# Intra-Day Trading System Design Based on the Integrated Model of Wavelet De-Noise and Genetic Programming

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## Abstract

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## 1. Introduction

## 2. Literature Review

#### 2.1. Technical Analysis

#### 2.2. Genetic Programming

#### 2.3. Applications of Wavelet in Financial Analysis

#### 2.4. Intra-Day Trading System

## 3. Methodology

#### 3.1. Wavelet and Wavelet De-Noise

#### 3.1.1. The Discrete Wavelet Transform

#### 3.1.2. Wavelet De-Noise

- Decomposition of the financial time series;
- Selection of the decomposed part based on wavelet coefficients;
- Reconstruction of the time series using the selected decomposed part of the original series. The dropped part of the original series is treated as noise that should be removed from this process.

#### 3.2. Generating Trading Rules with Genetic Programming

#### 3.2.1. Encoding of the Technical Indicators

- Functions:
- Arithmetic operators: +, −, *, /;
- Boolean operators: $and$, $or$, $not$;
- Relations operators: <, >;
- Boolean functions: if-then-else.
- Real functions (user defined functions, here are the technical indicators)

- Technical Indicators, Variable s Represents Constant Price:
- $Norm(r1,r2)$: absolute value of the difference between real number;
- $Avg(s,n)$: average of price over the past n periods;
- $EMA(s,n)$: exponential moving average of the past n periods;
- $Max(s,n)$: maximum value of price over the past n periods;
- $Min(s,n)$: minimum value of price over the past n periods;
- $Lag(s,n)$: price value lagged by n periods;
- $Volatility\left(n\right)$: variance in returns over the past n periods;
- $RSI\left(n\right)$: relative strength index;
- $ROC\left(n\right)$: rate of change.$$ROC\left(n\right)=(\frac{\mathit{closing}\mathit{price}\mathit{of}\mathit{the}\mathit{current}\mathit{minute}}{\mathit{closing}\mathit{price}\mathit{of}\mathit{n}\mathit{minutes}\mathit{ago}}-1)\times 100$$$RSI\left(n\right)=100-\left(\frac{100}{1+RS\left(n\right)}\right)$: $RS\left(n\right)=\frac{{\int}_{i\in {D}^{+\left(n\right)}}{r}_{i}}{-{\int}_{i\in {D}^{-\left(n\right)}}{r}_{i}}$, ${D}^{+}$ is the set of minutes with rising prices, ${D}^{-}$ is the set of minutes with falling prices and ${r}_{i}$ is the return of minute i, which is positive when the price is rising and negative otherwise.

- Terminals:
- Constants: chosen in the interval $[0,270]$, where 270 is the approximate number of minutes in a single trading day;
- Boolean: True, False;
- Others: Price
- Real variable: P price of the current minute;
- Order Types: Entry order and Exit order
- Entry order: Market Entry order: enter into the market at market price;
- Stop Entry order: these orders are placed above the market for a long entry and below the market for a short entry;
- Limit Entry order: these orders are placed below the market for a long entry and above the market for a short entry;
- Exit order: Exit at target profit, Exit at target percentage profit, Exit at Target price, Protective Stop, Trailing Stop, Exit after N Bars, Exit after N Bars profit, Exit after N Bars loss, Exit after certain time, Exit at Market, Exit End-of-Day.

#### 3.2.2. Fitness Evaluation Criteria

#### 3.2.3. Initialization of the Base Population

#### 3.2.4. Crossover, Mutation, Reproduction and Selection

#### 3.3. Design of the Experiment in This Paper

## 4. Empirical Experiment

#### 4.1. Parameter Settings

#### 4.2. Experiment Results

## 5. Conclusions and Future Work

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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Underlying Index | CSI 300 Index |
---|---|

Contract Multiplier | CNY 300 |

Unit | Index point |

Tick Size | 0.2 point |

Contract Months | Monthly: current month, next month, next two calendar quarters (four total) |

Trading Hours | 09:30 a.m.–11:30 a.m., 01:00 p.m.–03:00 p.m. |

Limit Up/Down | +/−10% of settlement price on the previous trading day |

Margin Requirement | 8% of the contract value |

Last Trading Day | Third Friday of the contract month, postponed to the next business day if it falls on a public holiday |

Delivery Day | Third Friday, same as “Last Trading Day” |

Settlement Method | Cash Settlement |

Transaction Code | IF |

Exchange | China Financial Futures Exchange |

Parameters | Value |
---|---|

Population size | 300 |

Number of generations | 30 |

Crossover percentage | 60% |

Mutation percentage | 50% |

Tree depth | 5 |

Tournament size | 5 |

Limit of entries per day | 8 |

Wait for exit before entering new trade | Yes |

Max bars looking back for Indicators | 30 |

Date | Out-of-Sample P/L${}^{1}$ | Out-of-Sample Cumulative P/L${}^{2}$ | Out-of-Sample P/L${}^{3}$ | Out-of-Sample Cumulative P/L${}^{4}$ | Out-of-Sample P/L${}^{5}$ | Out-of-Sample Cumulative P/L${}^{6}$ |
---|---|---|---|---|---|---|

29 Sep. 2014 | −960.00 | −960.00 | 300.00 | 300.00 | 360.00 | 360.00 |

30 Sep. 2014 | −1140.00 | −2100.00 | 2940.00 | 3240.00 | 900.00 | 1260.00 |

8 Oct. 2014 | 2100.00 | 0.00 | 420.00 | 3660.00 | 1380.00 | 2640.00 |

9 Oct. 2014 | 480.00 | 480.00 | −240.00 | 3420.00 | 1380.00 | 4020.00 |

10 Oct. 2014 | 6900.00 | 7380.00 | −600.00 | 2820.00 | −780.00 | 3240.00 |

13 Oct. 2014 | −840.00 | 6540.00 | 540.00 | 3360.00 | −720.00 | 2520.00 |

14 Oct. 2014 | 780.00 | 7320.00 | 1260.00 | 4620.00 | −60.00 | 2460.00 |

15 Oct. 2014 | 2100.00 | 9420.00 | 2160.00 | 6780.00 | −3780.00 | −1320.00 |

16 Oct. 2014 | −2640.00 | 6780.00 | −3600.00 | 3180.00 | −5160.00 | −6480.00 |

17 Oct. 2014 | 2640.00 | 9420.00 | −2460.00 | 720.00 | 1560.00 | −4920.00 |

20 Oct. 2014 | 960.00 | 10,380.00 | −540.00 | 180.00 | −2640.00 | −7560.00 |

21 Oct. 2014 | 0.00 | 10,380.00 | 4560.00 | 4740.00 | −2340.00 | −9900.00 |

22 Oct. 2014 | −5640.00 | 4740.00 | −5880.00 | −1140.00 | −5760.00 | −15,660.00 |

23 Oct. 2014 | 540.00 | 5280.00 | 840.00 | −300.00 | 2100.00 | −13,560.00 |

24 Oct. 2014 | 0.00 | 5280.00 | 1320.00 | 1020.00 | 2160.00 | −11,400.00 |

27 Oct. 2014 | −540.00 | 4740.00 | 420.00 | 1440.00 | 1980.00 | −9420.00 |

28 Oct. 2014 | −120.00 | 4620.00 | -360.00 | 1080.00 | −360.00 | −9780.00 |

29 Oct. 2014 | −1740.00 | 2880.00 | 600.00 | 1680.00 | 2580.00 | −7200.00 |

30 Oct. 2014 | −480.00 | 2400.00 | 300.00 | 1980.00 | −2940.00 | −10,140.00 |

31 Oct. 2014 | 3120.00 | 5520.00 | 13,260.00 | 15,240.00 | 9360.00 | −780.00 |

3 Nov. 2014 | −3060.00 | 2460.00 | −3480.00 | 11,760.00 | 4500.00 | 3720.00 |

Min | −5640 | −2100 | −5880 | −1140 | −5740 | −15,660 |

Max | 6900 | 10,380 | 13,260 | 15,240 | 9360 | 4020 |

Std | 2484 | NULL | 3619 | NULL | 3313 | NULL |

Date | Out-of-Sample Profit/Loss of Model Trained with Original Data | Out-of-Sample Profit/Loss of Model Trained with Hard Threshold De-Noised Data | Out-of-Sample Profit/Loss of Model Trained with Soft Threshold De-Noised Data |
---|---|---|---|

24 Oct.–3 Nov. 2014 | −37,320 | −34,140 | −22,260 |

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**MDPI and ACS Style**

Liu, H.; Ji, P.; Jin, J. Intra-Day Trading System Design Based on the Integrated Model of Wavelet De-Noise and Genetic Programming. *Entropy* **2016**, *18*, 435.
https://doi.org/10.3390/e18120435

**AMA Style**

Liu H, Ji P, Jin J. Intra-Day Trading System Design Based on the Integrated Model of Wavelet De-Noise and Genetic Programming. *Entropy*. 2016; 18(12):435.
https://doi.org/10.3390/e18120435

**Chicago/Turabian Style**

Liu, Hongguang, Ping Ji, and Jian Jin. 2016. "Intra-Day Trading System Design Based on the Integrated Model of Wavelet De-Noise and Genetic Programming" *Entropy* 18, no. 12: 435.
https://doi.org/10.3390/e18120435