In the socio-economic field, it is not surprising that decision-making is based on asymmetric information. Economic agents make decisions to forecast in primary and secondary industries related to the tourism sector. This study aims to provide knowledge in situations of asymmetric information with increasing randomness using time series for tourism accommodation markets. We are trying to solve the question of how consumers exchange their preferences for tourist accommodation between tourist apartments and hotel accommodation in Spain. The emergence of the sharing economy concept has emerged as a competitor to the traditional hotel accommodation in the tourist market. To do this, we will develop a theoretical framework to measure situations of uncertainty and their temporal evolution. Information Theory (IT) is the central axis of the study, particularly the concept of entropy. The Shannon entropy (SE) concept is a static measure of information. This work proposes to model the temporal arrangement of SE to discover the behaviors of the systems. The study in the domain of time and frequency allows us to understand the cycles of uncertainty between systems. To apply the theoretical framework, we will work with data from official Spanish sources for tourist accommodation from January 2008 to December 2019. The results of the empirical analysis show the decision changes of economic agents according to a seasonal pattern. Consumers have new accommodation options, and the answer we get from this work is that consumers have different preferences depending on seasonality. The use of SE allows us to make better predictions compared to SARIMA models, the traditional modelling of seasonal dummy variables, and VAR models. The results of the Matrix U1 Theil verify this hypothesis. The theoretical framework and empirical analysis find an answer to asymmetric information. The implications of this work contribute to the field of social sciences related to the tourism sector, in particular to thermodynamics, statistical mechanics, and IT. The modelling of uncertainty allows for the forecasting and control of accommodation tourist markets in random situations. The applications of this study can be tested in other areas of the economy such as finance, transportation, or investment. Full article

The article is devoted to the author’s approach and tools for regional industries’ modeling, analysis and forecasting, following the general idea of splitting time series into four components: trend, cycles, seasonal component, and residuals. However, the authors introduce new approaches, models, metrics, and identification algorithms, and the components’ interaction structures, having included the analysis of 12 industries in 82 regions of Russia. The models and forecast accuracy were tested on 3–12 month forecasts, thus proving their high accuracy. Therefore, the article proposes not only new systematic econometric tools but a methodology for decision making, developed to provide stable and adequate characteristics of complex non-linear evolutionary dynamics of Russian regions. Full article

Regime switching in conjunction with penalized likelihood techniques could be a robust tool concerning the modelling of dynamic behaviours of consultation rate data. To that end, in this work we propose a methodology that combines the aforementioned techniques, and its performance and capabilities are tested through a real application. Full article

This paper explores the scaling (size) effect in the seasonal patterns, a proxy for competitive threats, of Airbnb’s host providers, with the aim of understanding possible similarities and differences. This explorative study uses the city of Milan (Italy) as a case and daily occupancy data from Airbnb listings for four completed years (2015–2018). A mutual information-based technique was applied to assess possible synchronizations in the seasonal patterns. Empirical findings show progressive dissimilarities when moving from single to multiple listings, thus indicating a differentiation correlated to the presence of managed listings. There are fewer differences during the seasonal periods more centered around leisure clients and they are higher when considering business travelers. The evidence supports the scaling effect and its ability to reduce the competitive threat among different hosts. Full article

In this work, the land surface temperature time series derived using Thermal InfraRed (TIR) satellite data offers the possibility to detect thermal anomalies by using the PCA method. This approach produces very detailed maps of thermal anomalies, both in geothermal areas and in urban areas. Tests were conducted on the following three Italian sites: Solfatara-Campi Flegrei (Naples), Parco delle Biancane (Grosseto) and Modena city. Full article

Electric load forecasting is becoming increasingly challenging due to the growing penetration of decentralised energy generation and power-electronics based loads such as heat pumps and electric vehicles, which adds to a transition to more variable work patterns (accentuated by the COVID-19 pandemic in 2020). In this paper, three different Machine Leaning models are analysed to predict the energy load one week ahead for a period of time including the COVID-19 pandemic. It is shown that, by using the recently proposed TabNet model architecture, it is possible to achieve an accuracy comparable to more traditional approaches based on gradient boosting and artificial neural networks without the need of performing complex feature engineering. Full article

In this paper, we describe a machine learning approach for predicting machine health indicators with a large time horizon into the future. The approach uses state-of-the-art neural network architectures for sequence modelling and can incorporate numerical-sensor and categorical data using entity embeddings. Moreover, we describe an unsupervised labelling approach where classes are generated using continuous sensor values in the training data and a clustering algorithm. To validate our approach, we performed an ablation study to verify the effectiveness of each of our model’s components. In this context, we show that entity embeddings can be used to generate effective features from categorical inputs, that state-of-the-art models, while originally developed for a different set of problems, can nonetheless be transferred to perform industrial asset health classification and provide a performance boost over simpler networks that have been traditionally used, such as relatively shallow recurrent or convolutional networks. Taken together, we present a machine health monitoring system that can accurately generate asset health predictions. This system can incorporate both numerical and categorical information, the current state-of-the-art for sequence modelling, and generate labels in an unsupervised fashion when explicit labels are unavailable. Full article

This study compares the effectiveness of COVID-19 control policies on the virus’s spread and on the change of the infection dynamics in China, Germany, Austria, and the USA relying on a regression discontinuity in time and ‘earlyR’ epidemic models. The effectiveness of policies is measured by real-time reproduction number and cases counts. Comparison between the two lockdowns within each country showed the importance of people's risk perception for the effectiveness of the measures. Results suggest that restrictions applied for a long period or reintroduced later may cause at-tenuated effect on the circulation of the virus and the number of casualties. Full article

Periodic series of period T can be mapped into the set of permutations of $[T-1]=\{1,2,3,\dots ,T-1\}$. These permutations of period T can be classified according to the relative ordering of their elements by the horizontal visibility map. We prove that the number of horizontal visibility classes for each period T coincides with the number of triangulations of the polygon of $T+1$ vertices that, as is well known, is the Catalan number $C_{T-1}$. We also study the robustness against Gaussian noise of the permutation patterns for each period and show that there are periodic permutations that better resist the increase of the variance of the noise. Full article

A bootstrap-based hypothesis test of the goodness-of-fit for the marginal distribution of a time series is presented. Two metrics, the empirical survival Jensen–Shannon divergence ($\mathcal{E}SJS$) and the Kolmogorov–Smirnov two-sample test statistic ($KS2$), are compared on four data sets—three stablecoin time series and a Bitcoin time series. We demonstrate that, after applying first-order differencing, all the data sets fit heavy-tailed $\alpha$-stable distributions with $1<\alpha <2$ at the 95% confidence level. Moreover, $\mathcal{E}SJS$ is more powerful than $KS2$ on these data sets, since the widths of the derived confidence intervals for $KS2$ are, proportionately, much larger than those of $\mathcal{E}SJS$. Full article

This paper addresses wind speed prediction in the dynamic line rating (DLR) environment. We have described architecture of the DLR system as well as the main characteristics of nonlinear forecasting models, such as neural and fuzzy logic networks. Described models were tested and compared using real data (time series with data on wind speed, wind direction, air temperature, and solar radiation). The goal was to increase the accuracy and time of short-term prediction. The results show that neural networks outperform fuzzy logic and that the prediction time interval can be extended up to several hours, with no major compromise of the accuracy. Full article

This work represents any distribution of data by an Intervals’ Number (IN), hence it represents all-order data statistics, using a “small” number of L intervals. The INs considered are induced from images of grapes that ripen. The objective is the accurate prediction of grape maturity. Based on an established algebra of INs, an optimizable IN-regressor is proposed, implementable on a neural architecture, toward predicting future INs from past INs. A recursive scheme tests the capacity of the IN-regressor to learn the physical “law” that generates the non-stationary time-series of INs. Computational experiments demonstrate comparatively the effectiveness of the proposed techniques. Full article

Long-run forecasts of telecommunication services’ diffusion play an important role in policy, regulation, planning and portfolio decisions. Forecasting diffusion of telecommunication technologies is usually based on S-shaped models, mainly due to their accurate long-term predictions. Yet, the use of these models does not allow the introduction of risk in the forecast. In this paper, a methodology for the introduction of uncertainty in the underlying calculations is presented. It is based on the calibration of an Ito stochastic process and the generation of possible forecast paths via Monte Carlo Simulation. Results consist of a probabilistic distribution of future demand, which constitutes a risk assessment of the diffusion process under study. The proposed methodology can find applications in all high-technology markets, where a diffusion model is usually applied for obtaining future forecasts. Full article

A new Big Data cluster method was developed to forecast the hotel accommodation market. The simulation and training of time series data are from January 2008 to December 2019 for the Spanish case. Applying the Hierarchical and Sequential Clustering Analysis method represents an improvement in forecasting modelling of the Big Data literature. The model is presented to obtain better explanatory and forecasting capacity than models used by Google data sources. Furthermore, the model allows knowledge of the tourists’ search on the internet profiles before their hotel reservation. With the information obtained, stakeholders can make decisions efficiently. The Matrix U1 Theil was used to establish a dynamic forecasting comparison. Full article

This study is focused on energy production in Albania which involves different types of infrastructure at the various points of the energy production and distribution chain, as well as monitoring and early warning systems. At a time of rapid climate change, estimating the appropriate dimensions and design of such infrastructure and systems becomes crucial. The main objective is to analyze the seasonality pattern and main external climacteric factors, such as precipitation, average temperature, and water inflow. This work deals with the seasonality patterns of climacteric factors affecting energy production and considers different statistical learning methods for prediction. Full article

The increasing integration of renewable energy sources into the existing energy supply structure is challenging due to the intermittency typical of these energy sources, which implies problems of reliability and scheduling of grid operation. Concerning solar energy, the solar forecast tool predicts the photovoltaic (PV) power production and therefore permits a more efficient grid management. In this paper, the combination of clustering techniques and ANNs (Artificial Neural Networks) for day-ahead PV power forecast is analyzed. Clustering techniques are exploited to divide a dataset into different classes of days with similar weather conditions. Then, a dedicated ANN is developed for every group. The main goal is to assess the forecast improvement determined by the combination of ANNs and dataset clustering methods. Different combinations are compared on a real case study: a PV facility in SolarTech^LAB, in Politecnico di Milano. Full article

In this research, a new uncertainty method has been developed and applied to forecasting the hotel accommodation market. The simulation and training of Time Series data are from January 2001 to December 2018 in the Spanish case. The Log-log BeTSUF method estimated by GMM-HAC-Newey-West is considered as a contribution for measuring uncertainty vs. other prognostic models in the literature. The results of our model present better indicators of the RMSE and Ratio Theil’s for the predictive evaluation period of twelve months. Furthermore, the straightforward interpretation of the model and the high descriptive capacity of the model allow economic agents to make efficient decisions. Full article

In this paper, we want to find a continuous function fitting through the discrete covariance sequence generated by a stationary AR process. This function can be determined as soon as the Yule–Walker equations are found. The procedure consists of two steps. At first the inverse zeros of the characteristic polynomial of the AR process must be fixed. The second step is based on the fact that an AR process can also be seen as a difference equation. By solving this difference equation, it is possible to determine a class of functions from which a candidate for a continuous covariance function can be determined. To analyze if this function is applicable as a positive definite covariance function, it is analyzed mathematically in view of the power spectral density compared to the characteristics of the power spectral density for the discrete covariances. Then it is shown that this function is positive semi-definite. At the end, a simulation of a stationary AR(3) process is elaborated to illustrate the derived properties. Full article

The publication is devoted to studying asymptotic properties of statistical estimates of the distribution parameters $u\in R^q$ of a multidimensional random stationary time series $z_t\in R^m,t\in \mathbb{Z}$ satisfying the strong mixing conditions. We consider estimates ${\widehat{u}}_n^{\delta }\left({\overline{z}}_n\right)$, ${\overline{z}}_n={\left(z_1^{\mathrm{T}},\dots ,z_n^{\mathrm{T}}\right)}^{\mathrm{T}}\in R^{mn}$ that provide in asymptotic $n\to \infty$ the maximum values for some objective functions $Q_n\left({\overline{z}}_n;u\right)$, which have properties similar to the well-known property of local asymptotic normality. These estimates are constructed by solving the equations ${\delta }_n\left({\overline{z}}_n;u\right)=0$, where ${\delta }_n\left({\overline{z}}_n;u\right)$ are arbitrary functions for which ${\delta }_n\left({\overline{z}}_n;u\right)-\underset{h}{\mathrm{grad}}{Q}_n\left({\overline{z}}_n;u+n^{-1/2}h\right)\to 0$$\left(n\to \infty \right)$ in $P_{n,u}\left({\overline{z}}_n\right)$-probability uniformly on $u\in U$, were $U$ is compact in $R^q$. In many cases, the estimates ${\widehat{u}}_n^{\delta }\left({\overline{z}}_n\right)$ have the same asymptotic properties as well-known M-estimates defined by equations ${\widehat{u}}_n^Q\left({\overline{z}}_n\right)$$=\underset{u\in U}{arg\hspace{0.17em}max}{Q}_n\left({\overline{z}}_n;u\right)$ but often can be much simpler computationally. We consider an algorithmic method for constructing estimates ${\widehat{u}}_n^{\delta }\left({\overline{z}}_n\right)$, which is similar to the accumulation method first proposed by R. Fischer and rigorously developed by L. Le Cam. The main theoretical result of the article is the proof of the theorem, in which conditions of the asymptotic normality of estimates ${\widehat{u}}_n^{\delta }\left({\overline{z}}_n\right)$ are formulated, and the expression is proposed for their matrix of asymptotic mean-square deviations $\underset{n\to \infty }{\lim }n{\mathrm{E}}_{n,u}\left\{\left({\widehat{u}}^{\delta }\left({\overline{z}}_n\right)-u\right){\left({\widehat{u}}^{\delta }\left({\overline{z}}_n\right)-u\right)}^{\mathrm{T}}\right\}$. Full article

Many geodetic measurement data can be modelled as a multivariate time series consisting of a deterministic (“functional”) model describing the trend, and a stochastic model of the correlated noise. These data are also often affected by outliers and their stochastic properties can vary significantly. The functional model of the time series is usually nonlinear regarding the trend parameters. To deal with these characteristics, a time series model, which can generally be explained as the additive combination of a multivariate, nonlinear regression model with multiple univariate, covariance-stationary autoregressive (AR) processes the white noise components of which obey independent, scaled t-distributions, was proposed by the authors in previous research papers. In this paper, we extend the aforementioned model to include prior knowledge regarding various model parameters, the information about which is often available in practical situations. We develop an algorithm based on Bayesian inference that provides a robust and reliable estimation of the functional parameters, the coefficients of the AR process and the parameters of the underlying t-distribution. We approximate the resulting posterior density using Markov chain Monte Carlo (MCMC) techniques consisting of a Metropolis-within-Gibbs algorithm. Full article

GNSS systems allow precise resolution of the geodetic positioning problem through advanced techniques of GNSS observation processing (PPP or relative positioning). Current instrumentation and communications capabilities allow obtaining geocentric and topocentric geodetic high frequencies time series, whose analysis provides knowledge of the tectonic or volcanic geodynamic activity of a region. In this work, the GNSS time series study was carried out through the use and adaptation of R packets to determine their behavior, obtaining displacement velocities, noise levels, precursors in the time series, anomalous episodes, and their temporal forecast. Statistical and analytical methods were studied, for example, ARMA, ARIMA models, least-squares methods, wavelet functions, and Kalman techniques. To carry out a comparative analysis of these techniques and methods, significant GNSS time series obtained in geodynamically active regions (tectonic and/or volcanic) were considered. Full article

This paper presents a systematic review of Python packages with a focus on time series analysis. The objective is to provide (1) an overview of the different time series analysis tasks and preprocessing methods implemented, and (2) an overview of the development characteristics of the packages (e.g., documentation, dependencies, and community size). This review is based on a search of literature databases as well as GitHub repositories. Following the filtering process, 40 packages were analyzed. We classified the packages according to the analysis tasks implemented, the methods related to data preparation, and the means for evaluating the results produced (methods and access to evaluation data). We also reviewed documentation aspects, the licenses, the size of the packages’ community, and the dependencies used. Among other things, our results show that forecasting is by far the most frequently implemented task, that half of the packages provide access to real datasets or allow generating synthetic data, and that many packages depend on a few libraries (the most used ones being numpy, scipy and pandas). We hope that this review can help practitioners and researchers navigate the space of Python packages dedicated to time series analysis. We also provide an updated list of the reviewed packages online. Full article

GNSS geodetic time series analysis allows the study of the geodynamic behavior of a specific terrestrial area. These time series define the temporal evolution of the geocentric or topocentric coordinates obtained from geodetic stations, which are linear or non-linear depending, respectively, on the tectonic or volcanic–tectonic character of a region. Linear series are easily modeled but, for the study of nonlinear series, it is necessary to apply filtering techniques that provide a more detailed analysis of their behavior. In this work, a comparative analysis is carried out between different filtering techniques and non–linear GNSS time series analysis: 1sigma–2sigma filter, outlier filter, wavelet analysis, Kalman filter and CATS analysis (Create and Analyze Time Series). This comparative methodology is applied to the time series that describe the volcanic process of El Hierro island (2010–2014). Among them, the time series of the slope distance variation between FRON (El Hierro island) and LPAL (La Palma island) stations is studied, detecting and analyzing the different phases involved in the process. Full article

Window operation is among one of the most influential factors on indoor air quality (IAQ). In this paper, we focus on the modeling of the windows’ opening state in a real open-plan office with five windows. The IAQ of this open-plan office was monitored over a whole year along with the opening state of the windows. A k-Nearest Neighbor (k-NN) classification model was implemented, based on a long time series of both indoor and outdoor monitored environmental factors such as temperature and relative humidity, and CO₂ indoor concentration. In addition, the month, the day of the week and the time of the day were included. The obtained model for the window state prediction performs well with an accuracy of 92% for the training set and 86% for the testing set. Full article

In this paper, we use the Logarithmic Mean Divisia Index (LMDI) to apply decomposition analysis on Carbon Dioxide (CO₂) emissions from transport systems in seven Eastern European countries over the period between 2005 and 2015. The results show that “economic activity” is the main factor responsible for CO₂ emissions in all the countries in our sample. The second factor causing increase in CO₂ emissions is the “fuel mix” by type and mode of transport. Modal share and energy intensity affect the growth of CO₂ emissions but in a less significant way. Finally, only the “population” and “emission coefficient” variables slowed the growth of these emissions in all the countries, except for Slovenia, where the population variable was found to be responsible for the increase in CO₂ emissions. These results not only contribute to advancing the existing literature but also provide important policy recommendations. Full article

The world changes at incredible speed. Global warming and enormous money printing are two examples, which do not affect every one of us equally. “Where and when to spend the vacation?”; “In what currency to store the money?” are just a few questions that might get asked more frequently. Knowledge gained from freely available temperature data and currency exchange rates can provide better advice. Classical time series decomposition discovers trend and seasonality patterns in data. I propose to visualize trend and seasonality data in one chart. Furthermore, I developed a calendar adjustment method to obtain weekly trend and seasonality data and display them in the chart. Full article

Eutrophication in fresh water has become a critical challenge worldwide and chlorophyll-a content is a key water quality parameter that indicates the extent of eutrophication and algae concentration in a body of water. In this paper, a forecasting model for the high accuracy prediction of chlorophyll-a content is proposed to enable aquafarm managers to take remediation actions against the occurrence of toxic algal blooms in the aquaculture industry. The proposed model combines the ensemble empirical mode decomposition (EEMD) technique and a deep learning (DL) long short-term memory (LSTM) neural network (NN). With this hybrid approach, the time-series data are firstly decomposed with the aid of the EEMD algorithm into manifold intrinsic mode functions (IMFs). Secondly, a multi-attribute selection process is employed to select the group of IMFs with strong correlations with the measured real chlorophyll-a dataset and integrate them as inputs for the DL LSTM NN. The model is built on water quality sensor data collected from the Loch Duart salmon aquafarm in Scotland. The performance of the proposed novel hybrid predictive model is validated by comparing the results against the dataset. To measure the overall accuracy of the proposed novel hybrid predictive model, the Mean Absolute Error (MAE), Mean Square Error (MSE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE) were used. Full article

This paper investigates the research question of whether the principle of parsimony carries over into interval forecasting, and proposes new semiparametric prediction intervals that apply the block bootstrap to the first-order autoregression. The AR(1) model is parsimonious in which the error term may be serially correlated. Then, the block bootstrap is utilized to resample blocks of consecutive observations to account for the serial correlation. The Monte Carlo simulations illustrate that, in general, the proposed prediction intervals outperform the traditional bootstrap intervals based on nonparsimonious models. Full article

At present, different methods are used for processing GPS time series data obtained from a network of GNSS stations. Solutions converted to velocity and displacement allow the generation of different geodynamic models in areas influenced by tectonic and volcanic activity. This study focuses on the comparative analysis of the solutions obtained through different processing techniques: Precise Point Positioning (PPP) and Relative Positioning using specialized scientific software (Bernese 5.2). Another important objective of this study is the analysis of the convergence of linear and non-linear time series to determine the accuracy in each component (east, north, up), in addition to the application of statistical techniques and data filtering (1-sigma, 2-sigma, kalman, wavelets, and CATS analysis) to check the behavior of the series. These processing and analysis techniques will be applied to different series obtained from the main stations used for tectonic and volcanic monitoring in the Central America region (Guatemala, El Salvador, Honduras, Nicaragua, and Costa Rica) in order to establish a regional geodynamic model. Full article

Picking an appropriate parameter setting (meta-parameters) for visualization and embedding techniques is a tedious task. However, especially when studying the latent representation generated by an autoencoder for unsupervised data analysis, it is also an indispensable one. Here we present a procedure using a cross-correlative take on the meta-parameters. This ansatz allows us to deduce meaningful meta-parameter limits using OPTICS, DBSCAN, UMAP, t-SNE, and k-MEANS. We can perform first steps of a meaningful visual analysis in the unsupervised case using a vanilla autoencoder on the MNIST and DeepVALVE data sets. Full article

Two-sample and independence tests with the kernel-based mmd and hsic have shown remarkable results on i.i.d. data and stationary random processes. However, these statistics are not directly applicable to nonstationary random processes, a prevalent form of data in many scientific disciplines. In this work, we extend the application of mmd and hsic to nonstationary settings by assuming access to independent realisations of the underlying random process. These realisations—in the form of nonstationary time-series measured on the same temporal grid—can then be viewed as i.i.d. samples from a multivariate probability distribution, to which mmd and hsic can be applied. We further show how to choose suitable kernels over these high-dimensional spaces by maximising the estimated test power with respect to the kernel hyperparameters. In experiments on synthetic data, we demonstrate superior performance of our proposed approaches in terms of test power when compared to current state-of-the-art functional or multivariate two-sample and independence tests. Finally, we employ our methods on a real socioeconomic dataset as an example application. Full article

The output gap, the difference between potential and actual output, has a direct impact on policy decisions, e.g., monetary policy. Estimating this gap and its further analysis remain the subject of controversial debates due to methodological problems. We propose a local polynomial regression combined with a Self-Exciting Threshold AutoRegressive (SETAR) model and its forecasting extension for a systematic output gap estimation. Furthermore, local polynomial regression is proposed for the (multivariate) OECD production function approach and its reliability is demonstrated in forecasting output growth. A comparison of the proposed gap to the Hodrick–Prescott filter as well as to estimations by experts from the FED and OECD shows a higher correlation of our output gap with those from those economic institutions. Furthermore, sometimes gaps with different magnitude and different positions above or below the trend are observed between different methods. This may cause competing policy implications which can be improved with our results. Full article

In this paper, we discuss the statistical coherence between financial time series in terms of Rényi’s information measure or entropy. In particular, we tackle the issue of the directional information flow between bivariate time series in terms of Rényi’s transfer entropy. The latter represents a measure of information that is transferred only between certain parts of underlying distributions. This fact is particularly relevant in financial time series, where the knowledge of “black swan” events such as spikes or sudden jumps is of key importance. To put some flesh on the bare bones, we illustrate the essential features of Rényi’s information flow on two coupled GARCH($1,1$) processes. Full article

This paper presents an analysis of the long-term dynamics of the terms of trade of primary commodities (TTPC) using an extended data set for the whole period 1900–2020. Following our original contribution, we implement three approaches of time series—the finite mixture of distributions, the Markov finite mixture of distributions, and the Markov regime-switching model. Our results confirm the hypothesis of the existence of a succession of three different dynamic regimes in the TTPC over the 1900–2020 period. It seems that the uncertainty characterising the long-term dynamic analysis of TTPC is better taken into account with a Markov hypothesis in the transition from one regime to another than without this hypothesis. In addition, this hypothesis improves the quality of the time series segmentation into regimes. Full article

The COVID-19 pandemic has left a mark on nearly all events since the start of the year 2020. There are many studies that examine the medical, economic, and social effects of the pandemic; however, only a few are concerned with how the reactions of society affect the spread of the virus. The goal of our study is to explore and analyze the connection between the communication of pandemic sceptics and the spread of the COVID-19 pandemic and its caused damages. We aim to investigate the causal relationship between communication about COVID-19 on social media, anti-mask events, and epidemiological indicators in three countries: the USA, Spain, and Hungary. Full article

The availability of massive amounts of temporal data opens new perspectives of knowledge extraction and automated decision making for companies and practitioners. However, learning forecasting models from data requires a knowledgeable data science or machine learning (ML) background and expertise, which is not always available to end-users. This gap fosters a growing demand for frameworks automating the ML pipeline and ensuring broader access to the general public. Automatic machine learning (AutoML) provides solutions to build and validate machine learning pipelines minimizing the user intervention. Most of those pipelines have been validated in static supervised learning settings, while an extensive validation in time series prediction is still missing. This issue is particularly important in the forecasting community, where the relevance of machine learning approaches is still under debate. This paper assesses four existing AutoML frameworks (AutoGluon, H₂O, TPOT, Auto-sklearn) on a number of forecasting challenges (univariate and multivariate, single-step and multi-step ahead) by benchmarking them against simple and conventional forecasting strategies (e.g., naive and exponential smoothing). The obtained results highlight that AutoML approaches are not yet mature enough to address generic forecasting tasks once compared with faster yet more basic statistical forecasters. In particular, the tested AutoML configurations, on average, do not significantly outperform a Naive estimator. Those results, yet preliminary, should not be interpreted as a rejection of AutoML solutions in forecasting but as an encouragement to a more rigorous validation of their limits and perspectives. Full article

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. Full article

In the age of AI, companies strive to extract benefits from data. In the first steps of data analysis, an arduous dilemma scientists have to cope with is the definition of the ’right’ quantity of data needed for a certain task. In particular, when dealing with energy management, one of the most thriving application of AI is the consumption’s optimization of energy plant generators. When designing a strategy to improve the generators’ schedule, a piece of essential information is the future energy load requested by the plant. This topic, in the literature it is referred to as load forecasting, has lately gained great popularity; in this paper authors underline the problem of estimating the correct size of data to train prediction algorithms and propose a suitable methodology. The main characters of this methodology are the Learning Curves, a powerful tool to track algorithms performance whilst data training-set size varies. At first, a brief review of the state of the art and a shallow analysis of eligible machine learning techniques are offered. Furthermore, the hypothesis and constraints of the work are explained, presenting the dataset and the goal of the analysis. Finally, the methodology is elucidated and the results are discussed. Full article

Wind power forecasting is a tool used in the energy industry for a wide range of applications, such as energy trading and the operation of the grid. A set of models known as decomposition-based hybrid models have stood out in recent times due to promising results in terms of performance. As many publications on this matter are found in the literature, a comparison of these models is difficult, because they are tested under different conditions in terms of data, prediction horizon, and time resolution. In this paper, we provide a comparison unifying these parameters using the main decomposition algorithms and a set of artificial neural network-based models for very short-term wind power forecasting (up to 30 min ahead). For this purpose, a case study using data from an Irish wind farm is performed to analyze the models in terms of accuracy and robustness for a variety of wind power generation scenarios. Full article

The contribution of this paper is two-fold. First, we present ProbCast—a novel probabilistic model for multivariate time-series forecasting. We employ a conditional GAN framework to train our model with adversarial training. Second, we propose a framework that lets us transform a deterministic model into a probabilistic one with improved performance. The motivation of the framework is to either transform existing highly accurate point forecast models to their probabilistic counterparts or to train GANs stably by selecting the architecture of GAN’s component carefully and efficiently. We conduct experiments over two publicly available datasets—an electricity consumption dataset and an exchange-rate dataset. The results of the experiments demonstrate the remarkable performance of our model as well as the successful application of our proposed framework. Full article

In this paper, the scope is to study whether and how the COVID-19 situation affected the unemployment rate in Greece. To achieve this, a vector autoregression (VAR) model is employed and data analysis is carried out. Another interesting question is whether the situation affected more heavily female and the youth unemployment (under 25 years old) compared to the overall unemployment. To predict the future impact of COVID-19 on these variables, we used the Impulse Response function. Furthermore, there is taking place a comparison of the impact of the pandemic with the other European countries for overall, female, and youth unemployment rates. Finally, the forecasting ability of such a model is compared with ARIMA and ANN univariate models. Full article

This paper aims at comparing different forecasting strategies combined with the STL decomposition method. STL is a versatile and robust time series decomposition method. The forecasting strategies we consider are as follows: three statistical methods (ARIMA, ETS, and Theta), five machine learning methods (KNN, SVR, CART, RF, and GP), and two versions of RNNs (CNN-LSTM and ConvLSTM). We conduct the forecasting test on six horizons (1, 6, 12, 18, and 24 months). Our results show that, when applied to monthly industrial M3 Competition data as a preprocessing step, STL decomposition can benefit forecasting using statistical methods but harms the machine learning ones. Moreover, the STL-Theta combination method displays the best forecasting results on four over the five forecasting horizons. Full article

This work deals with the Traffic State Estimation (TSE) problem for urban networks, using heterogeneous sources of data such as stationary flow sensors, Floating Car Data (FCD), and Automatic Vehicle Identifiers (AVI). A data-based flow and density estimation method is presented and tested using real traffic data. This work presents a study case applied to the downtown of the city of Grenoble in France, using the Grenoble Traffic Lab for urban networks (GTL-Ville), which is an experimental platform for real-time collection and analysis of traffic data. Full article

Scrub typhus, an infectious disease caused by a bacterium transmitted by “chigger” mites, constitutes a public health problem in Thailand. Predicting epidemic peaks would allow implementing preventive measures locally. This study analyses the predictability of the time series of incidence of scrub typhus aggregated at the provincial level. After stationarizing the time series, the evaluation of the Hurst exponents indicates the provinces where the epidemiological dynamics present a long memory and are predictable. The predictive performances of ARIMA (autoregressive integrated moving average model), ARFIMA (autoregressive fractionally integrated moving average) and fractional Brownian motion models are evaluated. The results constitute the reference level for the predictability of the incidence data of this zoonosis. Full article

The Matrix Profile (MP) algorithm has the potential to revolutionise many areas of data analysis. In this article, several applications to financial time series are examined. Several approaches for the identification of similar behaviour patterns (or motifs) are proposed, illustrated, and the results discussed. While the MP is primarily designed for single series analysis, it can also be applied to multi-variate financial series. It still permits the initial identification of time periods with indicatively similar behaviour across individual market sectors and indexes, together with the assessment of wider applications, such as general market behaviour in times of financial crisis. In short, the MP algorithm offers considerable potential for detailed analysis, not only in terms of motif identification in financial time series, but also in terms of exploring the nature of underlying events. Full article

COVID-19 is one of the biggest challenges that countries face at the present time, as infections and deaths change daily and because this pandemic has a dynamic spread. Our paper considers two tasks. The first one is to develop a system for modeling COVID-19 based on time-series models due to their accuracy in forecasting COVID-19 cases. We developed an “Epidemic. TA” system using R programming for modeling and forecasting COVID-19 cases. This system contains linear (ARIMA and Holt’s model) and non-linear (BATS, TBATS, and SIR) time-series models and neural network auto-regressive models (NNAR), which allows us to obtain the most accurate forecasts of infections, deaths, and vaccination cases. The second task is the implementation of our system to forecast the risk of the third wave of infections in the Russian Federation. Full article

On the Island of Vulcano (Aeolian Archipelago, Italy) the temperatures of fumarole emissions, have ranged from about 700 °C to the boiling point. Since the end of the last eruption (1890 A.D.), many periods of increased heating of hydrothermal systems, underlying the La Fossa area have been identified, but an eruptive condition has not yet been reached. The time variation of the high temperature fumaroles has been tracked by the network of sensors located at a few discrete sites on the summit area of La Fossa cone. The same continuous monitoring network has been working for more than 30 years. The time series shows that a natural cyclic modulation has repeated after almost 20 years, and its periodicity yet has to be discussed and interpreted. The statistical approach and the spectral analysis could provide an objective evaluation to reveal the timing, intensity, and general significance of the thermodynamic perturbations that occurred in the hydrothermal circuits of La Fossa caldera, during the study period. The continuous monitoring data series avoid unrealistic interpolations and allow promptly recognizing changes, which perturb the hydrothermal circuits, highlighting—possibly in near real time—the transient phases of energy release from the different sources (hydrologic/magmatic). Full article

In this study, a Takagi-Sugeno (TS) fuzzy rule-based (FRB) model is used for ensembling precipitation time series. The TS FRB model takes precipitation predictions of grid-based regional climate models (RCMs) from the EUR11 domain, available from the CORDEX database, as inputs to generate ensembled precipitation time series for two meteorological stations (MSs) in the Mediterranean region of Turkey. For each MS, RCM data that are available at the closest grid to the corresponding MSs are used. To generate the fuzzy rules of the TS FRB model, the subtractive clustering algorithm (SC) is utilized. Together with the TS FRB, the simple ensemble mean approach is also applied, and the performances of these two model results and individual RCM predictions are compared. The results show that ensembled models outperform individual RCMs, for monthly precipitation, for both MSs. On the other hand, although ensemble models capture the general trend in the observations, they underestimate the peak precipitation events. Full article

Forecasting often involves multiple time-series that are hierarchically organized (e.g., sales by geography). In that case, there is a constraint that the bottom level forecasts add-up to the aggregated ones. Common approaches use traditional forecasting methods to predict all levels in the hierarchy and then reconcile the forecasts to satisfy that constraint. We propose a new algorithm that automatically forecasts multiple hierarchically organized time-series. We introduce a combination of additive Gaussian processes (GPs) with a hierarchical piece-wise linear function to estimate, respectively, the stationary and non-stationary components of the time-series. We define a flexible structure of additive GPs generated by each aggregated group in the hierarchy of the data. This formulation aims to capture the nested information in the hierarchy while avoiding overfitting. We extended the piece-wise linear function to be hierarchical by defining hyperparameters shared across related time-series. From our experiments, our algorithm can estimate hundreds of time-series at once. To work at this scale, the estimation of the posterior distributions of the parameters is performed using mean-field approximation. We validate the proposed method in two different real-world datasets showing its competitiveness when compared to the state-of-the-art approaches. In summary, our method simplifies the process of hierarchical forecasting as no reconciliation is required. It is easily adapted to non-Gaussian likelihoods and multiple or non-integer seasonalities. The fact that it is a Bayesian approach makes modeling uncertainty of the forecasts trivial. Full article

Recently, there has been growing interest in using machine learning based methods for forecasting renewable energy generation using time-series prediction. Such forecasting is important in order to optimize energy management systems in future micro-grids that will integrate a large amount of solar power generation. However, predicting solar power generation is difficult due to the uncertainty of the solar irradiance and weather phenomena. In this paper, we quantify the impact of uncertainty of machine learning based time-series predictors on the forecast accuracy of renewable energy generation using long-term time series data available from a real micro-grid in Sweden. We use clustering to build different ML forecasting models using LSTM and Facebook Prophet. We evaluate the accuracy impact of using interpolated weather and radiance information on both clustered and non-clustered models. Our evaluations show that clustering decreases the uncertainty by more than 50%. When using actual on-side weather information for the model training and interpolated data for the inference, the improvements in accuracy due to clustering are the highest, which makes our approach an interesting candidate for usage in real micro-grids. Full article

We present a new forecasting scheme based on the credibility distribution of fuzzy events. This approach allows us to build prediction intervals using the first differences of the time series data. Additionally, the credibility expected value enables us to estimate the k-step-ahead pointwise forecasts. We analyze the coverage of the prediction intervals and the accuracy of pointwise forecasts using different credibility approaches based on the upper differences. The comparative results were obtained working with yearly time series from the M4 Competition. The performance and computational cost of our proposal, compared with automatic forecasting procedures, are presented. Full article

Epidemiology maths resorts to Susceptible-Infected-Recovered (SIR)-like models to describe contagion evolution curves for diseases such as Covid-19. Other time series estimation approaches can be used to fit and forecast curves. We use data from the Covid-19 pandemic infection curves of 20 countries to compare forecasting using SEIR (a variant of SIR), polynomial regression, ARIMA and Prophet. Polynomial regression deg2 (POLY d(2)) on differentiated curves had lowest 15 day forecast errors (6% average error over 20 countries), SEIR (errors 25–68%) and ARIMA (errors 15–85%) were better for spans larger than 30 days. We highlight the importance of SEIR for longer terms, and POLY d(2) in 15-days forecasting. Full article

Estimation of COVID-19 dynamics and its evolution is a multidisciplinary effort, which requires the unification of heterogeneous disciplines (scientific, mathematics, epidemiological, biological/bio-chemical, virologists and health disciplines to mention the most relevant) to work together towards a better understanding of this pandemic. Time series analysis is of great importance to determine both the similarity in the behavior of COVID-19 in certain countries/states and the establishment of models that can analyze and predict the transmission process of this infectious disease. In this contribution, an analysis of the different states of the United States will be carried out to measure the similarity of COVID-19 time series, using dynamic time warping distance (DTW) as a distance metric. A parametric methodology is proposed to jointly analyze infected and deceased persons. This metric allows comparison of time series that have a different time length, making it very appropriate for studying the United States, since the virus did not spread simultaneously in all the states/provinces. After a measure of the similarity between the time series of the states of United States was determined, a hierarchical cluster was created, which makes it possible to analyze the behavioral relationships of the pandemic between different states and to discover interesting patterns and correlations in the underlying data of COVID-19 in the United States. With the proposed methodology, nine different clusters were obtained, showing a different behavior in the eastern zone and western zone of the United States. Finally, to make a prediction of the evolution of COVID-19 in the states, Logistic, Gompertz and SIR models were computed. With these mathematical models, it is possible to have a more precise knowledge of the evolution and forecast of the pandemic. Full article

As the world’s largest exporter and second-largest importer, China has made exchange rate stability a top priority for its economic growth. With development over decades, however, China now holds excess dollar reserves that have suffered a huge paper loss because of quantitative easing in the United States. In this reality, China has been provoked into speeding RMB internationalization as a strategy to reduce the cost and get rid of the excessive dependence on the US dollar. Thus, this study attempts to investigate the volatility contagion effect and dynamic conditional correlation among four assets, namely China’s onshore exchange rate (CNY), China’s offshore exchange rate (CNH), China’s foreign exchange reserves (FER), and RMB internationalization level (RGI). Considering the huge changes before and after China’s “8.11” exchange rate reform in 2015, we separate the period of study into two sub-periods. The Diagonal BEKK-GARCH model is employed for this analysis. The results exhibit large GARCH effects and relatively low ARCH effects among all periods and evidence that, before August 2015, there was a weak contagion effect among them. However, after September 2015, the model validates a strengthened volatility contagion within CNY and CNH, CNY and RGI, and CNH and RGI. However, the contagion effect is weakened between FER and CNY, FER and CNH, and FER and RGI. Full article

Simulation-based forecast model selection considers two candidate forecast model classes, simulates from both models fitted to data, applies both forecast models to simulated structures, and evaluates the relative benefit of each candidate prediction tool. This approach, for example, determines a sample size beyond which a candidate predicts best. In an application, aggregate household consumption and disposable income provide an example for error correction. With panel data for European countries, we explore whether and to what degree the cointegration properties benefit forecasting. It evolves that statistical evidence on cointegration is not equivalent to better forecasting properties by the implied cointegrating structure. Full article

This paper addresses the problem of the unsupervised approach of credit card fraud detection in unbalanced datasets using the ARIMA model. The ARIMA model is fitted to the regular spending behaviour of the customer and is used to detect fraud if some deviations or discrepancies appear. Our model is applied to credit card datasets and is compared to four anomaly detection approaches, namely, the K-means, box plot, local outlier factor and isolation forest approaches. The results show that the ARIMA model presents better detecting power than that of the benchmark models. Full article

Real-world time series data often contain missing values due to human error, irregular sampling, or unforeseen equipment failure. The ability of a computational interpolation method to repair such data greatly depends on the characteristics of the time series itself, such as the number of periodic and polynomial trends and noise structure, as well as the particular configuration of the missing values themselves. The interpTools package presents a systematic framework for analyzing the statistical performance of a time series interpolator in light of such data features. Its utility and features are demonstrated through evaluation of a novel algorithm, the Hybrid Wiener Interpolator. Full article

The current pandemic situation of SARS-Cov-2 is negatively influencing people worldwide, and leading to high mortality and excess mortality, due to more reasons than only the disease itself. Thus, forecasting of the mortality rates and consequent population projections would have been complicated since 2020. Paper models mortality in the Czech Republic and Spain and assesses the possible impact of the COVID-19 on the forecasts. We use a Lee–Carter model and apply it to data from 1981 to 2019 (forecast A) and 1981 to 2020 (forecast B). Our results show differences in forecasts up to 2030 by mean square difference. The highest is in ages above 50 for Spain, where it was observed that the COVID-19 pandemic affected the mortality rates in a way that they were higher, and decreased at a slower pace than they would without taking 2020 into account. In the Czech Republic (CR), the forecast does not seem to be affected yet, but it could be in the future when the number of deaths (not only due to COVID-19, but altogether) increases significantly. Nevertheless, we have to verify our preliminary results on real data as soon as they are available. Full article

Terrestrial laser scanners (TLS) capture a large number of 3D points rapidly, with high precision and spatial resolution. These scanners are used for applications as diverse as modeling architectural or engineering structures, but also high-resolution mapping of terrain. The noise of the observations cannot be assumed to be strictly corresponding to white noise: besides being heteroscedastic, correlations between observations are likely to appear due to the high scanning rate. Unfortunately, if the variance can sometimes be modeled based on physical or empirical considerations, the latter are more often neglected. Trustworthy knowledge is, however, mandatory to avoid the overestimation of the precision of the point cloud and, potentially, the non-detection of deformation between scans recorded at different epochs using statistical testing strategies. The TLS point clouds can be approximated with parametric surfaces, such as planes, using the Gauss–Helmert model, or the newly introduced T-splines surfaces. In both cases, the goal is to minimize the squared distance between the observations and the approximated surfaces in order to estimate parameters, such as normal vector or control points. In this contribution, we will show how the residuals of the surface approximation can be used to derive the correlation structure of the noise of the observations. We will estimate the correlation parameters using the Whittle maximum likelihood and use comparable simulations and real data to validate our methodology. Using the least-squares adjustment as a “filter of the geometry” paves the way for the determination of a correlation model for many sensors recording 3D point clouds. Full article