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Nonlinearity in human resting, eyes-closed EEG: an in-depth case study

100%

Pritchard W. S. , Stam C. J.

Acta Neurobiologiae Experimentalis

2000

tom 60

nr 1

109-121

The question of nonlinearity in the human electroencephalogram (EEG) is important, since linear methods of EEG analysis are more well-developed and computationally faster than nonlinear methods. Furthermore, the presence or absence of nonlinearity has important theoretical implications for understanding the nature of the brain's oscillatory activity. Using a linear summary measure as a control, we report a failure to reject the null hypothesis of a (largely) stationary linear-Gaussian process for normal, resting, eyes-closed EEG from a single participant. We found significant evidence of nonlinearity at two occipital sites (O1 and O2) where the 8-12.5<%0> Hz alpha rhythm was prominent. However, this element of nonlinear structure appeared trivial, as (1) we found no evidence of time irreversibility at these loci, and (2) best-fitting linear models accounted on-average for over 94% of the variance in the data with nonlinear modeling doing no better. Half of the remaining variance could be accounted for by nonstationarity. While our findings technically apply only to the one individual tested, his EEG was typical of those seen under the conditions that we employed.

SIMPLE UNIT ROOT TEST ROBUST TO OUTLIERS

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Rosiak-Lada K.

Przegląd Statystyczny

2007

tom 54

nr 4

34-48

In this article an alternative method for analysis the integration of time series is proposed. The procedure is appropriate in the presence of outliers and was called 'linearized Dickey-Fuller test'. The method is based on the assumption that the data is generated by some ARIMA (Autoregressive integrated moving average) proces. In the first step, the outliers are identified on the basis of likelihood ratio tests, using REGARIMA model. Then, the estimated effect of outliers is removed from the data. In the last step, the Dickey-Fuller test is applied to the adjusted series. It is shown, via simulations, that the procedure leads to the unit root test with accurate finite sample size and considerably improved power.

MULTILAYER PERCEPTRONS AS APPROXIMATIONS TO PROBABILITY DENSITY FUNCTIONS IN TIME SERIES FORECASTING

100%

Morajda J.

Przegląd Statystyczny

2007

tom 54

nr 1

20-33

The paper presents the method of utilisation of multilayer perceptron neural networks to probability densiity function approximation in the problem of time series forecasting. The theoretical background has been given and the specification of neural prediction model, which generates the probability distribution of the forecasted variable in the issue of financial time series predicition, has been described. Next, the research concerning the performance of such model designed for the forecasting of the Polish stock index WIG has been discussed. Two versions of the model have been applied: first - comprised of 12 perceptron networks with single output each, second - based on one network with 12 outputs. Three test cases (for subsequent stock exchange sessions ) have been analysed. Obtained probability distributions are somewhat similar to empirical distribution (achieved for model development data), but they clearly indicate predicted tendency of index change and show specific uncertainty of the forecast.

DETEKCE A KOREKCE PŘEDVELIKONOČNÍHO A VELIKONOČNÍHO EFEKTU

100%

Arteche J. , Majovská R. , Mariel P. , Orbe S.

Ekonomický časopis (Journal of Economics)

2011

tom 59

nr 5

472 – 487

This study compares eight different alternatives of detection and correction of Easter and pre-Easter effect. These are two calendar effects, which are usually subtracted from the time series analysed before its decomposition into trend/ cycle, seasonality and irregular part. The proposed alternatives differ by the duration of these effects and are compared using regression coefficients, information criteria and recursive estimation. Data of Index of industrial production of Czech Republic, Poland and Slovak Republic and three north-Spanish provinces data of Index of industrial production of Czech Republic, Poland and Slovak Republic and three north-Spanish provinces are used in the empirical application. The conclusions, which can be drawn from the study and which are based on very different data, are that the Easter effect should be always detected and corrected separately and not together with another calendar effect.

Statystyczne funkcje głębi we wstępnej analizie szeregu czasowego

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Kosiorowski D.

Zeszyty Naukowe Uniwersytetu Ekonomicznego w Krakowie

2012

nr 884

43-58

In this paper I present selected applications of data depth-based statistical procedures for a preliminary analysis of time series. I focus our attention on simple methods induced by halfspace depth, regression depth and generalised band depth proposed by Pintado-Lopez and Romo. The Monte Carlo studies and empirical examples show our procedures to have good robustness properties.