A Comparison of Autometrics and Penalization Techniques under Various Error Distributions: Evidence from Monte Carlo Simulation

This work compares Autometrics with dual penalization techniques such as minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD) under asymmetric error distributions such as exponential, gamma, and Frechet with varying sample sizes as well as predictors. Comprehensive simulations, based on a wide variety of scenarios, reveal that the methods considered show improved performance for increased sample size. In the case of low multicollinearity, these methods show good performance in terms of potency, but in gauge, shrinkage methods collapse, and higher gauge leads to overspecification of the models. High levels of multicollinearity adversely affect the performance of Autometrics. In contrast, shrinkage methods are robust in presence of high multicollinearity in terms of potency, but they tend to select a massive set of irrelevant variables. Moreover, we find that expanding the data mitigates the adverse impact of high multicollinearity on Autometrics rapidly and gradually corrects the gauge of shrinkage methods. For empirical application, we take the gold prices data spanning from 1981 to 2020. While comparing the forecasting performance of all selected methods, we divide the data into two parts: data over 1981–2010 are taken as training data, and those over 2011–2020 are used as testing data. All methods are trained for the training data and then are assessed for performance through the testing data. Based on a root-mean-square error and mean absolute error, Autometrics remain the best in capturing the gold prices trend and producing better forecasts than MCP and SCAD.

Tide-induced magnetic signals and their errors derived from CHAMP and Swarm satellite magnetometer observations

Satellite-measured tidal magnetic signals are of growing importance. These fields are mainly used to infer Earth’s mantle conductivity, but also to derive changes in the oceanic heat content. We present a new Kalman filter-based method to derive tidal magnetic fields from satellite magnetometers: KALMAG. The method’s advantage is that it allows to study a precisely estimated posterior error covariance matrix. We present the results of a simultaneous estimation of the magnetic signals of 8 major tides from 17 years of Swarm and CHAMP data. For the first time, robustly derived posterior error distributions are reported along with the reported tidal magnetic fields. The results are compared to other estimates that are either based on numerical forward models or on satellite inversions of the same data. For all comparisons, maximal differences and the corresponding globally averaged RMSE are reported. We found that the inter-product differences are comparable with the KALMAG-based errors only in a global mean sense. Here, all approaches give values of the same order, e.g., 0.09 nT-0.14 nT for M2. Locally, the KALMAG posterior errors are up to one order smaller than the inter-product differences, e.g., 0.12 nT vs. 0.96 nT for M2. Graphical Abstract

Little Support for Discrete Item Limits in Visual Working Memory

Some theorists argue that working memory is limited to a discrete number of items, and additional items are not encoded at all. Others assume that all items are represented with variable quality. Adam, Vogel, and Awh (2017) presented evidence supporting the item-limit hypothesis: Participants reproduced visual features of up to six items in a self-chosen order. After the third or fourth response, error distributions were indistinguishable from guessing. I present four experiments with young adults (each N=24) testing the assumption that the brief, simultaneous display of visual arrays has led to failures of encoding in the experiments of Adam et al. (2017). Experiment 1 presented items slowly and sequentially. Experiment 2 presented them simultaneously but longer than in the experiments of Adam et al. (2017). Experiments 3 and 4 exactly replicated one original experiment. There was no evidence for an encoding limit. However, all four experiments failed to replicate the evidence for guessing-like error distributions. Modelling data from individuals revealed a mixture of some who do and others who don’t produce guessing-like distributions. This heterogeneity increases the credibility of an alternative to the item-limit hypothesis: Some individuals decide to guess on hard trials even when they have weak information in memory.

Reduced non-Gaussianity by 30 s rapid update in convective-scale numerical weather prediction

Non-Gaussian forecast error is a challenge for ensemble-based data assimilation (DA), particularly for more nonlinear convective dynamics. In this study, we investigate the degree of the non-Gaussianity of forecast error distributions at 1 km resolution using a 1000-member ensemble Kalman filter, and how it is affected by the DA update frequency and observation number. Regional numerical weather prediction experiments are performed with the SCALE (Scalable Computing for Advanced Library and Environment) model and the LETKF (local ensemble transform Kalman filter) assimilating phased array radar observations every 30 s. The results show that non-Gaussianity develops rapidly within convective clouds and is sensitive to the DA frequency and the number of assimilated observations. The non-Gaussianity is reduced by up to 40 % when the assimilation window is shortened from 5 min to 30 s, particularly for vertical velocity and radar reflectivity.

Number attraction in verb and anaphor production: narrowing a production–comprehension contrast

Although reflexive–antecedent agreement shows little susceptibility to number attraction in comprehension, prior production research using the preamble-completion paradigm has demonstrated attraction for both verbs and anaphora. In four production experiments, we compared number attraction effects on subject–verb and reflexive–antecedent agreement using a novel scene-description task in addition to a more traditional preamble elicitation paradigm. While the results from the preamble task align with prior findings, the more naturalistic scene description task produced the same contrast observed in comprehension, with robust verb attraction but minimal anaphor attraction. In addition to analyzing agreement error distributions, we also analyzed the production time-course of participant responses, finding timing effects that pattern with error distributions, even when no error is present. The results suggest that production agreement processes show similar profiles to comprehension processes. We discuss potential sources of variable susceptibility to agreement attraction, suggesting that differences may arise from the time-course of information processing across tasks and linguistic dependencies.

Testing the inferred transcription rates of a dynamic, gene network model in absolute units

The circadian clock coordinates plant physiology and development. Mathematical clock models have provided a rigorous framework to understand how the observed rhythms emerge from disparate, molecular processes. However, models of the plant clock have largely been built and tested against RNA timeseries data in arbitrary, relative units. This limits model transferability, refinement from biochemical data and applications in synthetic biology. Here, we incorporate absolute mass units into a detailed model of the clock gene network in Arabidopsis thaliana. We re-interpret the established P2011 model, highlighting a transcriptional activator that overlaps the function of REVEILLE 8/LHY-CCA1-LIKE 5. The U2020 model incorporates the repressive regulation of PRR genes, a key feature of the most detailed clock model KF2014, without greatly increasing model complexity. We tested the experimental error distributions of qRT-PCR data calibrated for units of RNA transcripts/cell and of circadian period estimates, in order to link the models to data more appropriately. U2019 and U2020 models were constrained using these data types, recreating previously-described circadian behaviours with RNA metabolic processes in absolute units. To test their inferred rates, we estimated a distribution of observed, transcriptome-wide transcription rates (Plant Empirical Transcription Rates, PETR) in units of transcripts/cell/hour. The PETR distribution and the equivalent degradation rates indicated that the models’ predicted rates are biologically plausible, with individual exceptions. In addition to updated clock models, FAIR data resources and a software environment in Docker, this validation process represents an advance in biochemical realism for models of plant gene regulation.

GARCH Models under Power Transformed Returns: Empirical Evidence from International Stock Indices

This study evaluates the empirical performance of four power transformation families: extended Tukey, Modulus, Exponential, and Yeo--Johnson, in modeling the return in the context of GARCH(1,1) models with two error distributions: Gaussian (normal) and Student-t. We employ an Adaptive Random Walk Metropolis method in Markov Chain Monte Carlo scheme to draw parameters. Using 19 international stock indices from the Oxford-Man Institute and basing on the log likelihood, Akaike Information Criterion, Bayesian Information Criterion, and Deviance Information Criterion, the use of power transformation families to the return series clearly improves the fit of the normal GARCH(1,1) model. In particular, the Modulus transformation family provides the best fit. Under Student's t-error distribution assumption, the GARCH(1,1) models under power transformed returns perform better in few cases.

Generalized Linear Models (GLM)

Chapter 7 introduces one of the most useful statistical frameworks for the modern life scientist: the generalized linear model (GLM). GLMs extend the linear model to an array of non-normally distributed data such as Poisson, negative binomial, binomial, and Gamma distributed data. These models dramatically improve the breadth of data that can be properly analysed without resorting to non-parametric statistics. Using the same RxP dataset, readers learn how to assess the error distribution of their data and evaluate competing models to achieve the best, most robust analysis possible. Diagnostic plots and assessing model fit is continually taught as is how to interpret the model output and calculate summary statistics. Plotting non-normal error distributions with ggplot2 is taught, as is using the predict() function.

Modelling and forecasting stock volatility and return: a new approach based on quantile Rogers–Satchell volatility measure with asymmetric bilinear CARR model

This paper proposes quantile Rogers–Satchell (QRS) measure to ensure robustness to intraday extreme prices. We add an efficient term to correct the downward bias of Rogers–Satchell (RS) measure and provide scaling factors for different interquantile range levels to ensure unbiasedness of QRS. Simulation studies confirm the efficiency of QRS measure relative to the intraday squared returns and RS measures in the presence of extreme prices. To smooth out noises, QRS measures are fitted to the CARR model with different asymmetric mean functions and error distributions. By comparing to two realised volatility measures as proxies for the unobserved true volatility, results from Standard and Poor 500 and Dow Jones Industrial Average indices show that QRS estimates using asymmetric bilinear mean function provide the best in-sample model fit based on two robust loss functions with heavier penalty for under-prediction. These fitted volatilities are then incorporated into return models to capture the heteroskedasticity of returns. Model with a constant mean, Student-t errors and QRS estimates gives the best in-sample fit. Different value-at-risk (VaR) and conditional VaR forecasts are provided based on this best return model. Performance measures including Kupiec test for VaRs are evaluated to confirm the accuracy of the VaR forecasts.