My research contribution has mostly been to do with nonparametric and semiparametric methods. I am also interested in Financial Econometrics. My dissertation was on Edgeworth expansions for semiparametric regression models. The practical application of this work is to bandwidth choice and to efficiency comparisons between first order equivalent procedures. This lead me into a closer examination of the nonparametric methods used in semiparametric procedures. The main practical problems there seem to be: How to choose bandwidth; The curse of dimensionality; How to obtain good approximations to the actual sampling variability of the estimators.

Investigation of the curse of dimensionality, leads one to consider models like additive regression that only involve one dimensional functions. In economics, a number of different separability concepts have been employed in demand and production analysis, and the additive regression model is just one example. These models are often difficult to estimate nonparametrically. The problem is that the functions of interest often cannot be directly expressed as a regression function of observable data; estimating such models requires some tricks to express the quantity of interest as a suitable function of observables. My work with Jens Perch Nielsen led to a number of papers on estimating additive and other separable models. We introduced a new method which we called marginal integration for estimating additive nonparametric regression. This procedure is much simpler than the main competitor called backfitting, which was promoted by Hastie and Tibshirani (1990). More recently, I have worked with Jens Perch Nielsen and Enno Mammen on deriving the asymptotic properties of a general class of iterative smoothing procedures which includes as a special case a variant of backfitting. It turns out that the backfitting method can be shown to be more efficient than the marginal integration method (under homoskedasticity) and to be better behaved in the boundaries, although the finite sample comparison is more complex, see the simulation study by Stefan Sperlich. I am also working with Arthur Lewbel on estimating a general class of nonparametric index models, which includes models for censored and truncated regression as well as models representing homotheticity. These structures also lead to non-standard estimation problems. 

I am also interested in financial econometrics. I am interested in discrete time volatiity models like GARCH models, their properties and estimation methods thereof, both parametric and nonparametric. This is a fairly mature area but recent work has focused on multivariate models and models that can also work in high frequency data settings where observation times are neither equally spaced nor necessarily exogenous. It is also of current interest to go beyond models that impose global stationarity, which is a questionable assumption for long financial time series. The concept of local stationarity initiated by Rainer Dahlhaus seems particularly relevant for many financial time series, and yields a straightforward weakening of many assumptions made in phase 1 of "the GARCH project". I am interested in the econometrics of continuous time, realized volatility and its uses. This field has developed rapidly in the last 10 years and much new theory is being written about the estimation of ex post volatility using high frequency data in a context of microstructure noise and occasional large price movements. Again, the multivariate environment presents substantial challenges that are slowly being faced. I have been working with Greg Connor on estimating a class of semiparametric factor models that are useful for large cross-section and low frequency (ie monthly) time series. These types of datasets are very widely analysed in finance and economics and the amount of information in both time and space is increasing, allowing the sophistication of the models we can estimate and interpret to improve. This type of data allows one to step back a bit from the hubub of the high frequency trading of todays financial markets and look at fundamental determinants of asset prices. There is still an important role to play for nonlinearity in such models.

I am currently a member of the Dept of BIS Go-Science Foresight Lead Expert Group on The Future of Computer Trading in Financial Markets.