This paper overviews recent developments in series estimation of stochastic processes and some of their applications in econometrics. Underlying this approach is the idea that a stochastic process may under certain conditions be represented in terms of a set of orthonormal basis functions,...

We present a new theory for the conduct of nonparametric inference about the latent spot volatility of a semimartingale asset price process. In contrast to existing theories based on the asymptotic notion of an increasing number of observations in local estimation blocks, our theory treats the...

This paper studies the spurious regressions among stationary Gegenbauer processes, stationary harmonic processes and deterministic trigonometric series. We find the spurious regression can occur between two stationary Gegenbauer processes, as long as their generalized fractional differencing...

When estimating and forecasting realized volatility in the presence of jumps, a form of bias-variance tradeoff is present in the selection of the truncation threshold. We propose an optimal method for threshold selection that minimizes the out-of-sample forecasting loss. The use of a forecasting...