Šárka Hudecová

Tests for time series of counts based on the probability-generating functions for time series of counts based on the probability-generating function

We propose testing procedures for the hypothesis that a given set of discrete observations may be formulated as a particular time series of counts with a specific conditional law. The new test statistics incorporate the empirical probability-generating function computed from the observations. Special emphasis is given to the popular models of integer autoregression and Poisson autoregression. The asymptotic properties of the proposed test statistics are studied under the null hypothesis as well as under alternatives. A Monte Carlo power study on bootstrap versions of the new methods is included as well as real-data examples.

The physico-chemical properties and biostimulative activities of humic substances regenerated from lignite

The positive effect of humic acids on the growth of plant roots is well known, however, the mechanisms and role of their physical structure in these processes have not been fully explained yet. In this work, South-Moravian lignite was oxidized by means of nitric acid and hydrogen peroxide to produce a set of regenerated humic acids. The elemental composition, solid state stability and solution characteristics were determined and correlated in vitro with their biological activity. A modified hydroponic method was applied to determine the effects of their potassium salts on Zea mays seedlings roots with respect to the plant weight, root length, root division, and starch and protein content. The relations between the determined parameters were evaluated through Principal Component Analysis and Pearson’s correlation coefficients. The results indicated that the most important factor determining the biological activity of South-Moravian lignite potassium humates is related to the nature of self-assemblies, while the chemical composition had no direct connection with the root growth of Zea mays seedlings. It was demonstrated a controlled processing that provided humic substances with different chemical and physicochemical properties and variable biological activity.

Detection of Changes in INAR Models

In the present paper we develop on-line procedures for detecting changes in the parameters of integer valued autoregressive models of order one. Tests statistics based on probability generating functions are constructed and studied. The asymptotic behavior of the tests under the null hypothesis as well as under certain alternatives is derived.

Change Detection in INARCH Time Series of Counts

In the present paper we develop an online procedure for detecting changes in the parameters of integer ARCH models of order one. The test statistic utilizes the notion of the empirical probability generating function. The asymptotic behavior of the test under the null hypothesis is derived.

Modelling prescription behaviour of general practitioners

Abstract The health care costs have been rapidly rising in recent years and the public health insurance companies are highly interested in prescription policies of general practitioners. In our contribution, a complex model for prescription behaviour of Belgian general practitioners is built using the structural equation modelling (SEM) framework. The model involves a large number of prescribed medicament groups as well as doctors’ and patients’ characteristics. As one of the results, a relatively small number of medicament groups, which effectively describe the prescription behaviour of a given doctor, is obtained. These indicators are consequently used in a generalized linear model for predicting the drug expenses per patient. Such a model can be used as a useful guideline for the expenses’ assessment of a particular practitioner.

Extreme precipitation and long-term precipitation changes in a Central European sedge-grass marsh in the context of flood occurrence

ABSTRACT This study offers a detailed analysis of the extreme precipitation and long-term precipitation changes in a sedge-grass marsh in the “Wet Meadows” area in the Czech Republic (Central Europe) in the context of flood occurrence. Namely, trends in annual maxima of daily precipitation and trends in the occurrence and amount of rainfall are investigated. The analysis is based on daily measurements of precipitation from 1977 to 2015. We found out that extreme precipitation has become significantly more frequent in recent years, and there are also other significant changes in the rainfall distribution. Possible negative effects on the wetland can be linked to a change of carbon exchange between the ecosystem and the atmosphere and a change of biodiversity. Awareness of these changes is necessary for possible positive human intervention when a desirable wetland functioning is threatened.

On Some Properties of Autopersistence Functions and Autopersistence Graphs

The classical autocorrelation function might not be very informative when measuring a dependence in binary time series. Recently, alternative tools, namely the autopersistence functions (APF) and their sample counterparts, the autpersistence graphs (APG), have been proposed for the analysis of dependent dichotomous variables. In this article, we summarize properties of the autopersistence functions for general binary series as well as for some important particular cases. We suggest a normalized version of APF which might be more convenient for a practical use. The asymptotic properties of autopersistence graphs are investigated. The consistency and asymptotic normality is discussed. The theoretical results are illustrated by a simulation study.