19 problems

Previous-visits conjecture. To predict the next step in a time series, a good indication should come from the previous visits the system had made to the phase-space neighborhood co…

AE-KDE robustness conjecture. AE-KDE's particularly poor performance was due to its robustness: the reconstruction loss was low during the injected time period, causing false-negat…

Let $(x_{it}: i\in\mathbb N, t\in\mathbb Z)$ be an infinite-dimensional rank-deficient purely non-deterministic process such that $\operatorname{rk} f_x^n=q<\infty$ almost everywhe…

The system's time series may exhibit characteristic higher-order statistics, namely statistical features beyond the autocorrelation and variance used in critical-slowing-down indic…

Conjecture on RMod extensions. It should also be possible to construct and study RMod series in several different settings, including multivariate RMod series and RMod random field…

Optimal-alignment conjecture. The sum of differences of edge weights is minimized only under an optimal alignment; that is,

Local-mixing conjecture. When local mixing occurs in a data set, high sampling rates can lead to reversal of the normal ordering of permutation entropy with changing $\tau$.

Near second-order Markov conjecture. The MA filtering of the first-order Markov process generates nearly a second-order Markov process.

Convergence-rate conjecture. Similar convergence rates to those established for the corresponding encoder-decoder neural-network forecasting models should be obtainable under appro…

Consider prewhitening time series using autoregressive models $\operatorname{AR}(p)$ or autoregressive moving-average models $\operatorname{ARMA}(p,q)$, where $p$ and $q$ denote th…

The discussion concerns statistical tests for linear dependence between time series, including prewhitening, Granger causality, and $F$- or $\chi^2$-tests; autocorrelation in the u…

Moment-assumption conjecture. The assumption that all moments of $X_{t,n}$ and $\tilde X_t(\theta)$ exist can be dropped.

Let $\mathcal{L}_{mfd}(h)$ denote the Legendre spectrum estimated using multifractal detrended fluctuation analysis (MFDFA), and consider processes with negative regularity. Finite…

Genericity conjecture. It should be possible to prove, similarly to the genericity result for the negative result and the generic resolution result for the adjustment procedure, th…

Let a horizontal visibility graph be constructed from a time series, and let $P(\kappa)$ denote the node degree distribution, where $\kappa$ is the node degree. Lacasa–Toral conjec…

Smoothness-weakening conjecture. The constraints in Theorems 1 and 1a can be weakened to some kind of condition on the total variation of $\psi_l(u)$.

A linear process is understood in the setting above, with coefficient operators whose appropriate summability is assumed, and with finite moments as specified below. Four-moment su…

Let $\bar{I}(\tau)$ and $\hat{I}(\tau)$ denote the two population time-delayed mutual information estimators, and define their difference by … A population is statistically homogen…

Let $T_n$ be the infeasible test statistic, and let $T_n(\hat{\pmb{\theta}})$ and $T_n(\hat{\pmb{\gamma}})$ be the two feasible test statistics, with bandwidth parameter $B_n$. Div…