We suggest improved tests for cointegration rank in the vector autoregressive (VAR) model and develop asymptotic distribution theory and local power results. The tests are (quasi-)likelihood ratio tests based on a Gaussian likelihood, but of course the asymptotic results apply more generally....

The paper introduces the model confidence set (MCS) and applies it to the selection of models. A MCS is a set of models that is constructed such that it will contain the best model with a given level of confidence. The MCS is in this sense analogous to a confidence interval for a parameter. The...

Asymptotic properties of jump tests rely on the property that any jump occurs within a single time interval no matter what the observation frequency is. Market microstructure effects in relation to news-induced revaluation of the underlying variable is likely to make this an unrealistic...

We propose a bootstrap method for estimating the distribution (and functionals of it such as the variance) of various integrated covariance matrix estimators. In particular, we first adapt the wild blocks of blocks bootstrap method suggested for the pre-averaged realized volatility estimator to...

We explore intraday transaction records from NASDAQ OMX Commodities Europe from January 2006 to October 2013. We analyze empirical results for a selection of existing realized measures of volatility and incorporate them in a Realized GARCH framework for the joint modeling of returns and realized...

The GARCH framework has been used for option pricing with quite some success. While the initial work assumed conditional Gaussian innovations, recent contributions relax this assumption and allow for more flexible parametric specifications of the underlying distribution. However, until now the...

We study the forecasting of future realized volatility in the foreign exchange, stock, and bond markets from variables in the information set, including implied volatility backed out from option prices. Realized volatility is separated into its continuous and jump components, and the...

A review is given of parametric estimation methods for discretely sampled multivariate diffusion processes. The main focus is on estimating functions and asymptotic results. Maximum likelihood estimation is briefly considered, but the emphasis is on computationally less demanding martingale...

This paper reviews basic notions of return variation in the context of a continuous-time arbitrage-free asset pricing model and discusses some of their applications. We first define return variation in the infeasible continuous-sampling case. Then we introduce realized measures obtained from...

A general theory of efficient estimation for ergodic diffusions sampled at high fre- quency is presented. High frequency sampling is now possible in many applications, in particular in finance. The theory is formulated in term of approximate martingale estimating functions and covers a large...