Theory and Applications of Time Series Analysis and Forecasting

In this paper, we address nonstatistical methods for forecasting and detection of structural breaks in time series. Our methods are based on the application of the unique fuzzy modeling method called fuzzy transform (F-transform) and selected methods of fuzzy natural logic (FNL). The latter provides a formal model of the semantics of a part of natural language and methods for reasoning based on it. Using F-transform, we first estimate the trend-cycle. Then, using methods of FNL, we extract a sort of expert information that enables us to forecast the trend-cycle. Since F-transform also makes it possible to estimate the slope of time series over an imprecisely specified area (ignoring its volatility), we identify structural breaks through evaluation of changes in the slope by a suitable evaluative linguistic expression. We will demonstrate the effectiveness of our methods on several real time series and compare our results of forecasting with the classical ARIMA statistical method. Our methods are computationally very effective.

Many energy time series captured by real-time systems contain errors or anomalies that prevent accurate forecasts of time series evolution. However, accurate forecasting of load time series and fluctuating renewable energy feed-in as well as subsequent optimisation of the dispatch of controllable generators, storage and loads is crucial to ensure a cost-effective, sustainable and reliable energy supply. Therefore, we investigate methods and approaches for a system solution that automatically detect and replace anomalies in time series to enable accurate forecasts. Here, we introduce a hybrid anomaly detection system for energy consumption time series, which consists of two different neural networks (Seq2Seq and autoencoder) and two more classical approaches (entropy, SVM classification). This network is able to detect different types of anomalies, namely, outliers, zero points, incomplete data, change points and anomalous (parts of) time series. These types are defined for the first time mathematically. Our results show a clear advantage of the hybrid modelling approach for detecting anomalies in previously unknown energy time series compared to the single approaches. In addition, due to the generalisation capability of the hybrid model, our approach allows very good estimation of energy values without requiring a large amount of historical data to train the model.

There is a wide variety of non-seasonal and seasonal unit root tests. However, it is not always obvious which tests can be relied upon due to uncertainties in identifying the data generating process, often with respect to the presence of deterministic terms and the initial conditions. We evaluate the size and power of a large set of unit root tests on time series that are simulated to be representative of economic time series in the M4 competition data. Furthermore, using a conditional random forest-based elimination algorithm, we assess which tests should be combined to improve the performance of each individual test.

In this article, we propose a framework for seasonal time series probabilistic forecasting. It aims at forecasting (in a probabilistic way) the whole next season of a time series, rather than only the next value. Probabilistic forecasting consists in forecasting a probability distribution function for each future position. The proposed framework is implemented combining several machine learning techniques (1) to identify typical seasons and (2) to forecast a probability distribution of the next season. This framework is evaluated using a wide range of real seasonal time series. On the one side, we intensively study the alternative combinations of the algorithms composing our framework (clustering, classification), and on the other side, we evaluate the framework forecasting accuracy. As demonstrated by our experiences, the proposed framework outperforms competing approaches by achieving lower forecasting errors.

This is an overview paper, in which we briefly present results obtained over several years in the analysis, forecasting, and mining information from time series using methods that predominantly have nonstatistical character. Our main goal is to show the readers from the area of probability theory and statistics that nonstatistical methods can be pretty successful in time series processing. Besides the standard tasks such as estimation of trend/trend-cycle and forecasting, our methods are also powerful in providing additional information that can hardly be obtained using the statistical methods, namely, evaluation of the local course, finding perceptually important points, identification of structural breaks, finding periods of monotonous behavior including its evaluation, or summarization of information about large sets of time series. Our goal is not to beat statistical methods, but vice versa—to benefit from the synergy of both.

Coherent forecasting techniques account for the discrete nature of count processes. Besides point and interval forecasts, a third way for achieving coherent forecasts is to consider the full predictive probability mass function (PMF) as the actual forecast value. For a large variety of count processes, the performance of PMF forecasting under estimation uncertainty is analyzed. Furthermore, also Gaussian approximate PMF forecasting is investigated. Different approaches for performance evaluation are taken into consideration, with the main focus on mean squared errors computed for either the full PMF or its lower and upper tails, respectively. A real-world example from finance is presented for illustration.

A novel first-order autoregressive moving average model for analyzing discrete-time series observed at irregularly spaced times is introduced. Under Gaussianity, it is established that the model is strictly stationary and ergodic. In the general case, it is shown that the model is weakly stationary. The lowest dimension of the state-space representation is given along with the one-step linear predictors and their mean squared errors. The maximum likelihood estimation procedure is discussed, and their finite-sample behavior is assessed through Monte Carlo experiments. These experiments show that the bias, the root mean square error, and the coefficient of variation are smaller when the length of the series increases. Further, the method provides good estimations for the standard errors, even with relatively small sample sizes. Also, the irregularly spaced times seem to increase the estimation variability. The application of the proposed model is made through two real-life examples. The first is concerned with medical data, whereas the second describes an astronomical data set analysis.

In this paper, we develop an economic policy uncertainty (EPU) index for the USA and Canada using natural language processing (NLP) methods. Our EPU-NLP index is based on an application of several algorithms, including the rapid automatic keyword extraction (RAKE) algorithm, a combination of the RoBERTa and the Sentence-BERT algorithms, a PyLucene search engine, and the GrapeNLP local grammar engine. For comparison purposes, we also develop an index based on a strictly Boolean method. We find that the EPU-NLP index captures COVID-19-related uncertainty better than the Boolean index. Using a structural VAR approach, we find that a one-standard deviation (SD) economic policy uncertainty shock with EPU-NLP leads, both for Canada and the USA, to larger declines in key macroeconomic variables than a one SD EPU-Boolean shock. In line with the COVID-19 impact, the SVAR model shows an abrupt contraction in economic variables both in Canada and the USA. Moreover, an uncertainty shock with the EPU-NLP caused a much larger contraction for the period including the COVID-19 pandemic than for the pre-COVID-19 period.

The increasing volatility experienced in financial and commodity markets has motivated the search of frequency functions with more complex attributes to characterize their asset returns distribution. In this research, two semi-nonparametric distributions are proposed and compared, the Gram-Charlier expansion and a novel Edgeworth expansion for the Student’s t, to estimate the value-at-risk and the expected shortfall in four indices related to energy, metals, mining, and physical commodities. Backtesting performance is assessed in terms of Kupiec and Independence tests for value at risk and the recent proposal by Acerbi and Székely for the expected shortfall. Our results indicate that the Student’s t expansion density adequately fits the returns of different indices and exhibits the best performance for value at risk and expected shortfall backtesting. Consequently, the Student’s t expansion density, which encompasses the Gram-Charlier distribution as the degrees of freedom parameter tends to infinity, reveals as a flexible and accurate methodology for risk management purposes in energy and commodity markets.

This paper aims to forecast the long-term trend of housing prices in the Spanish cities with more than 25,000 inhabitants, a total of 275 individual municipalities. Based on a causal model explaining housing prices based on six fundamental variables (changes in population, income, number of mortgages, interest rates, vacant and housing prices), a pool VECM technique is used to estimate a housing price model and calculate the ‘stable long-term price’, a central concept defined in the formal valuation process. The model is estimated for the period 1995–2020, and the long term is approached from 2000 to 2026, so the prediction exercise includes backcast and forecast period allowing to extract the long-term cycle housing price have followed during last 20 years and project it further 6 years. The analytical process follows three steps. Firstly, it identifies the cities following a common pattern in their housing market by clustering twice the cities: (1) using house price time series and (2) using a machine learning approach with the six fundamental variables. Results give a comprehensible evolution of the long-term component of housing prices, and the model also permits the understanding of the main drivers of housing prices in each Spanish region. Clustering cities with two statistical tools gives pretty similar results in some cities but is different in others. The challenge of finding the correct grouping is critical to understanding the housing market and forecasting their prices.

Bitcoin has been the most used blockchain platform in business and finance in recent years. This paper aims to find a reliable prediction model that improves a combination of prediction models. Exponential smoothing, ARIMA, artificial neural networks (ANNs) models, and forecasts combination models are among the techniques used in this Paper. The effect of artificial intelligence models in enhancing the results of compound prediction models is the study’s most obvious finding. The second major finding was that a model of a robust combination forecasting model that responds to the many variations that occur in the bitcoin time series and Error improvement should be adopted. The results of the prediction accuracy criterion and matching curve fitting in this paper showed that if the residuals of the changed model are white noise, the forecasts are unbiased. A future study investigating robust combination forecasting would be very interesting.

This paper presents an analysis of both the past and future of the Hungarian retail debt program from a cost-risk standpoint. A quarter of the Hungarian central government debt is held through retail securities. From purely a nominal coupon point of view and analyzed in isolation, retail debt seems to be a comparatively more expensive form of funding. The paper has two goals. First, to estimate the historical cost of the retail debt program compared to alternative domestic sources of funding, taking portfolio effects and risks into account. Second, to simulate the future effects of retail debt based on security-level transaction data and a Vector Error Correction macroeconomic model in order to utilize quantitative tools for the perspective rethink of the retail debt strategy once the current strategic objectives are achieved in the near future.

Central banks, statistical agencies, and international organizations such as the IMF and OECD typically use information about the exchange rate some weeks before the publication date as the basis for their exchange rate forecasts. This paper tests if exchange rate forecasts can be made more accurate by utilizing information about exchange rate movements closer to the publication date. To this end, we apply recent tests of equal predictability and encompassing for path forecasts. We find that the date on which the exchange rate forecast is based is crucial. Using exchange rate forecasts made by Statistics Norway over the period 2001–2018, we find that the random walk, when based on the exchange rate 1 day ahead of the publication deadline, encompasses the predicted path by Statistics Norway. However, when using the exchange rate 15 days before the publication deadline, the random walk path and the predicted exchange rate path by Statistics Norway have equal predictability.

Forecast systems related to forecasting infection cases of Covid-19 are based on time series models because they are considered to be highly accurate in forecasting Covid-19 cases due to their accuracy over epidemiological models that are related to forecasting Covid-19 cases. In this paper, we have two tasks. The first task is to improve forecasting and decrease MAPE% errors in forecasting infection cases through the development of the “Epidemic.TA” system. The development of this algorithm will be called the ensembling time series and neural network system (ET-system). The development of the system was completed by adding a cubic smoothing spline model. This system also applies the method of ensembling between these models in the system (neural network autoregression, Box-Cox transformation, ARMA residuals Trend and Seasonality, trigonometric Box-Cox transformation, ARMA residuals Trend and Seasonality, Holt’s linear trend, autoregressive integrated moving average, and cubic smoothing splines). We applied ensembling by using two methods. The first is the aggregation (average) of results from these models, and the second is ensembling by using average weight by using a prioritizer. The prioritizer gives weights to time series models and neural network models and then gets the ensembling model’s average weight and compares the errors between these models to choose the best forecast model. The results of the developed system (ET-system) were more accurate than the “Epidemic.TA.” On the other hand, the second task in this paper is to use the bootstrap aggregating (bagging) methodology for the NNAR model to decrease the error value of the peak of the wave of infection cases.

This paper proposes a model for the daily electricity demand in Uruguay, identifying the incidence of special days (calendar effects, holidays, among others) and climatic variables such as temperature, humidity, winds, and heliophany. We propose a non-linear model to represent the association between energy consumption and climate variables. Applying Markov switching models and considering hot and cold months separately, identify breaks in the energy demand function associated with temperature thresholds. Predictive analysis during 2020, the first year of the health emergency, shows that the COVID-19 sanitary crisis did not deteriorate the model performance.

Transmission system operator (TSO) have to ensure grid stability economically. This requires highly accurate load forecasts for the transmission grids. The ENTSO-E transparency platform (ETP) currently provides a load estimation and a day-ahead load prediction for different TSO in Germany. This paper shows a hybrid model architecture of a feedforward network based on calendar features to extract the general behaviour of a time-series and a temporal convolutional network to extract the relations between short-historical and future time-series values. This research shows a significant improvement of the current day-ahead load forecast and additionally a model robustness while training with a non-optimal data set.

The increasing number of cybersecurity threats affects the security situation of organisations. The maintenance of the operational picture of the organisation, which integrates all relevant information for selecting appropriate countermeasures, becomes a vital role for organisations. In this paper, we focus on network security situation awareness forecasting. The paper aims to answer two questions—the influence of loss function in neural networks on network security situation awareness forecasting and a comparison of statistical methods and neural networks in network security situation awareness forecasting. For this purpose, we used two-time series representing cybersecurity alerts collected by system Warden. This paper shows an analysis according to which the MAE and MASE loss functions give better results than MSE. Also, we can state that neural networks are more accurate for network security situation awareness forecasting.

This study offers two sets of empirical results to model the daily COVID-19 contagion time series. The Markov-switching models with ARMA structure are implemented assuming that time-series dependence is nonlinear, whereas regimes are data-driven. The first set of results consists of models estimated for the following European countries: Italy, Germany, the United Kingdom, and Russia during the first epidemic wave. The second set of results deals with modeling time series for Italy over the second and the third epidemic waves. Given the empirical findings reached, we have distinguished among several regimes during the epidemic wave. The persistence of time series over each regime is also discussed.

Many countries are undertaking their energy transition process, by investing in renewable energy technologies, in order to face climate change and energy security problems. This paper investigates the temporal trends of the diffusion process of renewable energies, namely, wind and solar, in leading countries for their consumption. In doing so, a bivariate diffusion model is employed to investigate the possibly competitive dynamics between renewables and the top source for electricity production in each country. The obtained results confirm a significant competitive pressure enacted by renewables on the top source. A notable exception is represented by the USA, where renewables appear to reinforce the dominant position of gas.

The main aim of this paper is to investigate the state of employment and employment trends in the water transport system of the European Union and the Republic of Croatia. The purpose of this paper is to find answers to the question of how to turn negative employment trends in the Croatian water transport system into positive ones. To answer this question, several scientific methods were applied, in particular descriptive statistics and correlation and regression analysis. The increase in goods transport and the growth of the gross domestic product have been recognized as major factors in increasing employment in the water transport system. The main findings of this paper can be helpful to transport managers at all levels for human resource planning in the water transport system.

The presented paper analyzes the relationship between economic growth, demographic development, and CO₂ emissions for 30 industrialized countries using time-series data from 1982–2014 in the well-known IPAT/STIRPAT setting. In contrast to the general assumption of IPAT/STIRPAT modeling, which in most cases proposes a one-way causality running from the anthropogenic factors to the environment, applied Granger-causality tests indicate a reversed causal relationship. Therefore, the paper suggests to add a new perspective to the IPAT/STIRPAT approach by setting up a stochastic model that explains impacts on economic growth (affluence) by regression on population, carbon emissions (as a proxy for energy use or ecosystem services), and technology. The results confirm that GDP per capita growth rates of highly industrialized economies are significantly driven by the development of CO₂ emissions, population, and energy intensity. Coefficients remain robust with or without integrating structural and energy variables and for the short- and long-run perspective.