Accurate financial time series forecasting is critical for effective decision making in areas such as risk management, portfolio optimization, and trading. Given the complexity and volatility of financial markets, traditional forecasting methods often fail to capture the underlying dynamics. Recent advances in artificial neural network (ANN) forecasting research indicate that ANNs present a valuable alternative to traditional linear methods, such as autoregressive integrated moving average (ARIMA). However, time series are typically influenced by a combination of factors which require to consider both linear and non-linear characteristics. This paper proposes a new hybrid model that integrates ARIMA and ANN models such as long short-term memory and gated recurrent unit neural network to leverage the distinct strengths of both linear and non-linear modeling. Moreover, the goodness of the proposed model is evaluated through a comparative analysis of the ARIMA, ANN and Zhang hybrid model, using three financial datasets (i.e., Unicredit SpA stock price, EUR/USD exchange rate and Bitcoin closing price). Various absolute and relative error metrics, computed to evaluate the performance of models, can support the use of the proposed approach. The Diebold–Mariano (DM) test is also implemented to asses the significance of the obtained differences of the hybrid model with respect to the other competing models.

A common approach for calculating the spatial distribution of groundwater level changes consists in choosing a set of different times, interpolating the groundwater level data available at each time over a spatial grid, and then calculating changes in each period by subtracting the interpolated values for these times. However, this can produce misleading results when the data are available in different positions for consecutive times. This paper presents an alternative procedure based on the interpolation of the groundwater level with spatio-temporal kriging, the assessment of the temporal groundwater elevation changes over a regional semiconfined aquifer, and the estimation of their error standard deviations. A comparative analysis of cross-validation results and error standard deviations provides a quantitative measure of the superiority of the introduced approach with respect to the one given in the literature. Moreover, the spatio-temporal case produces more reasonable estimates than the spatial kriging, notably fewer extreme recoveries and drawdowns, in an area under high water stress, such as the upper aquifer of the southern part of the Basin of Mexico aquifer system.

Modelling multivariate spatio-temporal data with complex dependency structures is a challenging task but can be simplified by assuming that the original variables are generated from independent latent components. If these components are found, they can be modelled univariately. Blind source separation aims to recover the latent components by estimating the unknown linear or nonlinear unmixing transformation based on the observed data only. In this paper, we extend recently introduced identifiable variational autoencoder to the nonlinear nonstationary spatio-temporal blind source separation setting and demonstrate its performance using comprehensive simulation studies. Additionally, we introduce two alternative methods for the latent dimension estimation, which is a crucial task in order to obtain the correct latent representation. Finally, we illustrate the proposed methods using a meteorological application, where we estimate the latent dimension and the latent components, interpret the components, and show how nonstationarity can be accounted and prediction accuracy can be improved by using the proposed nonlinear blind source separation method as a preprocessing method.

The definition of an index to synthesize the tourism appeal of a holiday destination is complex due to the effect of different aspects, such as the economic, socio-demographic, cultural, geographical ones regarding both demand and supply-side. In this paper, several spatially-referenced factors, related to the tourism attractiveness, are analyzed through the geographically weighted principal components analysis (GWPCA). However, the automatic setting of its kernel bandwidth, often used in practice, provides sometimes a not satisfactory result, since it is too small, with possible abrupt variation in the spatial domain, or too large, disregarding the spatial dependence. For this reason, a new approach, based on variography and minimum spatial correlation distance characterizing the covariates, is proposed for the GWPCA. A comparison with respect to the outputs of the GWPCA, based on automatic fitting, is discussed. Moreover, tourism composite spatial indicators are developed in order to support the policy makers in planning possible actions to boost tourism over the region of interest.