A goodness-of-fit test is a frequently used modern statistics tool. However, it is still unclear what the most reliable approach is to check assumptions about data set normality. A particular data set (especially with a small number of observations) only partly describes the process, which leaves many options for the interpretation of its true distribution. As a consequence, many goodness-of-fit statistical tests have been developed, the power of which depends on particular circumstances (i.e., sample size, outlets, etc.). With the aim of developing a more universal goodness-of-fit test, we propose an approach based on an N-metric with our chosen kernel function. To compare the power of 40 normality tests, the goodness-of-fit hypothesis was tested for 15 data distributions with 6 different sample sizes. Based on exhaustive comparative research results, we recommend the use of our test for samples of size $n\ge 118$.

The testing of multivariate normality remains a significant scientific problem. Although it is being extensively researched, it is still unclear how to choose the best test based on the sample size, variance, covariance matrix and others. In order to contribute to this field, a new goodness of fit test for multivariate normality is introduced. This test is based on the mean absolute deviation of the empirical distribution density from the theoretical distribution density. A new test was compared with the most popular tests in terms of empirical power. The power of the tests was estimated for the selected alternative distributions and examined by the Monte Carlo modeling method for the chosen sample sizes and dimensions. Based on the modeling results, it can be concluded that a new test is one of the most powerful tests for checking multivariate normality, especially for smaller samples. In addition, the assumption of normality of two real data sets was checked.

Prediction of exchange rates volatility is a challenging problem in investigation of financial markets. Various econometrical models are widely used in predicting of foreign exchange rates. Construction of optimal model is complicated problem due to many factors which can influent volatility of   foreign exchange rate. Values and impact of factors on the exchange rate are changing over time; therefore investors should be cautious for the fact that there always be a certain level of risk investing in foreign currency.  The article investigates the dynamics of hourly exchange rates of the Euro (EUR) against USA dollar (USD). Foreign exchange (forex) rate dynamic is a complex process that can be better understood through investigation of its characteristics. The idea of describing fluctuations by calculating sum of absolute differences (SAD) of a time series is developed. SAD value time series are supposed to be easier predicted since it takes into account of only the magnitude of exchange rate oscillation ignoring its direction. For the analysis and investigation of exchange rates volatility is applied both additive and multiplicative versions of Holt – Winter exponential smoothing techniques. These methods are appropriate for series with a linear trend and seasonal variations. The analysis of EUR/USD exchange rates data in major financial centers showed that they obey intraday periodical variations, so it was used the mentioned model. Two different statistics: mean absolute error (MAE) and root mean squared error (RMSE) were applied for selection of optimal parameters of the model. The modeling results of models were compared. After investigation it was noted that the best prediction results are given by simplified multiplicative model. DOI: http://dx.doi.org/10.5755/j01.ee.26.4.5210

There are real life applications (e.g., requests of http sessions in web browsing) with a finite number of events and correlated inter-arrival times. Terminating point processes can be used to model such behavior. Transient Markov arrival processes (TMAPs) are computationally appealing terminating point processes which are terminating versions of Markov arrival processes. In this work we propose algorithms for creating a TMAP based on empirical measurement data and compare various (series/parallel, CPU/GPU) implementations of the EM method for TMAP fitting.