This paper presents a tuturial introduction to predictions of stock time series. The various approaches of technical and fundamental analysis is presented and the prediction problem is formulated as a special case of inductive learning. The problems with performance evaluation of near-random-walk processes are illustrated with examples together with guidelines for avoiding the risk of data-snooping. The connections to concepts like "the bias-variance dilemma", overtraining and model complexity are further covered. Existing benchmarks and testing metrics are surveyed and some new measures are introduced.

This paper proposes a nonparametric forecasting method for univariate time series that contain little or no noise. For practical purposes it is assumed that the time series is generated by a nonlinear dynamic system governed by the following equations,

Invasive electroencephalographic (EEG) recordings from depth and subdural electrodes, performed in eight patients with temporal lobe epilepsy, are analyzed using a variety of nonlinear techniques. A surrogate data technique is used to find strong evidence for nonlinearities in epileptogenic regions of the brain. Most of these nonlinearities are characterized as "spiking"' by a wavelet analysis. A small fraction of the nonlinearities are characterized as "recurrent" by a nonlinear prediction algorithm. Recurrent activity is found to occur in spatio-temporal patterns related to the location of the epileptogenic focus. Residual delay maps, used to characterize "lag-one nonlinearity", are remarkably stationary for a given electrode, and exhibit striking variations among electrodes. The clinical and theoretical implications of these results are discussed. Keywords: Epileptogenic focus, Invasive EEG; Nonlinear prediction; Surrogate data; Wavelets 1. Introduction Invasive electroencep...

In this paper we describe the winning entry of the time series prediction competition which was part of the International Workshop on Advanced Black-Box Techniques for Nonlinear Modeling,held at K.U. Leuven, Belgium on July 8–10, 1998. We also describe the source of the data set, a nonlinear transform of a 5-scroll generalized Chua’s circuit. Participants were given 2000 data points and were asked to predict the next 200 points in the series. The winning entry exploited symmetry that was discovered during exploratory data analysis and a method of local modeling designed specifically for the prediction of chaotic time series. This method includes an exponentially weighted metric, a nearest trajectory algorithm, integrated local averaging, and a novel multi-step ahead cross-validation estimation of model error for the purpose of parameter optimization. 2 1

We propose a new measure of synchronization of multichannel ictal and interictal EEG signals. The measure is based on the residual covariance matrix of a multichannel autoregressive model. A major advantage of this measure is its ability to be interpreted both in the framework of stochastic and deterministic models. A preliminary analysis of EEG data from three patients using this measure documents the expected increased synchronization during ictal periods but also reveals that increased synchrony persists for prolonged periods (up to 2 hours or more) in the postictal period. Key words: neural synchronization, epilepsy, multichannel autoregressive model, nonlinear dynamics, seizure 1 Introduction Epileptic seizures are by nature episodic events. Experimental models of epilepsy, as well as patient observations, suggest that the transition to ictal events is characterized by an abnormal increase in synchronization of neural activity. 1 Corresponding author. Tel.: 410-706-2805; Fax: 41...

A hybrid approach, incorporating concepts of nonlinear dynamics in artificial neural networks (ANN), is proposed to model time series generated by complex dynamic systems. We introduce well known features used in the study of dynamic systems- time delay τ and embedding dimension d- for ANN modelling of time series. These features provide a theoretical basis for selecting the optimal size for the number of neurons in the input layer. The main outcome of the new approach for such problems is that to a large extent it defines the ANN architecture and leads to better predictions. We illustrate our method by considering computer generated periodic and chaotic time series. The ANN model developed gave excellent quality of fit for the training and test sets as well as for iterative dynamic predictions for future values of the two time series. Further, computer experiments were conducted by introducing Gaussian noise of various degrees in the two time series, to simulate real world effects. We find rather surprising results that upto a limit introduction of noise leads to a smaller network with good generalizing capability.

Abstract. Nearest neighbor forecasting models are attractive with their simplicity and the ability to predict complex nonlinear behavior. They rely on the assumption that observations similar to the target one are also likely to have similar outcomes. A common practice in nearest neighbor model selection is to compute the globally optimal number of neighbors on a validation set, which is later applied for all incoming queries. For certain queries, however, this number may be suboptimal and forecasts that deviate a lot from the true realization could be produced. To address the problem we propose an alternative approach of training ensembles of nearest neighbor predictors that determine the best number of neighbors for individual queries. We demonstrate that the forecasts of the ensembles improve significantly on the globally optimal single predictors. 1

Local models have emerged as one of the most accurate methods of time series prediction, but their performance is sensitive to the choice of user-specified parameters such as the size of the neighborhood, the embedding dimension, and the distance metric. This paper describes a new method of optimizing these parameters to minimize the multi-step cross-validation error. Empirical results indicate that multi-step optimization is susceptible to shallow local minima unless the optimization is limited to ten or fewer steps ahead. The models optimized using the new method consistently performed better than those optimized with adaptive analog forecasts.

Deriving a relationship that allows to predict future values of a time series is a challenging task when the underlying law is highly non linear. Usually, when facing with a problem of non-linear prediction, we are provided with the past history of the time series and we want to extract from that set of data a mathematical function that relates a certain window of past values with the value T time steps ahead in the future. In practical problems the discovering of a forecasting function is hard since we deal with processes corrupted by noise due to an inaccurate modeling of the system and to the measurement procedure. Another important characteristic of the signal that has to be considered is its stationarety. An adaptive forecasting technique should be devised for non-stationary processes. This is particularly true for the analysis and for all the attempts in forecasting financial time series. It seems that such series are intrinsecally non stationary and that a complete model requires not only the knowledge of past values of the series but also some other information regarding the environment. The results in this field are contradictory but it is clear that trying to infer a global unchanging model from the historical information leads to results comparable with a random walk [8]. We try to use a different approach for prediction rather than dynamical system modeling that is usually the basis for time series characterization. We transform the prediction problem in a classification task and we use a statistical approach based on the k-nearest neighbors algorithm to obtain the most probable variation with respect to the present price value. Index terms: Nearest-neighbors, Financial time series.

The Delay Vector Variance (DVV) method, which analyses the nature of a time series with respect to the prevalence of deterministic or stochastic components, is introduced. Due to the standardisation within the DVV method, it is possible both to statistically test for the presence of nonlinearities in a time series, and to visually inspect the results in a DVV scatter diagram. This approach is convenient for interpretation as it conveys information about the linear or nonlinear nature, as well as about the prevalence of deterministic or stochastic components in the time series, thus unifying the existing approaches which deal either with only deterministic versus stochastic, or the linear versus nonlinear aspect. The results on biomedical time series, namely heart rate variability (HRV) and functional Magnetic Resonance Imaging (fMRI) time series, illustrate the applicability of the proposed DVV-method.