We propose a data-driven framework to calibrate signal-to-noise ratios (SNRs) in predictive modeling based on empirical forecast errors from time series data. By matching observed forecast error magnitudes with simulated outcomes, we infer realistic noise levels that reflect actual predictive difficulty—without requiring knowledge of the data-generating process (DGP). This enables model evaluations under empirically plausible SNRs. In a macroeconomic case study on support recovery, we demonstrate that variable selection may fail even under sparsity—not due to model misspecification, but because the signal is too weak to recover. Our results emphasize a crucial but underexplored distinction between structural failure and informational limits.

Copula-based time series models implicitly assume a finite Markov order. In reality, a time series may not follow the Markov property. We modify copula-based time series models by introducing a moving aggregate (MAG) part into the model updating equation. The functional form of the MAG-part is given as the inverse of a conditional copula. The resulting MAG-modified autoregressive copula-based time series model (MAGMAR-Copula) is discussed in detail, and distributional properties are derived in a D-vine framework. First, we investigate stationarity and mixing of the time series, and then we explore the asymptotic properties of maximum-likelihood estimators.

We propose a function-on-function linear regression model for time-dependent curve data that is consistently estimated by imposing factor structures on the regressors. An integral operator based on cross-covariances identifies two components for each functional regressor: a predictive low-dimensional component, along with associated factors that are guaranteed to be correlated with the dependent variable, and an infinite-dimensional component that has no predictive power. In order to consistently estimate the correct number of factors for each regressor, we introduce a functional eigenvalue difference test. Our setting allows us to construct a novel central limit theorem for the regression parameters in a fully functional model, making it possible to construct confidence bands and conduct statistical inference. The model is applied to forecast electricity price curves in three different energy markets. Its prediction accuracy is found to be comparable to popular machine learning approaches, while providing statistically valid inference and interpretable insights into the conditional correlation structures of electricity prices.

Bai, Kao, and Ng (2009, Journal of Econometrics 149, 82--99) propose continuously updated (CUP) estimators for panel cointegrating regression models with cross-sectional dependence generated by unobserved global stochastic trends. While the CUP estimation approach generally performs well, test statistics based upon the CUP estimators suffer from enormous size distortions in finite samples. To address this problem, we propose a block-diagonal VAR sieve bootstrap to capture the second-order time series and cross-section dependence structure in the data and prove bootstrap consistency for the test statistics based upon the CUP estimators under sequential limits with $N\rightarrow \infty$ after $T\rightarrow\infty$. Simulation results reveal that using bootstrap critical values reduces size distortions of the test considerably, with negligible power losses under the alternative. An empirical application demonstrates the importance of the block-diagonal VAR sieve bootstrap in practice by analyzing the Fisher effect in 19 OECD countries.