10 problems

Monotonicity conjecture. The function $\Sigma^2(k)$ is monotone increasing in $r$.

Let $X$ be a process observed at times indexed by $i=1,\ldots,n$, with sampling interval $h_n$, spot volatility process $\sigma_t$, and finite jump activity. For each observation i…

Change-point consistency conjecture. With jumps in $(X_t)$, an analogous result holds true under the conditions of Proposition $$ .

Asymptotic minimax-optimality conjecture. The above test yields an asymptotic minimax-optimal decision rule.

Generalization conjecture. Certain generalizations of the results to these three types of noise are possible.

Consider the rescaled price model with observation horizon parameter $T$ and the alternative non-rescaled price model with intensity $n\lambda(t)$, where $n\to\infty$. In the resca…

Gobet–Hoffmann–Reiß conjecture. The estimator also performs well in the high-frequency regime, meaning when $\Delta\to 0$.

General lower-bound conjecture. The analogous asymptotic variance determined for the general model should constitute the general lower bound.

The paper considers a general semimartingale experiment in which spectral estimators are used to estimate integrated volatility and covolatility, and asymptotic efficiency is asses…

Consider a microstructure-noise model whose kernel is … and whose volatility satisfies $\sigma\left(s,t\right)=\sigma\left(s\right)$. Here $\alpha$ denotes the Hölder smoothness of…