Temporal Pattern Recognition in Noisy Non-stationary Time Series Based on Quantization into Symbolic Streams: Lessons Learned from Financial Volatility Trading

In this paper we investigate the potential of the analysis of noisy non-stationary time series by quantizing it into streams of discrete symbols and applying finitememory symbolic predictors. The main argument is that careful quantization can reduce the noise in the time series to make model estimation more amenable given limited numbers of samples that can be drawn due to the non-stationarity in the time series. As a main application area we study the use of such an analysis in a realistic setting involving financial forecasting and trading. In particular, using historical data, we simulate the trading of straddles on the financial indexes DAX and FTSE 100 on a daily basis, based on predictions of the daily volatility differences in the underlying indexes. We propose a parametric, data-driven quantization scheme which transforms temporal patterns in the series of daily volatility changes into grammatical and statistical patterns in the corresponding symbolic streams. As symbolic predictors operating on the quantized streams we use the classical fixed-order Markov models, variable memory length Markov models and a novel variation of fractal-based predictors introduced in its original form in [1]. The fractal-based predictors are designed to efficiently use deep memory. We compare the symbolic models with continuous techniques such as time-delay neural networks with continuous and categorical outputs, and GARCH models. Our experiments strongly suggest that the robust information reduction achieved by quantizing the real-valued time series is highly beneficial. To deal with nonstationarity in financial daily time series, we propose two techniques that combine “sophisticated” models fitted on the training data with a fixed set of simple-minded symbolic predictors not using older (and potentially misleading) data in the training set. Experimental results show that by quantizing the volatility differences and then using symbolic predictive models, market makers can generate a statistically significant excess profit. However, with respect to our prediction and trading techniques, the option market on the DAX does seem to be efficient for traders and non-members of the stock exchange. There is a potential for traders to make an excess profit on the FTSE 100. We also mention some interesting observations regarding the memory structure in the studied series of daily volatility differences.