Predicting Daily Probability Distributions Of S&P500 Returns

Most approaches in forecasting merely try to predict the next value of the time series. In contrast, this paper presents a framework to predict the full probability distribution. It is expressed as a mixture model: the dynamics of the individual states is modeled with so-called "experts" (potentially nonlinear neural networks), and the dynamics between the states is modeled using a hidden Markov approach. The full density predictions are obtained by a weighted superposition of the individual densities of each expert. This model class is called "hidden Markov experts". Results are presented for daily S&P500 data. While the predictive accuracy of the mean does not improve over simpler models, evaluating the prediction of the full density shows a clear out-of-sample improvement both over a simple GARCH(1,l) model (which assumes Gaussian distributed returns) and over a "gated experts" model (which expresses the weighting for each state non-recursively as a function of external inputs). Several interpretations are given: the blending of supervised and unsupervised learning, the discovery of hidden states, the combination of forecasts, the specialization of experts, the removal of outliers, and the persistence of volatility.Information Systems Working Papers Serie

A First Application of Independent Component Analysis to Extracting Structure from Stock Returns

This paper discusses the application of a modern signal processing technique known as independent component analysis (ICA) or blind source separation to multivariate financial time series such as a portfolio of stocks. The key idea of ICA is to linearly map the observed multivariate time series into a new space of statistically independent components (ICs). This can be viewed as a factorization of the portfolio since joint probabilities become simple products in the coordinate system of the ICs. We apply ICA to three years of daily returns of the 28 largest Japanese stocks and compare the results with those obtained using principal component analysis. The results indicate that the estimated ICs fall into two categories, (i) infrequent but large shocks (responsible for the major changes in the stock prices), and (ii) frequent smaller fluctuations (contributing little to the overall level of the stocks). We show that the overall stock price can be reconstructed surprisingly well by using a small number of thresholded weighted ICs. In contrast, when using shocks derived from principal components instead of independent components, the reconstructed price is less similar to the original one. Independent component analysis is a potentially powerful method of analyzing and understanding driving mechanisms in financial markets. There are further promising applications to risk management since ICA focuses on higher-order statistics.Information Systems Working Papers Serie

Understanding of multimetallic cluster growth

The elucidation of formation mechanisms is mandatory for understanding and planning of synthetic routes. For (bio-)organic and organometallic compounds, this has long been realized even for very complicated molecules, whereas the formation of ligand-free inorganic molecules has widely remained a black box to date. This is due to poor structural relationships between reactants and products and the lack of structurally related intermediates—due to the comparably high coordination flexibility of involved atoms. Here we report on investigations of the stepwise formation of multimetallic clusters, based on a series of crystal structures and complementary quantum-chemical studies of (Ge2As2)2−, (Ge7As2)2−, [Ta@Ge6As4]3−, [Ta@Ge8As4]3− and [Ta@Ge8As6]3−. The study makes use of efficient quantum-chemical tools, enabling the first detailed screening of the energy hypersurface along the formation of ligand-free inorganic species for a semi-quantitative picture. The results can be generalized for an entire family of multimetallic clusters

Using Synchronization for Prediction of High-Dimensional Chaotic Dynamics

We experimentally observe the nonlinear dynamics of an optoelectronic time-delayed feedback loop designed for chaotic communication using commercial fiber optic links, and we simulate the system using delay differential equations. We show that synchronization of a numerical model to experimental measurements provides a new way to assimilate data and forecast the future of this time-delayed high-dimensional system. For this system, which has a feedback time delay of 22 ns, we show that one can predict the time series for up to several delay periods, when the dynamics is about 15 dimensional.Comment: 10 pages, 4 figure

Dynamic scaling approach to study time series fluctuations

We propose a new approach for properly analyzing stochastic time series by mapping the dynamics of time series fluctuations onto a suitable nonequilibrium surface-growth problem. In this framework, the fluctuation sampling time interval plays the role of time variable, whereas the physical time is treated as the analog of spatial variable. In this way we found that the fluctuations of many real-world time series satisfy the analog of the Family-Viscek dynamic scaling ansatz. This finding permits to use the powerful tools of kinetic roughening theory to classify, model, and forecast the fluctuations of real-world time series.Comment: 25 pages, 7 figures, 1 tabl