We provide a new framework for modeling trends and periodic patterns in high-frequency financial data. Seeking adaptivity to ever-changing market conditions, we enlarge the Fourier flexible form into a richer functional class: both our smooth trend and the seasonality are non-parametrically...

We propose a multiplicative component model for intraday volatility. The model consists of a seasonality factor, as well as a semiparametric and parametric component. The former captures the well-documented intraday seasonality of volatility, while the latter two account for the impact of the...

We establish a feasible central limit theorem with convergence rate $n^{1/8}$ for the estimation of the {integrated volatility of volatility} (VoV) based on noisy high-frequency data with jumps. This is the first inference theory ever built for VoV estimation under such a general setup. The...

Particle Filter algorithms for filtering latent states (volatility and jumps) of Stochastic-Volatility Jump-Diffusion (SVJD) models are being explained. Three versions of the SIR particle filter with adapted proposal distributions to the jump occurrences, jump sizes, and both are derived and...

This paper proposes efficient estimators of risk measures in a semiparametric GARCH model defined through moment constraints. Moment constraints are often used to identify and estimate the mean and variance parameters and are however discarded when estimating error quantiles. In order to prevent...

In mathematical finance diffusion models are widely used and a variety of different parametric models for the drift and diffusion coefficient coexist in the literature. Since derivative prices depend on the particular parametric model of the diffusion coefficient function of the underlying, a...

In this paper we use the covariate quantile autoregression approach to test whether consumption is a constant unit root process, as predicted by the permanent income hypothesis (PIH). We find evidence that at low quantiles of the conditional quantile function of consumption the persistence of...

Short-term analysis is generally performed with seasonally adjusted data from which further estimation of the business cycle is performed through well-known filters (HP, Baxter-King). However, the whole procedure is not fully consistent, because seasonal adjustment and trend-cycle estimation do...

This paper investigates the properties of the decomposition of a time series presented in a companion paper (Lacroix, (2008)). The procedure relies upon an extension of Beveridge-Nelson methodology. We focus on its empirical implementation and show the need for additional steps in order to...