# Reducing Exchange Rate Risks in International Trade: A Hybrid Forecasting Approach of CEEMDAN and Multilayer LSTM

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. EMD, EEMD, and CEEMDAN

- The number of extrema and the number of zero-crossings of IMF must be equal or not more than one difference.
- The mean of the upper envelope defined by the local maxima and the lower envelope formed by the local minima is zero.

- Find out all the maxima and minima of the original signal A, and fit the upper, lower envelopes and a mean line M(t) of the original data with three spline interpolation functions. The distribution of the three lines is shown in Figure 1.

- 2.
- Subtract the original data A from the mean M(t) of the envelopes. If the new data meets the IMF constraints, the data is the IMF.

- 3.
- The result of subtracting the original data from the IMF is the residue data. Using the residue data as the new data and repeating the above process, the next IMF can be obtained.$${R}_{K}(t)=X(t)-{\displaystyle \sum _{i=1}^{K}I}M{F}_{i}$$$${R}_{K+1}(t)={R}_{K}(t)-IM{F}_{K+1}$$

- Add the Gaussian white noise to the original data.
- The decomposition of EMD is performed to obtain the IMF components.
- Repeat steps 1 and 2, adding a new normal distribution white noise data each time.
- Integrating the obtained IMFs according to the order to get the mean, each component of EEMD can be obtained.

- Generate a particular white noise and add it to original signal: $[x(t)+{w}_{0}]$ Here $x(t)$ represent the original signal and ${w}_{0}$ is the first white noise of finite variance. Then, we extract all the IMFs from the new series by EMD. The mean of these IMFs is the first mode of CEEMDAN.$$\overline{im{f}_{1}}=\frac{1}{n}{\displaystyle \sum _{j=1}^{n}i}m{f}_{1}^{j}(t)$$

- 2.
- Calculate the first-order residue:

- 3.
- Decompose the residue to get the second-order IMF and calculate the second-order residue:

- 4.
- Decompose the k-th residue and extract the first mode, and the k-th mode can be obtained using the following equation (k = 2, 3, …K):

#### 2.2. RNN, LSTM, MRNN and MLSTM

#### 2.2.1. RNN

#### 2.2.2. LSTM

#### 2.2.3. CEEMDAN–MLSTM

- Decompose the original data into relatively simple IMFs by CEEMDAN.
- Input the IMFs into the multilayer LSTM neural network separately and predict each extracted IMF.
- Finally, sum up the IMF and residual of each training. Then, we get the expected prediction.

## 3. Experiment

#### 3.1. Data Preparing and Description

#### 3.2. Data Decomposition

#### 3.3. Building of MLSTM

#### 3.3.1. Loss

#### 3.3.2. Learning Rate

#### 3.3.3. Batch_size

#### 3.3.4. Optimizer

#### 3.3.5. Metrics

- MAE:

- 2.
- RMSE:

- 3.
- MAPE:

#### 3.3.6. Dependencies in MLSTM

#### 3.4. Experimental Results and Analysis

#### 3.4.1. Prediction and Analysis Based on Undecomposed Data

#### 3.4.2. Prediction and Analysis Based on Decomposition Data

- Decompose the three preprocessed identical exchange rate data by EMD, EEMD, and CEEMDAN methods to obtain three sets of different IMFs.
- Divide each group of IMFs into training set and test set, and input the training set into RNN, MRNN, LSTM, and MLSTM models for training.
- Enter the test data set and observation values into the trained deep learning model to obtain the final evaluation result.

#### 3.5. Discussion

#### 3.5.1. Performance of Different Step-Ahead Forecasts

#### 3.5.2. Impact of Different Lag Orders

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The diagram of the envelope: the original data in the thin black line, the upper and the lower envelopes in the dot-dashed lines, and their mean in the blue solid line.

**Figure 2.**Structure of recurrent neural network (RNN); X is current input; Y is the output of neural network; U, V, and W are parameters of the neural network; S is the neuron state of the hidden layer, which stores the memory of the neural network; The state S at time t is related to the current input X and the memory at time t−1. The formula is expressed as follows: The state S at time t is related to the current input X and the memory at time t−1. The formula is expressed as:${S}_{t}=f(U{X}_{t-1}+W{S}_{t-1})$

**Figure 5.**The architecture of complete ensemble empirical mode decomposition based multilayer LSTM(CEEMDAN–MLSTM).

**Figure 8.**The time–frequency spectrums of IMFs obtained by ensemble empirical mode decomposition(EEMD) and Complete EEMD with adaptive noise(CEEMDAN); (

**a**) the IMFs and residue of the USD–GBP exchange rate obtained by EEMD; (

**b**) the IMFs and residue of the USD–GBP exchange rate obtained by CEEMDAN.

Parameter | Description |
---|---|

spline_kind | Defines type of spline, which connects extrema |

nbsym | Number of extrema used in boundary mirroring |

max_imf | IMF number to which decomposition should be performed |

ensemble_size | Number of trials or EMD performance with added noise |

noise_strength | Standard deviation of the Gaussian random numbers used as additional noise. |

Method | nbsym | max_imf | trials | noise_width/epsilon |
---|---|---|---|---|

EMD | 2 | ALL | -- | -- |

EEMD | 2 | ALL | 100 | 0.05 |

CEEMDAN | 2 | ALL | 100 | 0.05 |

Model | Number of Hidden Layers | Number of Hidden Units | MAE | RMSE | MAPE(%) |
---|---|---|---|---|---|

ARIMA | - | - | 0.087 | 0.116 | 6.148 |

Bayesian | - | - | 0.034 | 0.038 | 2.327 |

SVM | - | - | 0.035 | 0.040 | 2.629 |

RNN | 1 | 200 | 0.032 | 0.036 | 2.598 |

MRNN | 2 | 200,200 | 0.023 | 0.025 | 1.836 |

LSTM | 1 | 200 | 0.020 | 0.021 | 1.614 |

MLSTM | 2 | 200,200 | 0.014 | 0.015 | 1.090 |

Model | Number of Hidden Layers | No. of Hidden Units | MAE | RMSE | MAPE |
---|---|---|---|---|---|

EMD-RNN | 1 | 200 | 0.017 | 0.023 | 0.01304 |

EMD-MRNN | 2 | 200,200 | 0.021 | 0.025 | 0.01590 |

EMD-LSTM | 1 | 200 | 0.020 | 0.024 | 0.01456 |

EMD-MLSTM | 2 | 200,200 | 0.012 | 0.015 | 0.00886 |

Model | Number of Hidden Layers | Number of Hidden Units | MAE | RMSE | MAPE |
---|---|---|---|---|---|

EEMD-RNN | 1 | 200 | 0.022 | 0.018 | 0.0136 |

EEMD-MRNN | 2 | 200,200 | 0.013 | 0.016 | 0.0095 |

EEMD-LSTM | 1 | 200 | 0.013 | 0.017 | 0.0101 |

EEMD-MLSTM | 2 | 200,200 | 0.010 | 0.013 | 0.0077 |

Model | Number of Hidden Layers | Number of Hidden Units | MAE | RMSE | MAPE |
---|---|---|---|---|---|

CEEMDAN-–RNN | 1 | 200 | 0.111 | 0.015 | 0.0083 |

CEEMDAN–MRNN | 2 | 200,200 | 0.012 | 0.016 | 0.0088 |

CEEMDAN–LSTM | 1 | 200 | 0.014 | 0.011 | 0.0091 |

CEEMDAN–MLSTM | 2 | 200,200 | 0.009 | 0.012 | 0.0064 |

MAE Horizon | Methods | |||
---|---|---|---|---|

CEEMDAN–MLSTM | CEEMDAN–LSTM | CEEMDAN–MRNN | CEEMDAN–RNN | |

One | 0.0096 | 0.0145 | 0.0124 | 0.1116 |

Two | 0.0124 | 0.0153 | 0.0161 | 0.0252 |

Three | 0.0203 | 0.0232 | 0.0306 | 0.0317 |

Four | 0.0406 | 0.0543 | 0.0589 | 0.0411 |

RMSEHorizon | CEEMDAN–MLSTM | CEEMDAN–LSTM | CEEMDAN–MRNN | CEEMDAN–RNN |

One | 0.0122 | 0.0157 | 0.0168 | 0.0157 |

Two | 0.0143 | 0.0183 | 0.0206 | 0.0241 |

Three | 0.0189 | 0.0259 | 0.0317 | 0.0345 |

Four | 0.0559 | 0.0625 | 0.0646 | 0.0759 |

MAPEHorizon | CEEMDAN–MLSTM | CEEMDAN–LSTM | CEEMDAN–MRNN | CEEMDAN–RNN |

One | 0.0064 | 0.0091 | 0.0088 | 0.0083 |

Two | 0.0109 | 0.0118 | 0.0133 | 0.0147 |

Three | 0.0347 | 0.0412 | 0.0462 | 0.0512 |

Four | 0.1056 | 0.1263 | 0.1502 | 0.1753 |

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**MDPI and ACS Style**

Lin, H.; Sun, Q.; Chen, S.-Q.
Reducing Exchange Rate Risks in International Trade: A Hybrid Forecasting Approach of CEEMDAN and Multilayer LSTM. *Sustainability* **2020**, *12*, 2451.
https://doi.org/10.3390/su12062451

**AMA Style**

Lin H, Sun Q, Chen S-Q.
Reducing Exchange Rate Risks in International Trade: A Hybrid Forecasting Approach of CEEMDAN and Multilayer LSTM. *Sustainability*. 2020; 12(6):2451.
https://doi.org/10.3390/su12062451

**Chicago/Turabian Style**

Lin, Hualing, Qiubi Sun, and Sheng-Qun Chen.
2020. "Reducing Exchange Rate Risks in International Trade: A Hybrid Forecasting Approach of CEEMDAN and Multilayer LSTM" *Sustainability* 12, no. 6: 2451.
https://doi.org/10.3390/su12062451