Robust methods similar to exponential smoothing are suggested in this paper. First previous results for exponential smoothing in L1
are generalized using the regression quantiles, including a generalization to more parameters. Then a method based on the classical sign test is introduced that should deal not only with outliers but also with level shifts, including a detection of change points. Properties of various approaches are investigated by means of a simulation study. A real data example is used as an illustration.
The paper deals with extensions of exponential smoothing type methods for univariate time series with irregular observations. An alternative method to Wright's modification of simple exponential smoothing based on the corresponding ARIMA process is suggested. Exponential smoothing of order for irregular data is derived. A similar method using a DLS () estimation of polynomial trend of order is derived as well. Maximum likelihood parameters estimation for forecasting methods in irregular time series is suggested. The suggested methods are compared with the existing ones in a simulation numerical study.
Recursive time series methods are very popular due to their numerical simplicity. Their theoretical background is usually based on Kalman filtering in state space models (mostly in dynamic linear systems). However, in time series practice one must face frequently to outlying values (outliers), which require applying special methods of robust statistics. In the paper a simple robustification of Kalman filter is suggested using a simple truncation of the recursive residuals. Then this concept is applied mainly to various types of exponential smoothing (recursive estimation in Box-Jenkins models with outliers is also mentioned). The methods are demonstrated using simulated data.
We give characterizations for uniform exponential stability and uniform exponential instability of linear skew-product flows in terms of Banach sequence spaces and Banach function spaces, respectively. We present a unified approach for uniform exponential stability and uniform exponential instability of linear skew-product flows, extending some stability theorems due to Neerven, Datko, Zabczyk and Rolewicz.
In this paper, the exponential stability of periodic solutions for inertial Cohen-Grossberg-type neural networks are investigated. First, by properly chosen variable substitution the system is transformed to first order differential equation. Second, some sufficient conditions which can ensure the existence and exponential stability of periodic solutions for the system are obtained by using constructing suitable Lyapunov function and differential mean value theorem, applying the analysis method and inequality technique. Finally, two examples are given to illustrate the effectiveness of the results.
In this paper, stochastic interval Hopfield neural networks with time-varying delays are investigated. By applying the Razumikhin-type theorem as well as inequality technique, a set of novel sufficient criteria independent of delays are given for the exponential stability of such networks. As a by-product, for the deterministic Hopfield neural networks with time-varying delays, some delay-independent criteria for their global exponential robust stability are also obtained. The proposed results improve and extend them in the earlier literature and are easier to verify. A numerical example and simulation are also given to illustrate the effectiveness of our results.
This paper focuses on the problem of exponential stability analysis of uncertain complex-variable time delayed chaotic systems, where the parameters perturbation are bounded assumed. The aperiodically intermittent control strategy is proposed to stabilize the complex-variable delayed systems. By taking the advantage of Lyapunov method in complex field and utilizing inequality technology, some sufficient conditions are derived to ensure the stability of uncertain complex-variable delayed systems, where the constrained time delay are considered in the conditions obtained. To protrude the availability of the devised stability scheme, simulation examples are ultimately demonstrated.
We consider the primitive two-colored digraphs whose uncolored digraph has $n+s$ vertices and consists of one $n$-cycle and one $(n-3)$-cycle. We give bounds on the exponents and characterizations of extremal two-colored digraphs.
This study focuses on one of the elements in Czechoslovak cultural agreements that were entered into with ''Third World Countries'' from the 1950s. These agreements included training for foreign students, both in the form of grants for studying in Czechoslovakia, and the dispatch of Czechoslovak scholars abroad. These scholars were sent not only from higher education institutes, but also from the Czechoslovak Academy of Sciences (CSAS). This study focuses on CSAS scholars who worked in Iraq in the 1960s.