Does the Choice of Realized Covariance Measures Empirically Matter? A Bayesian Density Prediction Approach

This paper suggests a new approach to evaluate realized covariance (RCOV) estimators via their predictive power on return density. By jointly modeling returns and RCOV measures under a Bayesian framework, the predictive density of returns and ex-post covariance measures are bridged. The forecast performance of a covariance estimator can be assessed according to its improvement in return density forecasting. Empirical applications to equity data show that several RCOV estimators consistently perform better than others and emphasize the importance of RCOV selection in covariance modeling and forecasting.

A peroxide-responding sRNA evolved from a peroxidase mRNA

Small RNAs (sRNAs) are critical regulators of gene expression in bacteria, but we lack a clear understanding of how new sRNAs originate and get integrated into regulatory networks. A major obstacle to elucidating their evolution is the difficulty in tracing sRNAs across large phylogenetic distances. To overcome this roadblock, we investigated the prevalence of sRNAs in more than a thousand genomes across Enterobacterales, a bacterial order with a rare confluence of factors that allows robust genome-scale sRNA analyses: several well-studied organisms with fairly conserved genome structures, an established phylogeny, and substantial nucleotide diversity within a narrow evolutionary space. Using a covariance modeling-based approach, we analyzed the presence of hundreds of sRNAs and discovered that a majority of sRNAs arose recently, and uncovered protein-coding genes as a potential source for the generation of new sRNA genes. A detailed investigation of the emergence of OxyS, a peroxide-responding sRNA, demonstrated that it evolved from a fragment of a peroxidase mRNA. Collectively, our data show that the erosion of protein-coding genes can result in the formation of new sRNAs that continue to be part of the original regulon. This novel insight provides a fresh framework for understanding how new sRNAs originate and get incorporated into preexisting regulatory networks.

On the Family of Covariance Functions Based on ARMA Models

In time series analyses, covariance modeling is an essential part of stochastic methods such as prediction or filtering. For practical use, general families of covariance functions with large flexibilities are necessary to model complex correlations structures such as negative correlations. Thus, families of covariance functions should be as versatile as possible by including a high variety of basis functions. Another drawback of some common covariance models is that they can be parameterized in a way such that they do not allow all parameters to vary. In this work, we elaborate on the affiliation of several established covariance functions such as exponential, Matérn-type, and damped oscillating functions to the general class of covariance functions defined by autoregressive moving average (ARMA) processes. Furthermore, we present advanced limit cases that also belong to this class and enable a higher variability of the shape parameters and, consequently, the representable covariance functions. For prediction tasks in applications with spatial data, the covariance function must be positive semi-definite in the respective domain. We provide conditions for the shape parameters that need to be fulfilled for positive semi-definiteness of the covariance function in higher input dimensions.

On the drawback of local detrending in universal kriging in conditions of heterogeneously spaced regional TEC data, low-order trends and outlier occurrences

The study intercompares three stochastic interpolation methods originating from the same geostatistical family: least-squares collocation (LSC) known from geodesy, as well as ordinary kriging (OKR) and universal kriging (UKR) known from geology and other geosciences. The objective of this work is to assess advantages and drawbacks of fundamental differences in modeling between these methods in imperfect data conditions. These differences primarily refer to the treatment of the reference field, commonly called ‘mean value’ or ‘trend’ in geostatistical language. The trend in LSC is determined globally before the interpolation, whereas OKR and UKR detrend the observations during the modeling process. The approach to detrending leads to the evident differences between LSC, OKR and UKR, especially in severe conditions such as far from the optimal data distribution. The theoretical comparisons of LSC, OKR and UKR often miss the numerical proof, while numerical prediction examples do not apply cross-validation of the estimates, which is proven to be a reliable measure of the prediction precision and a validation of empirical covariances. Our study completes the investigations with precise parametrization of all these methods by leave-one-out validation. It finds the key importance of the detrending schemes and shows the advantage of LSC prior global detrending scheme in unfavorable conditions of sparse data, data gaps and outlier occurrence. The test case is the modeling of vertical total electron content (VTEC) derived from GNSS station data. This kind of data is a challenge for precise covariance modeling due to weak signal at higher frequencies and existing outliers. The computation of daily set of VTEC maps using the three techniques reveals the weakness of UKR solutions with a local detrending type in imperfect data conditions.