We perform out-of-sample predictions on a set of stock indices represented in a piecewise linear manner. 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. Then, we propose a practical method to determine the minimum embedding dimension from the segmented time series. The novelty of this approach is that it is applied on segmented representations and that it returns the minimum embedding dimension measured in number of segments. It also has the following advantages: (1) does not contain subjective parameters; (2) works with any number of segments; (3) can detect deterministic time series; (4) is computationally efficient. We use the minimum embedding dimension as an indicator of the length of patterns that can be retrieved from the time series own past using our pattern matching technique. This technique enables the matching of historical patterns 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.
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