Forecasting the movements of stock prices is one the most challenging problems in financial markets analysis. In this paper, we use Machine Learning (ML) algorithms for the prediction of future price movements using limit order book data. Two different sets of features are combined and evaluated: handcrafted features based on the raw order book data and features extracted by ML algorithms, resulting in feature vectors with highly variant dimensionalities. Three classifiers are evaluated using combinations of these sets of features on two different evaluation setups and three prediction scenarios. Even though the large scale and high frequency nature of the limit order book poses several challenges, the scope of the conducted experiments and the significance of the experimental results indicate that Machine Learning highly befits this task carving the path towards future research in this field.
The dynamics of the high frequency limit order book comprise a challenging field of study which has been investigated in past literature. An extensive survey on stochastic models and statistical techniques for modeling high frequency limit order book data can be found in @cite_31 , highlighting the inadequacies of statistical models as well as the need for more complex models, such as Machine Learning ones. Statistical models often make unrealistic assumptions about the distribution of the data, such as assuming a Poisson distribution of limit order events. Machine Learning techniques make no assumptions on the distribution of the data. Furthermore, the distribution of limit order events changes rapidly, not just from one day to the next but also within the same day. It is thus very challenging for statistical models which typically assume stationary signals to be used effectively used for modeling limit order book data. The drawbacks of statistical models and advantages of Machine Learning approaches have also been examined in @cite_2 . An extensive analysis of high frequency financial data can be found at @cite_3 , and the dynamics of limit order books are explained in detail in @cite_31 @cite_32 .
@cite_31 @cite_32 @cite_3 @cite_2
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We propose a machine learning framework to capture the dynamics of high-frequency limit order books in financial equity markets and automate real-time prediction of metrics such as mid-price movement and price spread crossing. By characterizing each entry in a limit order book with a vector of attributes such as price and volume at different levels, the proposed framework builds a learning model for each metric with the help of multi-class support vector machines. Experiments with real data establish that features selected by the proposed framework are effective for short-term price movement forecasts. Time-series forecasting has various applications in a wide range of domains, e.g., forecasting stock markets using limit order book data. Limit order book data provide much richer information about the behavior of stocks than its price alone, but also bear several challenges, such as dealing with multiple price depths and processing very large amounts of data of high dimensionality, velocity, and variety. A well-known approach for efficiently handling large amounts of high-dimensional data is the bag-of-features (BoF) model. However, the BoF method was designed to handle multimedia data such as images. In this paper, a novel temporal-aware neural BoF model is proposed tailored to the needs of time-series forecasting using high frequency limit order book data. Two separate sets of radial basis function and accumulation layers are used in the temporal BoF to capture both the short-term behavior and the long-term dynamics of time series. This allows for modeling complex temporal phenomena that occur in time-series data and further increase the forecasting ability of the model. Any other neural layer, such as feature transformation layers, or classifiers, such as multilayer perceptrons, can be combined with the proposed deep learning approach, which can be trained end-to-end using the back-propagation algorithm. The effectiveness of the proposed method is validated using a large-scale limit order book dataset, containing over 4.5 million limit orders, and it is demonstrated that it greatly outperforms all the other evaluated methods. The availability of high-frequency data on transactions, quotes, and order flow in electronic order-driven markets has revolutionized data processing and statistical modeling techniques in finance and brought up new theoretical and computational challenges. Market dynamics at the transaction level cannot be characterized solely in terms the dynamics of a single price, and one must also take into account the interaction between buy and sell orders of different types by modeling the order flow at the bid price, ask price, and possibly other levels of the limit order book. Signals consisting of a sequence of pulses show that inherent origin of the 1 f noise is a Brownian fluctuation of the average interevent time between subsequent pulses of the pulse sequence. In this paper, we generalize the model of interevent time to reproduce a variety of self-affine time series exhibiting power spectral density S(f) scaling as a power of the frequency f. Furthermore, we analyze the relation between the power-law correlations and the origin of the power-law probability distribution of the signal intensity. We introduce a stochastic multiplicative model for the time intervals between point events and analyze the statistical properties of the signal analytically and numerically. Such model system exhibits power-law spectral density S(f)∼1 fβ for various values of β, including β=12, 1 and 32. Explicit expressions for the power spectra in the low-frequency limit and for the distribution density of the interevent time are obtained. The counting statistics of the events is analyzed analytically and numerically, as well. The specific interest of our analysis is related with the financial markets, where long-range correlations of price fluctuations largely depend on the number of transactions. We analyze the spectral density and counting statistics of the number of transactions. The model reproduces spectral properties of the real markets and explains the mechanism of power-law distribution of trading activity. The study provides evidence that the statistical properties of the financial markets are enclosed in the statistics of the time interval between trades. A multiplicative point process serves as a consistent model generating this statistics.