Differences and similarities between precipitation patterns of different climates

In recent years water-related issues are increasing globally, some researchers even argue that the global hydrological cycle is accelerating, while the number of meteorological extremities is growing. With the help of large number of available measured data, these changes can be examined with advanced mathematical methods. In the outlined research we were able to collect long precipitation datasets from two different climatical regions, one sample area being Ecuador, the other one being Kenya. Using the methodology of spectral analysis based on the discrete Fourier-transformation, several deterministic components were calculated locally in the otherwise stochastic time series, while by the comparison of the results, also with previous calculations from Hungary, several global precipitation cycles were defined in the time interval between 1980 and 2019. The results of these calculations, the described local, regional, and global precipitation cycles can be a helpful tool for groundwater management, as precipitation is the major resource of groundwater recharge, as well as with the help of these deterministic cycles, precipitation forecasts can be delivered for the areas.

Forecasting of agricultural production volumes using methods of data mining

In this article, the future values of indicators were forecasted for production of grains and legumes on farms in Cherkasy region based on the time series expressed in physical units. Time series analysis as one of the data mining techniques was used during the research in order to make a forecast of production using the data (based on the model of dynamic series) from past years to predict the future production volumes. This method contains the following steps: a graphical analysis (allows you to choose the model equation in the best way), separation and analysis of deterministic components of the series, smoothing and filtering of time series, study of random components, construction and testing for the adequacy of the time series model, forecasting the behavior of the time series based on the conducted research.

Exit time as a measure of ecological resilience

Ecological resilience is the magnitude of the largest perturbation from which a system can still recover to its original state. However, a transition into another state may often be invoked by a series of minor synergistic perturbations rather than a single big one. We show how resilience can be estimated in terms of average life expectancy, accounting for this natural regime of variability. We use time series to fit a model that captures the stochastic as well as the deterministic components. The model is then used to estimate the mean exit time from the basin of attraction. This approach offers a fresh angle to anticipating the chance of a critical transition at a time when high-resolution time series are becoming increasingly available.

ЭНТРОПИЯ АБИОТИЧЕСКИХ ГЕОСФЕР И МОДЕЛЬ ДЛЯ ОЦЕНКИ И ПРОГНОЗА ИХ СОСТОЯНИЯ

It has been shown in the present work that the methods used to sum up the coefficients of concentrations (hazards) of different pollutants in the abiotic geospheres are not additive and therefore cannot be universal. Universal is the entropic model developed for the biological structures. However, the classic definition of entropy is not appropriate for the abiotic structures because it comprises both stochastic and deterministic components. In the present work, a novel formula for calculating entropy of abiotic structures based on the environmental risk is proposed and an entropic model for assessing the environmental stability of such structures has been constructed for forecasting their development. The model has been tested by comparing the results of assessing the conditions of a test plot according to the entropic and the classic methodology. The classing one being non-additive yields somewhat overrated rank estimates. The entropic methodology makes it possible to forecast the ecological conditions of the test plot.

Revealing the deterministic components in active avalanche-like dynamics

An ensemble of autonomous camphor discs exhibits avalanche-like dynamics with a characteristic/natural frequency. Furthermore, the dynamics show a resonant response to external forcing indicating the presence of a deterministic component in the system.

Model of the Vibration Signal of the Vibrating Sieving Screen Suspension for Condition Monitoring Purposes

Diagnostics of industrial machinery is a topic related to the need for damage detection, but it also allows to understand the process itself. Proper knowledge about the operational process of the machine, as well as identification of the underlying components, is critical for its diagnostics. In this paper, we present a model of the signal, which describes vibrations of the sieving screen. This particular type is used in the mining industry for the classification of ore pieces in the material stream by size. The model describes the real vibration signal measured on the spring set being the suspension of this machine. This way, it is expected to help in better understanding how the overall motion of the machine can impact the efforts of diagnostics. The analysis of real vibration signals measured on the screen allowed to identify and parameterize the key signal components, which carry valuable information for the following stages of diagnostic process of that machine. In the proposed model we take into consideration deterministic components related to shaft rotation, stochastic Gaussian component related to external noise, stochastic α-stable component as a model of excitations caused by falling rocks pieces, and identified machine response to unitary excitations.

A Parameterization of Models for Unit Root Processes: Structure Theory and Hypothesis Testing

We develop and discuss a parameterization of vector autoregressive moving average processes with arbitrary unit roots and (co)integration orders. The detailed analysis of the topological properties of the parameterization—based on the state space canonical form of Bauer and Wagner (2012)—is an essential input for establishing statistical and numerical properties of pseudo maximum likelihood estimators as well as, e.g., pseudo likelihood ratio tests based on them. The general results are exemplified in detail for the empirically most relevant cases, the (multiple frequency or seasonal) I(1) and the I(2) case. For these two cases we also discuss the modeling of deterministic components in detail.

Generalized Forecast Averaging in Autoregressions with a Near Unit Root

Summary This paper develops a new approach to forecasting a highly persistent time series that employs feasible generalized least squares (FGLS) estimation of the deterministic components in conjunction with Mallows model averaging. Within a local-to-unity asymptotic framework, we derive analytical expressions for the asymptotic mean squared error and one-step-ahead mean squared forecast risk of the proposed estimator and show that the optimal FGLS weights are different from their ordinary least squares (OLS) counterparts. We also provide theoretical justification for a generalized Mallows averaging estimator that incorporates lag order uncertainty in the construction of the forecast. Monte Carlo simulations demonstrate that the proposed procedure yields a considerably lower finite-sample forecast risk relative to OLS averaging. An application to U.S. macroeconomic time series illustrates the efficacy of the advocated method in practice and finds that both persistence and lag order uncertainty have important implications for the accuracy of forecasts.