The autodependogram is a graphical device recently proposed in the literature to analyze autodependencies. It is defined computing the classical Pearson χ2-statistics of independence at various lags in order to point out the presence lag-depedencies. This paper proposes an improvement of this diagram obtained by substituting the χ2-statistics with an estimator of the Kullback-Leibler divergence between the bivariate density of two delayed variables and the product of their marginal distributions. A simulation study, on well-established time series models, shows that this new autodependogram is more powerful than the previous one. An application to a well-known financial time series is also shown.

A new portmanteau test statistic is proposed for detecting nonlinearity in time series data. The new portmanteau statistic is calculated from the log of the determinant of a matrix comprised of the autocorrelations and cross-correlations of the residuals and squared residuals of a fitted time series. The asymptotic distribution of the proposed test statistic is derived as a linear combination of chi-square distributed random variables and can be approximated by a gamma distribution. A bootstrapping approach is shown to be robust when distributional assumptions are relaxed. The efficacy of the statistic is studied against linear and nonlinear dependency structures of some stationary time series models. It is shown that the new test can provide higher power than other tests in many situations. We demonstrate the advantages of the proposed test by investigating linear and nonlinear effects in an economic series and two environmental time series.

BACKGROUND: Prediction models have gained immense importance in various fields for decision-making purposes. In the context of tennis, relying solely on the probability of winning a single match may not be sufficient for predicting a player\'s future performance or ranking. The performance of a tennis player is influenced by the timing of their matches throughout the year, necessitating the incorporation of time as a crucial factor. This study aims to focus on prediction models for performance indicators that can assist both tennis players and sports analysts in forecasting player standings in future matches.
METHODS: To predict player performance, this study employs a dynamic technique that analyzes the structure of performance using both linear and nonlinear time series models. A novel approach has been taken, comparing the performance of the non-linear Neural Network Auto-Regressive (NNAR) model with conventional stochastic linear and nonlinear models such as Auto-Regressive Integrated Moving Average (ARIMA), Exponential Smoothing (ETS), and TBATS (Trigonometric Seasonal Decomposition Time Series).
RESULTS: The study finds that the NNAR model outperforms all other competing models based on lower values of Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). This superiority in performance metrics suggests that the NNAR model is the most appropriate approach for predicting player performance in tennis. Additionally, the prediction results obtained from the NNAR model demonstrate narrow 95% Confidence Intervals, indicating higher accuracy and reliability in the forecasts.
CONCLUSIONS: In conclusion, this study highlights the significance of incorporating time as a factor when predicting player performance in tennis. It emphasizes the potential benefits of using the NNAR model for forecasting future player standings in matches. The findings suggest that the NNAR model is a recommended approach compared to conventional models like ARIMA, ETS, and TBATS. By considering time as a crucial factor and employing the NNAR model, both tennis players and sports analysts can make more accurate predictions about player performance.

This article investigates the performance of three models - Autoregressive Integrated Moving Average (ARIMA), Threshold Autoregressive Moving Average (TARMA) and Evidential Neural Network for Regression (ENNReg) - in forecasting the Brent crude oil price, a crucial economic variable with a significant impact on the global economy. With the increasing complexity of the price dynamics due to geopolitical factors such as the Russo-Ukrainian war, we examine the impact of incorporating information on the war on the forecasting accuracy of these models. Our analysis shows that incorporating the impact of the war can significantly improve the forecasting accuracy of the models, and the ENNReg model with the inclusion of the dummy variable outperforms the other models during the war period. Including the war variable has enhanced the forecasting accuracy of the ENNReg model by 0.11%. These results carry significant implications regarding policymakers, investors, and researchers interested in developing accurate forecasting models in the presence of geopolitical events such as the Russo-Ukrainian war. The results can be used by the governments of oil-exporting countries for budget policies.

The coronavirus disease 2019 (COVID-19) has spread worldwide in unprecedented speed, and diverse negative impacts have seriously endangered human society. Accurately forecasting the number of COVID-19 cases can help governments and public health organizations develop the right prevention strategies in advance to contain outbreaks. In this work, a long-term 6-month COVID-19 pandemic forecast in second half of 2021 and a short-term 30-day daily ahead COVID-19 forecast in December 2021 are successfully implemented via a novel nanophotonic reservoir computing based on silicon optomechanical oscillators with photonic crystal cavities, benefitting from its simpler learning algorithm, abundant nonlinear characteristics, and some unique advantages such as CMOS compatibility, fabrication cost, and monolithic integration. In essence, the nonlinear time series related to COVID-19 are mapped to the high-dimensional nonlinear space by the optical nonlinear properties of nanophotonic reservoir computing. The testing-dataset forecast results of new cases, new deaths, cumulative cases, and cumulative deaths for six countries demonstrate that the forecasted blue curves are awfully close to the real red curves with exceedingly small forecast errors. Moreover, the forecast results commendably reflect the variations of the actual case data, revealing the different epidemic transmission laws in developed and developing countries. More importantly, the daily ahead forecast results during December 2021 of four kinds of cases for six countries illustrate that the daily forecasted values are highly coincident with the real values, while the relevant forecast errors are tiny enough to verify the good forecasting competence of COVID-19 pandemic dominated by Omicron strain. Therefore, the implemented nanophotonic reservoir computing can provide some foreknowledge on prevention strategy and healthcare management for COVID-19 pandemic.

Traffic management authorities in metropolitan areas use real-time systems that analyze high-frequency measurements from fixed sensors, to perform short-term forecasting and incident detection for various locations of a road network. Published research over the last 20 years focused primarily on modeling and forecasting of traffic volumes and speeds. Traffic occupancy approximates vehicular density through the percentage of time a sensor detects a vehicle within a pre-specified time interval. It exhibits weekly periodic patterns and heteroskedasticity and has been used as a metric for characterizing traffic regimes (e.g. free flow, congestion). This article presents a Bayesian three-step model building procedure for parsimonious estimation of Threshold-Autoregressive (TAR) models, designed for location- day- and horizon-specific forecasting of traffic occupancy. In the first step, multiple regime TAR models reformulated as high-dimensional linear regressions are estimated using Bayesian horseshoe priors. Next, significant regimes are identified through a forward selection algorithm based on Kullback-Leibler (KL) distances between the posterior predictive distribution of the full reference model and TAR models with fewer regimes. Given the regimes, the forward selection algorithm can be implemented again to select significant autoregressive terms. In addition to forecasting, the proposed specification and model-building scheme, may assist in determining location-specific congestion thresholds and associations between traffic dynamics observed in different regions of a network. Empirical results applied to data from a traffic forecasting competition, illustrate the efficacy of the proposed procedures in obtaining interpretable models and in producing satisfactory point and density forecasts at multiple horizons.

In this paper, we show that the presence of nonlinear coupling between time series may be detected using kernel feature space F representations while dispensing with the need to go back to solve the pre-image problem to gauge model adequacy. This is done by showing that the kernelized auto/cross sequences in F can be computed from the model rather than from prediction residuals in the original data space X . Furthermore, this allows for reducing the connectivity inference problem to that of fitting a consistent linear model in F that works even in the case of nonlinear interactions in the X -space which ordinary linear models may fail to capture. We further illustrate the fact that the resulting F -space parameter asymptotics provide reliable means of space model diagnostics in this space, and provide straightforward Granger connectivity inference tools even for relatively short time series records as opposed to other kernel based methods available in the literature.

The study aims to combine the autoregressive distributed lag (ARDL) cointegration framework with smooth transition autoregressive (STAR)-type nonlinear econometric models for causal inference. Further, the proposed STAR distributed lag (STARDL) models offer new insights in terms of modeling nonlinearity in the long- and short-run relations between analyzed variables. The STARDL method allows modeling and testing nonlinearity in the short-run and long-run parameters or both in the short- and long-run relations. To this aim, the relation between CO2 emissions and economic growth rates in the USA is investigated for the 1800-2014 period, which is one of the largest data sets available. The proposed hybrid models are the logistic, exponential, and second-order logistic smooth transition autoregressive distributed lag (LSTARDL, ESTARDL, and LSTAR2DL) models combine the STAR framework with nonlinear ARDL-type cointegration to augment the linear ARDL approach with smooth transitional nonlinearity. The proposed models provide a new approach to the relevant econometrics and environmental economics literature. Our results indicated the presence of asymmetric long-run and short-run relations between the analyzed variables that are from the GDP towards CO2 emissions. By the use of newly proposed STARDL models, the results are in favor of important differences in terms of the response of CO2 emissions in regimes 1 and 2 for the estimated LSTAR2DL and LSTARDL models.

Motivated by recent developments on dimension reduction (DR) techniques for time series data, the association of a general deterrent effect towards South Carolina (SC)\'s registration and notification (SORN) policy for preventing sex crimes was examined. Using adult sex crime arrestee data from 1990 to 2005, the the idea of Central Mean Subspace (CMS) is extended to intervention time series analysis (CMS-ITS) to model the sequential intervention effects of 1995 (the year SC\'s SORN policy was initially implemented) and 1999 (the year the policy was revised to include online notification) on the time series spectrum. The CMS-ITS model estimation was achieved via kernel smoothing techniques, and compared to interrupted auto-regressive integrated time series (ARIMA) models. Simulation studies and application to the real data underscores our model\'s ability towards achieving parsimony, and to detect intervention effects not earlier determined via traditional ARIMA models. From a public health perspective, findings from this study draw attention to the potential general deterrent effects of SC\'s SORN policy. These findings are considered in light of the overall body of research on sex crime arrestee registration and notification policies, which remain controversial.