65 problems

Identifiability conjecture. If

The data consist of a highly dependent time series with change-points, and the proposed algorithm estimates both the number and locations of the change-points without relying on ra…

Universality conjecture. Every compound Poisson measure can appear as a limiting distribution of an inhomogeneous INAR(1) process.

Monotonicity conjecture. $L(d)$ is increasing, and consequently the condition $L(d)+\mathbb{E}[\xi_0\log(\xi_0)]>0$ holds if and only if $d>d^*$, with $d^*=0$ if…

Weak-dependence conjecture. Some time series satisfy weak dependence conditions with fast enough decay rates to ensure a Donsker type theorem, but satisfy neither condition nor ano…

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…

Let $f(\lambda)=(2\pi)^{-1}|1-e^{i\lambda}|^{2r}$ and let $\mathcal{F}_r(g)$ be the class of spectral densities defined in the source. For each $r\in\mathbb{N}$, consider the BLUE…

For Day $i$, define … Here $x_i$ is the daily percentage alteration in temperature in New York City and $y_i$ is the daily percentage alteration in the Dow Jones Industrial Average…

Let $\widehat{\lambda}_{0,\delta_n}$ denote the AR(2)-based estimator of the spectral peak location for the stationary time series $\{X_{t,\delta_n},t\in\mathbb{Z}\}$. The estimato…

Let $\{W_j\}_{j\in\mathbb{Z}}$ be standard Gaussian variables and let $\epsilon_i=\sum_{j=i-t}^{i}W_j$ define a moving-average process of order $t$. Suppose $Y_i=f(X_i)+\epsilon_i$…

Wiener's conjecture. Under certain conditions, a stationary process can be expressed as a one-sided function of a sequence of i.i.d. random variables.

Let CEStGM denote the conditionally specified graphical model for stationary multivariate time series, with parameters $Phi_{\ell}^{(a,b)}$ and a process-wide conditional independe…

Let $T$ be the integral operator associated with the interaction kernel defining a conditionally specified stationary multivariate time-series model, and let stationarity mean that…

Let the two data streams be those used by the sliding-window canonical correlation analysis method, and suppose that the data satisfy relatively mild conditions, for example, that…

The result concerns robust mean estimation for data that are both Markovian and adversarially contaminated. In particular, the estimator texttt{RUMEM} achieves, under the stated Hu…

Conjecture on the absence of a good ARMA approximation. The process $X_t$ does not have a good ARMA model of the displayed form that is better than the simple $M+N$-term truncation…

Let $Y_t$ be a random variable with a symmetric distribution, and let $\tau$ denote the extremal precision functional. For a fixed horizon $h$, write $|Y_t|$ for the absolute value…

Input-extension conjecture. The results of this paper can be extended from white-noise inputs to more general inputs, including inputs generated by autoregressive models driven by…

Manifold reconstruction conjecture. Given the Manifold Hypothesis that time series data lie on a manifold, this method reconstructs this topological space from the input time serie…

Wu's Gumbel limit conjecture. It was conjectured that, when $m_n\to\infty$, $V_n$ follows asymptotically the Gumbel extreme-value distribution. This concerns the extreme-value beha…

Consider transfer learning for estimating Hungary's GDP trend using source data from Bulgaria, Croatia, Czechia, Estonia, Greece, Hungary, Latvia, Lithuania, Poland, Romania, the S…

The log-average periodogram is considered for Gaussian time series, with covariance matrices that may be positive semidefinite rather than positive definite. Extension conjecture.…

Let the error process satisfy … Consider the working model for $y_t$ and the corresponding estimation based on the residualized predictors $\mathbf{x}$, including cases in which th…

Fix $k\in\mathbb{N}$ and $C>0$. Suppose that the data-generating process satisfies … where the innovations are independent and identically distributed as $\mathcal{N}(0,\Lambda)$,…

Generalization conjecture. The notions of conditional correlation, conditional stationarity, and conditional nonstationarity should extend to time series that are not necessarily c…