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The paper presents monitoring of spatial displacements and deformation of hydraulic structures of hydroelectric power plants of the Dnipro and Dnister cascades using permanent deformation monitoring systems (PDMS). The architecture of the geodetic (measuring) component of monitoring systems deployed at Kaniv, Dnipro, Seredniodniprovska and Dnister HPP (all in Ukraine) are presented, as well as deformation monitoring structure of this systems. Analysis of the impact of geodynamic and seismic factors on the operation of selected monitoring systems are presented. The spatial deformations of the base points on all the studied monitoring systems were determined. As a result of the analysis of the obtained values, it was found that the deformations of the dam crest have a seasonal nature (with half-annual period) of movements, and are characterized by the corresponding vector field and the absolute value of spatial movements. [ABSTRACT FROM AUTHOR]

Periodic generalized autoregressive conditionally heteroscedastic (PGARCH) models were introduced by Bollerslev and Ghysels [T. Bollerslev and E. Ghysels, Periodic autoregressive conditional heteroscedasticity, J. Bus. Econom. Statist. 14 1996, 2, 139–151]; these models have gained considerable interest and continued to attract the attention of researchers. This paper is devoted to extensions of the standard absolute value GARCH (AVGARCH) model to the periodically time-varying coefficients (PAVGARCH) one. In this class of models, the parameters are allowed to switch between different regimes. Moreover, these models allow to integrate asymmetric effects in the volatility, Firstly, we give necessary and sufficient conditions ensuring the existence of stationary solutions (in the periodic sense). Secondary, a quasi-maximum likelihood (QML) estimation approach for estimating the PAVGARCH model is developed. The strong consistency and the asymptotic normality of the estimator are studied given mild regularity conditions, requiring strict stationarity and the finiteness of moments of some order for the errors term. Next, we present a set of numerical experiments illustrating the practical relevance of our theoretical results. Finally, we apply our model to two foreign exchange rates: of Algerian Dinar to the European currency Euro (Euro/Dinar) and the American currency Dollar (Dollar/Dinar). This empirical work shows that our approach also outperforms and fits the data well. [ABSTRACT FROM AUTHOR]