In the macroeconomic forecasting community, there is increasing interest in machine learning methods that can extract nonlinear predictive content from large datasets with a high number of predictors. Meanwhile, time-varying parameter (TVP) models are known to flexibly model time series by allowing regression coefficients to vary over time. This paper generalizes neural networks to allow for time variation of the weights of the final layer. The variance components of the time-varying weights are estimated alongside the fixed network weights via an EM algorithm. The result is the time-varying neural network (TVNN), a fully supervised, nonlinear model, which combines the desirable properties of classical econometric approaches with the predictive capacity of neural networks. The TVNN model yields improved forecasts over similarly tuned feedforward neural networks with fixed weights, recurrent network architectures, and benchmark autoregressive models on time series from the popular FRED-MD database.
The area under the receiver operating characteristic (AUROC) curve is a widely used tool for assessing and ranking global classifier performance. However, because AUROC ignores the scale of predicted probabilities, it can sometimes provide a misleading performance evaluation. To address this limitation, we build on the area under the Kuipers score curve (AUKSC), and reinterpret this metric by extending the traditional ROC curve into a three-dimensional framework that incorporates thresholds, leading to the area of the generalized ROC (AGROC) curve, thus providing a unified measure of classification performance. Through extensive Monte Carlo simulations, we demonstrate that AGROC effectively addresses the limitations of traditional AUROC metrics, offering a more robust tool for ranking probabilistic classifiers by balancing accuracy and probabilistic differentiation. In an empirical application, we show that AGROC accurately identifies recession probabilities derived from various Markov-switching models applied to US GDP growth data, aligning closely with NBER-defined business cycle phases.
Transformer-based models have witnessed remarkable advancements in the domain of time series forecasting. However, significant challenges persist in effectively handling large volumes of historical data and comprehensively capturing multiscale characteristics inherent in time series. This paper proposes a novel time series forecasting model that integrates the Discrete Wavelet Transform (DWT) and residual learning modules. This integration is aimed at enhancing the model's proficiency in capturing the intricate nonlinear and multiscale features of time series data. The proposed model leverages DWT to decompose the time series into multiple scales, enabling it to effectively capture both local and global features across diverse temporal resolutions. The residual learning modules are meticulously designed to improve the training stability of the model and augment its feature extraction capabilities. Additionally, local and global attention mechanisms are employed to comprehensively capture short- and long-term dependencies within time series data. Comprehensive experiments conducted on seven real-world datasets demonstrate that the proposed approach outperforms state-of-the-art deep learning models in long-term time series forecasting tasks. It achieves higher accuracy and better generalization performance. Ablation studies are also carried out, which further validate the individual contributions of each module to the overall performance of the proposed model, providing strong evidence for the effectiveness of the model's design.
Tracking house prices is crucial for identifying risks to the banking sector and overall financial stability, making accurate predictions essential. This study examines whether housing-related stock returns can predict house price fluctuations in the United Kingdom. Using monthly data from 1983 to 2023, empirical evidence suggests that these equity returns strongly predict UK house price changes 1 month ahead. Because housing-related stock prices provide reliable and easily accessible forecasts of housing market trends, the findings offer valuable insights for investors and policymakers.
In the area of econometrics, the investigation and characterization of processes that retain memory for the past are often of interest. This work overcomes collinearity problems that arise in distributed lag formulations by modeling these effects as structural elements within nonlinear dynamic models using transfer functions. Our main contribution lies in performing sequential Bayesian inference for nonlinear dynamic models, providing an efficient computational solution based on analytical approximations. The scalability offered by the proposed sequential method is particularly relevant in the econometric context, where long time series or multiple levels of disaggregation are often encountered. The proposed models incorporate stochastic volatility, achieved through the use of discount factors. An extensive simulation investigation validates the inferential approximation. The results of the proposed sequential and analytical approximation are compared with the inference obtained through Hamiltonian Monte Carlo in a particular application to real-world consumption data. The results show that the sequential approach produces results that are largely comparable while requiring a significantly shorter amount of computing time. Using the proposed Bayesian state-space framework and a thorough examination of the Phillips curve, a case study is developed focusing on the relationship between inflation and the output gap in the Brazilian scenario. We conclude with a substantial contribution, based on an innovative approach that preserves Bayesian sequential inference and offers a joint model for inflation and the output gap, with dynamic predictive structures assigned to the means, precisions, and correlation between both economic indicators.
Matrix- and tensor-valued time series models have emerged as effective tools to address the challenges posed by high-dimensional time series data. These models utilize the multi-classification structures inherent in data variables to decompose large interaction networks into smaller, more manageable sub-networks. To further reduce dimensionality, recent research has explored regularized matrix-valued time series models. This study builds upon this line of work by proposing the RR-S-MAR model—a matrix autoregressive (MAR) model that incorporates a reduced-rank structure on one side and a sparse structure on the other. We address key challenges related to the estimation, inference, and selection of the proposed model. For regularized estimation, we develop an alternating least-squares algorithm, while statistical inference is conducted using a bootstrapping method. To optimize the selection of rank and sparsity level, we introduce an extended Bayesian information criterion (EBIC). Simulation studies demonstrate the convergence of the estimation algorithm and validate the effectiveness of the proposed model selection criterion. Finally, we apply the RR-S-MAR model to economic data, showcasing its practical utility and providing insights through real-world analysis and interpretation.
A dynamic evolving fuzzy system (eFSi) method for interval-valued time series (ITS) data modeling and forecasting is suggested in this paper. The eFSi method simultaneously adapts the structure and the parameters of the models that it develops whenever it processes a new input data. Essentially, an eFSi model is a collection of interval-valued functional fuzzy rules. The participatory learning algorithm is used to identify the antecedents of the rules and the structure of the model. The parameters of the rule consequent are estimated using the recursive weighted least squares algorithm modified to handle the center and range representation of interval-valued data. Computational experiments are conducted to forecast financial high and low prices of different markets such as stocks, exchange rate, energy commodity, and cryptocurrency. The accuracy of one-step-ahead forecasts produced by the eFSi models are compared with classic, machine learning, and interval-valued methods. Economic evaluation of the models is done using the forecasts to predict range-based volatility. For both, high and low prices of S&P 500, EUR/USD, WTI crude oil, and Bitcoin, out-of-sample evaluations indicate that the interval-valued approaches offer more accurate forecasts because they process the data and produces forecasts that account for their intrinsic interval nature. In range-based volatility estimation, the eFSi generally achieves the highest accuracy. The interval-valued eFSi model emerges as a powerful prospective tool for ITS prediction.
The accurate prediction of the Coal Index is vital due to its substantial impact on economic and environmental policy. This study represents a significant advancement in the field of coal index forecasting by introducing a hybrid deep learning model that effectively tackles the challenge of nonlinear time series data. This innovation overcomes the limitations of traditional statistical and basic machine learning approaches. The core of this model is a unique combination of complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), variational mode decomposition (VMD), sentiment analysis from a multicloud platform, and a gated recurrent unit (GRU) with an attention mechanism. This research marks the inaugural application of sentiment analysis in the predictive domain of the coal industry, enhancing predictive accuracy. In this research, the CEEMDAN method is applied to decompose China's coal index data from March 2015 to November 2023, which, in conjunction with the sentiment analysis results, are processed using an attention-GRU layer to enhance the accuracy and depth of forecasting. Experimental results demonstrate that the proposed model achieves superior performance over several benchmarks in accuracy and error reduction. These results underscore the potential of advanced, integrated analytical techniques in enhancing economic forecasting models.
Reliable forecasts of infectious disease trajectories are indispensable for timely public health action and allocation of medical resources. However, most time-series forecasting frameworks still rely solely on historical case counts and thus struggle to capture sudden shifts in population behavior. Therefore, to quantify the value of external behavioral signals during the COVID-19 pandemic, this research assembled a 124-week (from May 31, 2020, to October 9, 2022) panel that fuses Google Community-Mobility indices with standard surveillance indicators such as new cases, deaths, tests, and vaccinations plus information about population density and the Oxford policy-stringency score for 20 countries spanning six continents. We proceed to assess two forecasting methodological families for predicting new cases using an 8-week hold-out window. The target-variable-only family comprised models using a 4-week rolling average, autoregressive integrated moving average (ARIMA), Prophet, and long short-term memory (LSTM) approaches. In contrast, the data-integration family employs distinct light gradient boosting machine (LightGBM) variants: LightGBM-Direct, which learns a single multi-output mapping for all periods in the horizon, and LightGBM-Recursive, which updates a one-step model and rolls its predictions forward. Performance is evaluated using root mean square error (RMSE) and two optimized weight indices (OWIs), which benchmark improvements over the rolling-average baseline and ARIMA, respectively. The results demonstrate that a mobility-enhanced LightGBM achieves the lowest RMSE in every country, reducing the overall median error by 83% compared with the baseline and by 87% against ARIMA. LightGBM-Direct excels in twelve nations, characterized by smoother trends, whereas LightGBM-Recursive dominates in the remaining eight, which exhibit rapid fluctuations in incidence. Notably, SHapley Additive exPlanations (TreeSHAP) identifies workplace and transit-station mobility, testing intensity, vaccinations, and policy stringency as the most influential predictors, denoting the importance of external behavioral signals in improving pandemic forecast accuracy.
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