Fast nonlinear deterministic forecasting of segmented stock indices using pattern matching and embedding techniques

We propose an automated system for out-of-sample predictions of a set of European stock indices. The system performs on piecewise linear representations of the time series. An automated segmentation algorithm converges to an optimum segmented time series representation, which achieves considerable data compression and allows variable sampling rate of the time series depending on different segments having different length. The minimum embedding segment dimension (MESD) algorithm, we propose, seeks for deterministic behavior of the processing data set. MESD returns the embedding dimension of the underlying dynamics of the series, measured in number of segments. Embedding dimension calculations have never been applied on segmented representations. We summarize the advantages of the method in the following: (i) it can detect high dimensional nonlinear deterministic behavior as being projected on a lower dimension segment space; (ii) it is computationally efficient; (iii) it converges to an optimum solution without a-priori parameterization. We use the minimum embedding segment dimension (MESD) as an indicator of the length of patterns that can be retrieved from the time series own past. Our pattern matching technique enables the matching of such historical patterns on others of similar shape which occur in different time scales. To define an appropriate similarity measure, we introduce the notation of Multiple Feature Sets (MFS) which employ Dynamic Time Warping (DTW), and first derivative and temporal features. An additional advantage of the system we propose is that the segmented representation scheme and the prediction model are both data driven and that the predictions are made using information only from the time-series own past without any a priori knowledge being injected into the model. We demonstrate that this approach may offer a useful decision support tool for stock market trading.