We introduce and investigate some properties of a class of nonlinear time series models based on the moving sample quantiles in the autoregressive data generating process. We derive a test fit to detect this type of nonlinearity. Using the daily realized volatility data of Standard & Poor's 500...

This paper develops a method to improve the estimation of jump variation using high frequency data with the existence of market microstructure noises. Accurate estimation of jump variation is in high demand, as it is an important component of volatility in finance for portfolio allocation,...

I provide conditions under which the trimmed FDQML estimator, advanced by McCloskey (2010) in the context of fully parametric short-memory models, can be used to estimate the long-memory stochastic volatility model parameters in the presence of additive low-frequency contamination in log-squared...

We introduce a dynamic statistical model for Skellam distributed random variables. The Skellam distribution can be obtained by taking differences between two Poisson distributed random variables. We treat cases where observations are measured over time and where possible serial correlation is...

I provide conditions under which the trimmed FDQML estimator, advanced by McCloskey (2010) in the context of fully parametric short-memory models, can be used to estimate the long-memory stochastic volatility model parameters in the presence of additive low-frequency contamination in log-squared...

For a semi-martingale Xt, which forms a stochastic boundary, a rate-optimal estimator for its quadratic variation (X;X)t is constructed based on observations in the vicinity of Xt. The problem is embedded in a Poisson point process framework, which reveals an interesting connection to the theory...

In the class of univariate conditional volatility models, the three most popular are the generalized autoregressive conditional heteroskedasticity (GARCH) model of Engle (1982) and Bollerslev (1986), the GJR (or threshold GARCH) model of Glosten, Jagannathan and Runkle (1992), and the...