14 problems

Let $\alpha$ and $g$ be as in Theorem $\mathrm{thm2}$, let $R_\alpha(k)$ and $r_\alpha(k)$ denote the covariance asymptotic quantities used there, and let $\delta>0$. Samarov–Taqqu…

Gaussianity conjecture. We conjecture that when

Let $(X_t)_{t \in \mathbb{Z}}$ be a max-stable stationary time series with $\alpha$-Fréchet margins and pairwise extremal coefficients $(\theta_t)_{t \in \mathbb{Z}}$. Let $p(u_n)$…

Let $(X_t)_{t \in \mathbb{Z}}$ be a max-stable stationary time series with $\alpha$-Fréchet margins and pairwise extremal coefficients $(\theta_t)_{t \in \mathbb{Z}}$. Assume that…

Let the stochastic approximation methods and the long-range dependent white noise processes considered in the paper be given, with convergence-rate exponent $\sigma$ and Hurst inde…

Long range dependence conjecture. The moving average $X$ is long range dependent if and only if

Let $\Phi$ have Hermite rank three or higher, and consider the random corrector $u_\varepsilon-\bar{u}$ in the long-range random potential setting described in the paper. Hermite-p…

Oblique-dependence scaling conjecture. Incongruous scaling should dramatically change the scaling transition: the transition point is always

Low-power conjecture. The test has only low power in the case of a gradual change, because its denominator is inflated as the ranks systematically deviate from the mean rank of the…

Let $(X_i)_{i\geq 0}$ be a stationary Gaussian sequence with mean $0$, variance $1$, and nonnegative correlations satisfying, for some $H\in[0,1)$, $K>0$, and slowly varying functi…

Scaling transition conjecture. The random field $X$ exhibits a scaling transition at

Conjecture on jump-addressing estimators. The performance of the test could be improved by using estimators addressing such jumps. The conjecture concerns the slight overestimation…

Extension conjecture. The special SRD and LRD mixed-case limit theorem holds without the restriction that $k_{j,L}$ be $1$ or $2$; in particular,

Let $p\geq 1$, and let $Y_{n,p}$ and $\sigma_{n,p}$ denote the process and normalizing sequence defined in the paper. Limsup conjecture. … This conjecture would identify the optima…