory and level shifts in modeling and forecasting the volatility of asset returns

We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in most high-frequency measures of volatility, whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons

Variation, jumps, market frictions and high frequency data in financial econometrics

We will review the econometrics of non-parametric estimation of the components of the variation of asset prices. This very active literature has been stimulated by the recent advent of complete records of transaction prices, quote data and order books. In our view the interaction of the new data sources with new econometric methodology is leading to a paradigm shift in one of the most important areas in econometrics: volatility measurement, modelling and forecasting. We will describe this new paradigm which draws together econometrics with arbitrage free financial economics theory. Perhaps the two most influential papers in this area have been Andersen, Bollerslev, Diebold and Labys(2001) and Barndorff-Nielsen and Shephard(2002), but many other papers have made important contributions. This work is likely to have deep impacts on the econometrics of asset allocation and risk management. One of our observations will be that inferences based on these methods, computed from observed market prices and so under the physical measure, are also valid as inferences under all equivalent measures. This puts this subject also at the heart of the econometrics of derivative pricing. One of the most challenging problems in this context is dealing with various forms of market frictions, which obscure the efficient price from the econometrician. Here we will characterise four types of statistical models of frictions and discuss how econometricians have been attempting to overcome them.