A volatility model must be able to forecast volatility; this is the central requirement in almost all financial applications. In this paper we outline some stylized facts about volatility that should be incorporated in a model: pronounced persistence and mean-reversion, asymmetry such that the...

A semiparametric model for observational data combines a parametric form for some component of the data generating process (usually the behavioral relation between the dependent and explanatory variables) with weak nonparametric restrictions on the remainder of the model (usually the...

A brief account is given of the methodology and theory for the bootstrap. Methodology is developed in the context of the "equation" approach, which allows attention to be focussed on specific criteria for excellence, such as coverage error of a confidence interval or expected value of a...

Asymptotic distribution theory is the primary method used to examine the properties of econometric estimators and tests. We present conditions for obtaining cosistency and asymptotic normality of a very general class of estimators (extremum estimators). Consistent asymptotic variance estimators...

This chapter reviews inference about large autoregressive or moving average roots in univariate time series, and structural change in multivariate time series regression. The "problem" of unit roots is cast more broadly as determining the order of integration of a series; estimation, inference,...

This chapter describes several nonparametric estimation and testing methods for econometric models. Instead of using parametric assumptions on the functions and distributions in an economic model, the methods use the restrictions that can be derived from the model. Examples of such restrictions...

This chapter provides an overview of asymptotic results available for parametric estimators in dynamic models. Three cases are treated: stationary (or essentially stationary) weakly dependent data, weakly dependent data containing deterministic trends, and nonergodic data (or data with...

We review different approaches to nonparametric density and regression estimation. Kernel estimators are motivated from local averaging and solving ill-posed problems. Kernel estimators are compared to k-NN estimators, orthogonal series and splines. Pointwise and uniform confidence bands are...