We develop parametric inference procedures for large panels of noisy option data in a setting, where the underlying process is of pure-jump type, i.e., evolves only through a sequence of jumps. The panel consists of options written on the underlying asset with a (different) set of strikes and maturities available across the observation times. We consider an asymptotic setting in which the cross-sectional dimension of the panel increases to infinity, while the time span remains fixed. The information set is augmented with high-frequency data on the underlying asset. Given a parametric specification for the risk-neutral asset return dynamics, the option prices are nonlinear functions of a time-invariant parameter vector and a time-varying latent state vector (or factors). Furthermore, no-arbitrage restrictions impose a direct link between some of the quantities that may be identified from the return and option data. These include the so-called jump activity index as well as the time-varying jump intensity. We propose penalized least squares estimation in which we minimize the L2 distance between observed and model-implied options. In addition, we penalize for the deviation of the model-implied quantities from their model-free counterparts, obtained from the high-frequency returns. We derive the joint asymptotic distribution of the parameters, factor realizations and high-frequency measures, which is mixed Gaussian. The different components of the parameter and state vector exhibit different rates of convergence, depending on the relative (asymptotic) informativeness of the high-frequency return data and the option panel.

This article investigates the statistical inference problem of whether a measurement equation is self-consistent in the logarithmic realized GARCH model (log-RealGARCH). First, we provide the sufficient and necessary conditions for the strict stationarity of both the log-RealGARCH model and the log-GARCH-X model. Under these conditions, strong consistency and asymptotic normality of the quasi-maximum likelihood estimators of these two models are obtained. Then, based on the asymptotic results, we propose a Hausman-type self-consistency test for diagnosing the suitability of the measurement equation in the log-RealGARCH model. Finally, the results of simulations and an empirical study are found to accord with the theoretical results.

The present article discusses panel unit root tests for two classes of models. One is the moving average (MA) model and the other is the error components model. We conduct score type tests for these models, allowing for various types of regressors, and examine the cross-sectional effect explicitly by presenting an efficient way of computing limiting local powers. It is found that the existence of common regressors does not affect the asymptotic behavior of tests, although heterogeneous regressors do. We also derive the limiting power envelopes for some simple panel models, which shows that the score type panel tests are asymptotically efficient, unlike the time series case.

We present novel theory for testing for reduction of GARCH-X type models with an exogenous (X) covariate to standard GARCH type models. To deal with the problems of potential nuisance parameters on the boundary of the parameter space as well as lack of identification under the null, we exploit a noticeable property of specific zero-entries in the inverse information of the GARCH-X type models. Specifically, we consider sequential testing based on two likelihood ratio tests and as demonstrated the structure of the inverse information implies that the proposed test neither depends on whether the nuisance parameters lie on the boundary of the parameter space, nor on lack of identification. Asymptotic theory is derived essentially under stationarity and ergodicity, coupled with a regularity assumption on the exogenous covariate X. Our general results on GARCH-X type models are applied to Gaussian based GARCH-X models, GARCH-X models with Student’s t-distributed innovations as well as integer-valued GARCH-X (PAR-X) models.

An estimator of a finite-dimensional parameter is said to be doubly robust (DR) if it imposes parametric specifications on two unknown nuisance functions, but only requires that one of these two specifications is correct in order for the estimator to be consistent for the object of interest. In this article, we study versions of such estimators that use local polynomial smoothing for estimating the nuisance functions. We show that such semiparametric two-step (STS) versions of DR estimators have favorable theoretical and practical properties relative to other commonly used STS estimators. We also show that these gains are not generated by the DR property alone. Instead, it needs to be combined with an orthogonality condition on the estimation residuals from the nonparametric first stage, which we show to be satisfied in a wide range of models.