Alexandros Leontitsis

A simulation approach on Cronbach's alpha statistical significance

In this work we propose the use of simulation for the solution of the Cronbachs alpha statistical significance problem. This coefficient measures the reliability of a questionnaires answers. Many analytical tests have been developed over the years which gave birth to very complicated formulas [2,4,6-9]. A simulation approach to the solution of this problem takes advantage of the computational power in order to give exact results for the distribution of the null hypothesis regarding this coefficient.

An adaptive way for improving noise reduction using local geometric projection

We propose an adaptive way to improve noise reduction by local geometric projection. From the neighborhood of each candidate point in phase space, we identify the best subspace that the point will be orthogonally projected to. The signal subspace is formed by the most significant eigendirections of the neighborhood, while the less significant ones define the noise subspace. We provide a simple criterion to separate the most significant eigendirections from the less significant ones. This criterion is based on the maximum logarithmic difference between the neighborhood eigendirection lengths, and the assumption that there is at least one eigendirection that corresponds to the noise subspace. In this way, we take into account the special characteristics of each neighborhood and introduce a more successful noise reduction technique. Results are presented for a chaotic time series of the Henon map and Ikeda map, as well as on the Nasdaq Composite index.

SPHERICAL SELF-ORGANIZING FEATURE MAP: AN INTRODUCTORY REVIEW

The self-organizing feature map (SOFM) has received great attention from researchers in a variety of areas such as engineering sciences, medicine, biology and economics. The topology of these maps is usually based on 1, 2, or 3 dimensions, forming a lattice. This article discusses various aspects of the spherical SOFMs along with examples illustrating its implementation on high-dimensional data. The main advantage of the spherical SOFM is the ability to visualize complex high-dimensional data by encapsulating physical measures of the data within the 3D attributes of its spherical lattice. The article presents the potential of the spherical SOFM to visualize nonlinear data using examples of two chaotic maps, Henon and Ikeda, with a fractal dimension of 1.2 and 1.7 respectively embedded in 2–5 dimensions.

Repel the swarm to the optimum

We improve the particle swarm optimization (PSO) by introducing the concept of the repellor. So far, the PSO algorithm is guided by the optimum of each particle and the optimum found by all the particles. We now add to the algorithm the location of the worst point found so far and location the worst point found by all the particles. These worst points have the property of repelling the particles to the local and the global optima, respectively. This way the PSO algorithm is improved in the sense that the swarm is able to locate the global optimum more rapidly. Empirical results are presented on archaeological data.

Large Noise Level Estimation

We generalize a method of noise estimation for chaotic time series due to [Schreiber, 1993] in cases where the noise level is relatively large. The noise estimation is based on the correlation integral, which, for small amounts of noise, is not affected by the attractors curvature effects. When the noise is large, however, one has to increase the range of the correlation integral and this brings about significant inaccuracies in its evaluation due to both curvature effects and noise. In this Letter, we present a modification of Schreibers noise level estimation method, which uses a robust error estimator based on L-∞ (rather than the usual L2) norm in the computations. Since L-∞ was proved less sensitive to curvature effects, it gives a more accurate estimation of the noise standard deviation compared with Schreibers results. Here, we illustrate our approach on the Henon map corrupted by Gaussian white noise with zero mean, as well as on real data obtained from the Nasdaq Composite time series of daily returns.

EXPLORING THE IMPACT OF CALENDAR EFFECTS ON THE DYNAMIC STRUCTURE AND FORECASTS OF FINANCIAL TIME SERIES

Several recently developed chaotic forecasting methods give better results than the random walk forecasts. However they do not take into account specific regularities of stock returns reported in empirical finance literature, such as the calendar effects. In this paper, we present a method for filtering the day-of-the-week and the holiday effect in a time series. Our main objective is twofold. On the one hand we study how the underlying dynamics of the Nasdaq Composite, and TSE 300 Composite returns series can be influenced by the presence of calendar effects. On the other hand we adapt our method to chaotic forecasting. Its computational advantages lead to significant improvements of forecasts.

Statistical significance of the LMS regression

We propose the use of simulation in order to obtain a statistical significance measure of the least median of squares (LMS) regression coefficients. We shuffle the values of the dependent variable many times (e.g. 100), so as to preserve their distribution, and we calculate the LMS regression coefficients for every shuffled data. In this way we form a confidence interval for the slope centered on 0, because the slopes of the shuffled data are considered statistically equal to 0. The coefficients of the original data are considered significant if they are not belong on the above mentioned interval.

Nonlinear forecast of financial time series through dynamical calendar correction

A method is presented that takes into account the day-of-the-week and the turn-of-the-month effect and the holiday effect and embodies them to neural network forecasting. It adjusts the time series in order to make its dynamics less distorted. After a predicted value is calculated by the network, the inverse adjustment is made to obtain the final predicted value. If there are no calendar effects on the time series this method has approximately the same performance as its classic counterpart. Empirical results are presented, based on NASDAQ Composite, and TSE 300 Composite indices using daily returns form 1984 to 2003.

Are the Greek preschool teachers able to use distance learning technologies

This study shows the attitude of the Greek preschool teachers towards the new technologies and distance learning technologies, as they become more and more important to the kindergartens. It shows that the teachers of our sample were partly informed and partly familiar with the new technologies. In contrast, those who were involved in distance learning are not only very familiar, hut also they are willing to use the new technologies in their classrooms. Collaboration and communication through the Internet is also boosted by the teachers who are familiar with the new technologies. Our sample consisted of 100 subjects, all of them women between 26-50 years old, graduates of preschool education departments.

Accounting for outliers and calendar effects in surrogate simulations of stock return sequences

Surrogate data analysis (SDA) is a statistical hypothesis testing framework for the determination of weak chaos in time series dynamics. Existing SDA procedures do not account properly for the rich structures observed in stock return sequences, attributed to the presence of heteroscedasticity, seasonal effects and outliers. In this paper we suggest a modification of the SDA framework, based on the robust estimation of location and scale parameters of mean-stationary time series and a probabilistic framework which deals with outliers. A demonstration on the NASDAQ Composite index daily returns shows that the proposed approach produces surrogates that faithfully reproduce the structure of the original series while being manifestations of linear-random dynamics.