1 Introduction
2 Background and method of research
2.1 Previous research
2.2 Method of research
3 Experimental setup
3.1 Parameters for training the models
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Number of features: The values used for the number of features were 1, 2, 3, 4, 5, and 6. Features used in our model are the difference of price between successive periods of time going back n periods from the current time (t). For instance, if the number of features is 1, it means that the model predicts the next output based on just one previous difference of price. Consequently, that model will have two parameters (since we are using linear kernel SVR), the coefficient and the intercept, and we extract those parameters to do a qualitative analysis of the model. If the number of features is n, the model predicts the next output based on n previous time frames and, therefore, the model will have \(n+1\) parameters.
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Length of timeframes: The lengths of timeframes (in minutes) used were 1, 2, 3, 4, 5, 7, 10, 20, 30, 40, 50, 60, and 70. These values were used to see if there is any correlation between the length of the timeframes and the performance metrics such as profits or hit ratio obtained. Although this could be extended to larger timeframes, we believe that it might not be fully reflective of the structure of high-frequency trading, where trading is very fast and timeframes are inherently small. We also considered that, in timeframes greater than 1 min, there may be multiple starting points from which the training set can begin. Therefore, we generate models for all the possible starting points (in minutes) within a timeframe and also average them.
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Size of training set: The values used for the number of training samples are 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, and 10,000.
Currency pairs | Average no. of price quote updates per minute | Average no. of transactions (deals) per minute | Average bid-ask spreads for minute data |
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EURUSD | 15.87 | 10.68 | 0.00021 |
GBPUSD | 10.17 | 0.49 | 0.00087 |
USDJPY | 13.90 | 6.73 | 0.02024 |
Currency pairs | 1 min | 2 min | 3 min | 4 min | 5 min | 7 min | 10 min |
---|---|---|---|---|---|---|---|
EURUSD | 1.009 | 1.006 | 1.007 | 1.007 | 1.007 | 1.009 | 1.010 |
GBPUSD | 1.020 | 1.013 | 1.011 | 1.009 | 1.008 | 1.007 | 1.006 |
USDJPY | 1.016 | 1.014 | 1.013 | 1.013 | 1.014 | 1.016 | 1.017 |
Currency pairs | 20 min | 30 min | 40 min | 50 min | 60 min | 70 min | |
---|---|---|---|---|---|---|---|
EURUSD | 1.011 | 1.013 | 1.011 | 1.012 | 1.011 | 1.011 | |
GBPUSD | 1.008 | 1.010 | 1.011 | 1.012 | 1.014 | 1.014 | |
USDJPY | 1.021 | 1.023 | 1.025 | 1.024 | 1.025 | 1.026 |
3.2 Performance metrics
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Hit ratio: The hit ratio, also known as directional symmetry, is a measure of how many times the model predicted the change correctly. In other words, if the model predicts upward movement and the actual data used for validation confirm it, then it counts as a hit.
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Profits: Profits are obtained as a result of simulated trading based on the predictions of our models and are simply the sum of the realized differences in best bid prices when the orders are executed. If the price at the closing of a timeframe t is price(t) and the prediction at the closing of the timeframe t is pred(t), then profit is given as follows:$$\begin{aligned} \hbox {Profit}=\sum [{\hbox {price}({t+1})-\hbox {price}(t)} ]\times \hbox {pred}(t). \end{aligned}$$(1)
4 Results and analysis
4.1 Performance metrics vs. length of timeframes
4.2 Performance metrics vs. training set size
4.3 Analyzing trained model parameters
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Case 1 (C1): Absolute value of intercept \(< 0.1\), all coefficients \(< -10\) (\(< 0\) for US Dollar/Japanese Yen),2 profits \(> 0\), and hit ratio \(\ge 60\%\).
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Case 2 (C2): Absolute value of intercept \(< 0.1\), all coefficients \(< -10\) (\(< 0\) for US Dollar/Japanese Yen), profits \(> 0\), and hit ratio \(\ge 50\%\) and \(< 60\%\).
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Case 3 (C3): Absolute value of intercept \(< 0.1\), all coefficients \(< -10\) (\(< 0\) for US Dollar/Japanese Yen), profits \(> 0\), and hit ratio \(< 50\%\).
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Case 4 (C4): Rest of the models (where not all coefficients are negative or absolute value of intercept \(> 0.1\), or profits \(< 0\)).
1 min | 5 min | 20 min | 60 min | |||||
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\(-\) 1 | \(+\) 1 | \(-\) 1 | \(+\) 1 | \(-\) 1 | \(+\) 1 | \(-\) 1 | \(+\) 1 | |
\(-\) 1 | 46.97 | 53.03 | 47.38 | 52.62 | 47.00 | 53.00 | 47.03 | 52.97 |
\(+\) 1 | 52.58 | 47.42 | 52.20 | 47.80 | 52.36 | 47.64 | 52.58 | 47.42 |
\(-\) 1, \(-\) 1 | 46.89 | 53.11 | 45.92 | 54.08 | 45.38 | 54.62 | 45.56 | 54.44 |
\(+\) 1, \(+\) 1 | 53.34 | 46.66 | 54.03 | 45.97 | 53.78 | 46.22 | 53.86 | 46.14 |
\(-\) 1, \(-\) 1, \(-\) 1 | 46.18 | 53.82 | 45.00 | 55.00 | 44.07 | 55.93 | 43.95 | 56.05 |
\(+\) 1, \(+\) 1, \(+\) 1 | 54.50 | 45.50 | 55.48 | 44.52 | 54.89 | 45.11 | 55.09 | 44.91 |
1 min | 5 min | 20 min | 60 min | |||||
---|---|---|---|---|---|---|---|---|
\(-\) 1 | \(+\) 1 | \(-\) 1 | \(+\) 1 | \(-\) 1 | \(+\) 1 | \(-\) 1 | \(+\) 1 | |
\(-\) 1 | 45.90 | 54.10 | 46.69 | 53.31 | 46.67 | 53.33 | 46.51 | 53.49 |
\(+\) 1 | 53.03 | 46.97 | 52.88 | 47.12 | 52.89 | 47.11 | 52.61 | 47.39 |
\(-\) 1, \(-\) 1 | 46.12 | 53.88 | 45.77 | 54.23 | 45.90 | 54.10 | 45.75 | 54.25 |
\(+\) 1, \(+\) 1 | 53.34 | 46.66 | 54.18 | 45.82 | 54.01 | 45.99 | 53.74 | 46.26 |
\(-\) 1, \(-\) 1, \(-\) 1 | 45.67 | 54.33 | 44.96 | 55.04 | 45.16 | 54.84 | 45.20 | 54.80 |
\(+\) 1, \(+\) 1, \(+\) 1 | 53.87 | 46.13 | 55.05 | 44.95 | 54.60 | 45.40 | 53.70 | 46.30 |
1 min | 5 min | 20 min | 60 min | |||||
---|---|---|---|---|---|---|---|---|
\(-\) 1 | \(+\) 1 | \(-\) 1 | \(+\) 1 | \(-\) 1 | \(+\) 1 | \(-\) 1 | \(+\) 1 | |
\(-\) 1 | 46.13 | 53.87 | 47.10 | 52.90 | 46.91 | 53.09 | 46.76 | 53.24 |
\(+\) 1 | 53.06 | 46.94 | 52.22 | 47.78 | 52.23 | 47.77 | 51.95 | 48.05 |
\(-\) 1, \(-\)1 | 45.97 | 54.03 | 45.69 | 54.31 | 45.69 | 54.31 | 45.60 | 54.40 |
\(+\) 1, \(+\) 1 | 53.86 | 46.14 | 53.85 | 46.15 | 53.73 | 46.27 | 52.71 | 47.29 |
\(-\) 1, \(-\) 1, \(-\) 1 | 45.12 | 54.88 | 44.37 | 55.63 | 44.60 | 55.40 | 44.39 | 55.61 |
\(+\) 1, \(+\) 1, \(+\) 1 | 54.80 | 45.20 | 55.44 | 44.56 | 54.90 | 45.10 | 54.10 | 45.90 |