## 4 Experimental Results and Discussion
### Impact of Three New Parameters on Pairs Trading Strategy  
To observe their impacts on the pairs trading strategy, we adjusted the three new parameters: the correlation coefficient calculation days (_cDay_), the moving average calculation days (_mDay_), and the forward observation days (_oDay_). In the experiments, we adjusted one parameter at a time, while using the default values for the others. The default values for _cDay_, _mDay_, and _oDay_ were 10, 10 and 1, respectively, and the values of _cLimit_, _BBentryWidth_ and _BBoutWidth_ were set to \(-\)0.73, 2.3 and 1.5.  
The experiments made on the four datasets are shown below: (1) experiments on the four-year dataset, from 2009 to 2012, shown in Figure 7; (2) experiments on the three-year dataset, from 2010 to 2012, shown in Figure 8; (3) experiments on  
Figure 7 shows that when _cDay_ is set to 5 and 10, the profits of the pairs trading strategy yield a positive profit, with the best profit at 4.25%. When _cDay_ is set to 15 and 20, the pairs trading strategy yields a negative profit, with the worst profit at \(-18.42\%\) when _cDay_ is set to 20. For the parameter _mDay_, the pairs trading strategy yields positive profits when _mDay_ is set to 10 and 15. When _mDay_ is set to 5 and 20, it yields negative profits, with the worst profit at \(-7.69\%\) when _mDay_ is set to 5. The experimental results for parameter _oDay_ show that the best profit is 4.25% when _oDay_ is set to 1, and the profit becomes worse when _oDay_ increases. When _oDay_ is set to 3, the profit is negative. Hence, for long training periods, the suggested parameter setting is 10, 10 and 1 for _cDay_, _mDay_, and _oDay_.  
In Figure 8, when _cDay_ is set to 5, 10 and 15, the pairs trading strategy yields no profits, or negative profits, on the three-year dataset. When _cDay_ is set to 20, the profit is best at 3.1%. For parameter _mDay_, the pairs trading strategy yields the best profit at 27.38% when _mDay_ is set to 15. For parameter _oDay_, the profit increases with increases in _oDay_; the best profit at 2.97% when _oDay_ is set to 3. As a result, for the three-year training period, the suggested parameter setting is 20, 15 and 3 for _cDay_, _mDay_, and _oDay_.  
From Figure 9, we see that in the two-year dataset, the worst profit is \(-5.62\%\) when _cDay_ is set to 5. For parameter _mDay_, the best profit is 13.32% when _mDay_ is set to 13.32%, and the profit is 0, 1.25, and 3.61 when _mDay_ is set to 10, 15, and 20, respectively. For _oDay_, the profit increases while the set of _oDay_ becomes larger; the best profit is 4.83% when _oDay_ is set to 3. Hence, for the two-year training period, the suggested parameter setting is 5 and 3 for _mDay_ and _oDay_. For _cDay_, however, additional experiments are needed to determine a suitable setting.  
The results of Figure 10 are as follows. For parameter _cDay_, the best profit is 6.97% when it is set to 10. When _cDay_ is set to 5, 15, 20, the profits are around zero. For parameter _mDay_, the positive profits are 1.82%, 6.97%, and 3.41% when _mDay_ is set to 5, 10, and 15, respectively. In addition, the best profit is 6.97% when _oDay_ is set to 1, and the worst is \(-0.93\%\) when _oDay_ is set to 3. Thus, for short training periods, the suggested parameter setting is 10, 10, and 1 for _cDay_, _mDay_, and _oDay_.  
Figure 9: Profits of different parameter settings on two-year dataset (2011–2012).  
Notably, the results show that various parameter settings influence the profit of the pairs trading model. That is, determining suitable parameters for the pairs trading strategy is a difficult task and constitutes an optimization problem. We thus use AGBCPT to determine parameters that yield better performance for the pairs trading strategy.