Exchange Rate Forecasting with Advanced Machine Learning Methods
Abstract
:1. Introduction
- Q:
- Do fundamentals from the PPP, UIP or MM model have forecasting power with regard to exchange rate movements, regardless of the functional form of the estimation equation?
- Q1:
- Can complex ML methods with economic fundaments beat the RW predictions in forecasting exchange rate differentials?
- Q2:
- Can complex ML methods with economic fundaments beat the RW predictions in forecasting exchange rate movement directions?
2. Related Literature
3. Methodology
3.1. Uncovered Interest Rate Parity (UIP) Model
3.2. Purchasing Power Parity (PPP) Model
3.3. Monetary Model (MM)
3.4. Artificial Neural Networks (ANN)
3.5. EXtreme Gradient Boosting (XGboost)
4. Data
5. Results
6. Discussion
7. Conclusions
Funding
Conflicts of Interest
References
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XGBoost—Regression—With Time Dummies | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
All fundamentals | MM fundamentals | PPP fundamentals | UIP fundamentals | |||||||||
Currency pair | DM | p-value | Theil Ratio | DM | p-value | Theil Ratio | DM | p-value | Theil Ratio | DM | p-value | Theil Ratio |
PTE/USD | 2.8188 | 0.005 *** | 1.037 | −0.2974 | 0.7663 | 0.9966 | −1.4645 | 0.1436 | 0.9888 | −0.0099 | 0.9921 | 0.9999 |
AUD/USD | 0.3755 | 0.7074 | 1.0027 | 0.86 | 0.39 | 1.0066 | −0.4406 | 0.6596 | 0.997 | 0.5876 | 0.5569 | 1.0039 |
CAN/USD | 0.3755 | 0.7074 | 1.0027 | 0.86 | 0.39 | 1.0066 | −0.4406 | 0.6596 | 0.997 | 0.5876 | 0.5569 | 1.0039 |
CHF/USD | 0.3755 | 0.7074 | 1.0027 | 0.86 | 0.39 | 1.0066 | −0.4406 | 0.6596 | 0.997 | 0.5876 | 0.5569 | 1.0039 |
DEM/USD | 2.0298 | 0.0427 ** | 1.0144 | 0.3154 | 0.7526 | 1.0025 | 1.7917 | 0.0735 * | 1.0114 | 0.7116 | 0.4769 | 1.0045 |
DNK/USD | 0.3176 | 0.7509 | 1.0024 | 0.3046 | 0.7607 | 1.0025 | 0.6475 | 0.5175 | 1.0036 | −0.3226 | 0.7471 | 0.9981 |
FRF/USD | 5.4862 | 0.0000 *** | 1.0465 | 2.7878 | 0.0054 * | 1.0292 | 1.9342 | 0.0534 * | 1.0139 | 2.5725 | 0.0103 *** | 1.0247 |
ITL/USD | 2.0298 | 0.0427 ** | 1.0144 | 0.3154 | 0.7526 | 1.0025 | 1.7917 | 0.0735 * | 1.0114 | 0.7116 | 0.4769 | 1.0045 |
JPY/USD | 0.3755 | 0.7074 | 1.0027 | 0.86 | 0.39 | 1.0066 | −0.4406 | 0.6596 | 0.997 | 0.5876 | 0.5569 | 1.0039 |
SEK/USD | 0.3755 | 0.7074 | 1.0027 | 0.86 | 0.39 | 1.0066 | −0.4406 | 0.6596 | 0.997 | 0.5876 | 0.5569 | 1.0039 |
XGBoost—Regression—No Time Dummies | ||||||||||||
All fundamentals | MM fundamentals | PPP fundamentals | UIP fundamentals | |||||||||
Currency pair | DM | p-value | Theil Ratio | DM | p-value | Theil Ratio | DM | p-value | Theil Ratio | DM | p-value | Theil Ratio |
PTE/USD | 2.8006 | 0.0053 ** | 1.0503 | 1.7965 | 0.0729 * | 1.0194 | 1.7516 | 0.0804 * | 1.0218 | 1.3372 | 0.1817 | 1.0216 |
AUD/USD | 0.5369 | 0.5914 | 1.005 | 2.0364 | 0.042 ** | 1.0162 | 2.231 | 0.0259 ** | 1.018 | 1.5522 | 0.1209 | 1.0092 |
CAN/USD | 0.5369 | 0.5914 | 1.005 | 2.0364 | 0.042 ** | 1.0162 | 2.231 | 0.0259 ** | 1.018 | 1.5522 | 0.1209 | 1.0092 |
CHF/USD | 0.5369 | 0.5914 | 1.005 | 2.0364 | 0.042 ** | 1.0162 | 2.231 | 0.0259 ** | 1.018 | 1.5522 | 0.1209 | 1.0092 |
DEM/USD | 2.7782 | 0.0056 * | 1.027 | 1.7247 | 0.0849 ** | 1.013 | 2.3919 | 0.017 ** | 1.0234 | 0.8883 | 0.3746 | 1.0059 |
DNK/USD | 1.6858 | 0.0922 * | 1.0198 | 3.3895 | 0.0007 *** | 1.0262 | 3.2347 | 0.0013 *** | 1.0233 | 1.9187 | 0.0553 | 1.0131 |
FRF/USD | 2.7165 | 0.0067 * | 1.0342 | 2.0077 | 0.045 ** | 1.0209 | 3.4899 | 0.0005 *** | 1.0451 | 0.5599 | 0.5757 | 1.0053 |
ITL/USD | 2.7782 | 0.0056 * | 1.027 | 1.7247 | 0.0849 * | 1.013 | 2.3919 | 0.017 ** | 1.0234 | 0.8883 | 0.3746 | 1.0059 |
JPY/USD | 0.5369 | 0.5914 | 1.005 | 2.0364 | 0.042 ** | 1.0162 | 2.231 | 0.0259 ** | 1.018 | 1.5522 | 0.1209 | 1.0092 |
SEK/USD | 0.5369 | 0.5914 | 1.005 | 2.0364 | 0.042 ** | 1.0162 | 2.231 | 0.0259 ** | 1.018 | 1.5522 | 0.1209 | 1.0092 |
ANN—Regression—With Time Dummies | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
All fundamentals | MM fundamentals | PPP fundamentals | UIP fundamentals | |||||||||
Currency pair | DM | p-value | Theil Ratio | DM | p-value | Theil Ratio | DM | p-value | Theil Ratio | DM | p-value | Theil Ratio |
PTE/USD | 2.0587 | 0.04 ** | 1.0472 | 2.3238 | 0.0205 ** | 1.0663 | 2.3042 | 0.0216 ** | 1.0507 | 1.905 | 0.0573 * | 1.0378 |
AUD/USD | −0.4744 | 0.6353 | 0.995 | 0.3059 | 0.7598 | 1.0023 | −1.2247 | 0.221 | 0.9966 | −0.3437 | 0.7312 | 0.9984 |
CAN/USD | −1.5079 | 0.1319 | 0.9887 | −0.8013 | 0.4231 | 0.998 | −1.1149 | 0.2652 | 0.9931 | 0.2258 | 0.8214 | 1.0033 |
CHF/USD | −0.6049 | 0.5454 | 1.0074 | −0.3143 | 0.7533 | 1.0031 | −0.6113 | 0.5411 | 0.995 | −0.5662 | 0.5714 | 0.9974 |
DEM/USD | 4.544 | 0.0000 *** | 1.0469 | 4.1126 | 0.0000 *** | 1.0447 | 5.3071 | 0.0000 *** | 1.0435 | 3.783 | 0.0002 *** | 1.027 |
DNK/USD | −1.3697 | 0.1711 | 0.9945 | −0.1012 | 0.9194 | 1.0107 | −0.2069 | 0.8361 | 1.0101 | 0.5283 | 0.5974 | 1.0122 |
FRF/USD | 5.895 | 0.0000 *** | 1.1146 | 6.4874 | 0.0000 *** | 1.0893 | 4.816 | 0.0000 *** | 1.0641 | 5.0974 | 0.0000 *** | 1.0781 |
ITL/USD | 4.9056 | 0.0000 *** | 1.0452 | 4.6223 | 0.0000 *** | 1.0659 | 5.0842 | 0.0000 *** | 1.0547 | 4.112 | 0.0000 *** | 1.0385 |
JPY/USD | 1.4623 | 0.144 | 1.0208 | −1.3256 | 0.1853 | 0.9942 | −1.4138 | 0.1577 | 0.9963 | −0.3669 | 0.7138 | 1.0038 |
SEK/USD | −1.1639 | 0.2448 | 0.9982 | −0.9254 | 0.355 | 0.9967 | 0.0905 | 0.9279 | 1.0082 | 0.1046 | 0.9167 | 1.0017 |
ANN—Regression—No Time Dummies | ||||||||||||
All fundamentals | MM fundamentals | PPP fundamentals | UIP fundamentals | |||||||||
Currency pair | DM | p-value | Theil Ratio | DM | p-value | Theil Ratio | DM | p-value | Theil Ratio | DM | p-value | Theil Ratio |
PTE/USD | 2.8867 | 0.004 *** | 1.0027 | 0.2556 | 0.7983 | 0.9958 | 0.7651 | 0.4445 | 0.9969 | −0.2006 | 0.8411 | 0.9947 |
AUD/USD | 1.529 | 0.1266 | 1.0026 | 1.3829 | 0.167 | 0.9988 | 1.0547 | 0.2918 | 0.9976 | 1.1906 | 0.2341 | 0.9984 |
CAN/USD | 0.1696 | 0.8654 | 0.9989 | 1.5529 | 0.1208 | 0.9994 | 2.0126 | 0.0444 ** | 1.0009 | 2.6056 | 0.0093 *** | 1.0043 |
CHF/USD | 1.7308 | 0.0838 | 1.002 | 2.3972 | 0.0167 ** | 1.0029 | 2.6225 | 0.0089 *** | 1.0026 | 2.484 | 0.0132 ** | 1.0021 |
DEM/USD | −1.434 | 0.1519 | 1.0001 | −2.4894 | 0.013 ** | 0.995 | −1.1249 | 0.2609 | 1.0028 | −1.4956 | 0.1351 | 0.9967 |
DNK/USD | 0.0051 | 0.9959 | 0.9977 | 0.498 | 0.6186 | 0.9972 | 2.7943 | 0.0053 *** | 1.0046 | 2.1206 | 0.0342 ** | 1.0005 |
FRF/USD | −1.3868 | 0.1659 | 0.9982 | −1.3869 | 0.1659 | 0.9957 | −1.1267 | 0.2602 | 0.9985 | −1.5057 | 0.1325 | 0.9978 |
ITL/USD | −1.4885 | 0.137 | 0.9972 | −1.7542 | 0.0797 | 0.9959 | −1.2554 | 0.2096 | 0.9977 | −1.7742 | 0.0763 * | 0.9977 |
JPY/USD | 1.4867 | 0.1374 | 1.001 | 1.8733 | 0.0613 | 1.0002 | 1.3946 | 0.1634 | 0.9988 | 2.7358 | 0.0063 *** | 1.0027 |
SEK/USD | 2.2396 | 0.0253 ** | 1.0039 | 3.186 | 0.0015 ** | 1.0079 | 1.8933 | 0.0586 * | 0.9995 | 1.7569 | 0.0792 * | 1.0001 |
XGBoost—Classification—With Time Dummies | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
All fundamentals | MM fundamentals | PPP fundamentals | UIP fundamentals | |||||||||
Currency pair | DM | p-value | CE | DM | p-value | CE | DM | p-value | CE | DM | p-value | CE |
PTE/USD | −2.4682 | 0.0139 ** | 0.4497 | −1.5584 | 0.1197 | 0.4681 | −1.5584 | 0.1197 | 0.4681 | −1.1472 | 0.2517 | 0.4765 |
AUD/USD | −0.6406 | 0.5219 | 0.4897 | −1.2821 | 0.2001 | 0.4795 | −1.2821 | 0.2001 | 0.4795 | −0.2562 | 0.7978 | 0.4959 |
CAN/USD | −0.6406 | 0.5219 | 0.4897 | −1.2821 | 0.2001 | 0.4795 | −1.2821 | 0.2001 | 0.4795 | −0.2562 | 0.7978 | 0.4959 |
CHF/USD | −0.6406 | 0.5219 | 0.4897 | −1.2821 | 0.2001 | 0.4795 | −1.2821 | 0.2001 | 0.4795 | −0.2562 | 0.7978 | 0.4959 |
DEM/USD | −1.2293 | 0.2192 | 0.4801 | −1.0998 | 0.2717 | 0.4822 | −1.4887 | 0.1369 | 0.4759 | −1.0998 | 0.2717 | 0.4822 |
DNK/USD | −1.2657 | 0.206 | 0.4789 | −0.9322 | 0.3515 | 0.4845 | −1.3324 | 0.1831 | 0.4778 | −0.9989 | 0.3181 | 0.4834 |
FRF/USD | −0.6915 | 0.4894 | 0.488 | −0.6223 | 0.5339 | 0.4892 | −0.8299 | 0.4068 | 0.4856 | −1.1762 | 0.2399 | 0.4797 |
ITL/USD | −1.2293 | 0.2192 | 0.4801 | −1.0998 | 0.2717 | 0.4822 | −1.4887 | 0.1369 | 0.4759 | −1.0998 | 0.2717 | 0.4822 |
JPY/USD | −0.6406 | 0.5219 | 0.4897 | −1.2821 | 0.2001 | 0.4795 | −1.2821 | 0.2001 | 0.4795 | −0.2562 | 0.7978 | 0.4959 |
SEK/USD | −0.6406 | 0.5219 | 0.4897 | −1.2821 | 0.2001 | 0.4795 | −1.2821 | 0.2001 | 0.4795 | −0.2562 | 0.7978 | 0.4959 |
XGBoost—Classification- No Time Dummies | ||||||||||||
All fundamentals | MM fundamentals | PPP fundamentals | UIP fundamentals | |||||||||
Currency pair | DM | p-value | CE | DM | p-value | CE | DM | p-value | CE | DM | p-value | CE |
PTE/USD | −0.0819 | 0.9348 | 0.4983 | −3.981 | 0.0001 *** | 0.4195 | −3.981 | 0.0001 *** | 0.4195 | −0.737 | 0.4614 | 0.4849 |
AUD/USD | −0.2562 | 0.7978 | 0.4959 | 0.1922 | 0.8477 | 0.5031 | −0.3203 | 0.7488 | 0.4949 | −1.4106 | 0.1587 | 0.4774 |
CAN/USD | −0.2562 | 0.7978 | 0.4959 | 0.1922 | 0.8477 | 0.5031 | −0.3203 | 0.7488 | 0.4949 | −1.4106 | 0.1587 | 0.4774 |
CHF/USD | −0.2562 | 0.7978 | 0.4959 | 0.1922 | 0.8477 | 0.5031 | −0.3203 | 0.7488 | 0.4949 | −1.4106 | 0.1587 | 0.4774 |
DEM/USD | −1.4887 | 0.1369 | 0.4759 | −1.4238 | 0.1548 | 0.477 | −1.4238 | 0.1548 | 0.477 | −0.3233 | 0.7466 | 0.4948 |
DNK/USD | −0.5991 | 0.5492 | 0.49 | 0.1331 | 0.8941 | 0.5022 | −1.0656 | 0.2869 | 0.4823 | −0.7323 | 0.4642 | 0.4878 |
FRF/USD | −1.1762 | 0.2399 | 0.4797 | −1.94 | 0.0527 * | 0.4665 | −1.94 | 0.0527 * | 0.4665 | 0.6915 | 0.4894 | 0.512 |
ITL/USD | −1.4887 | 0.1369 | 0.4759 | −1.4238 | 0.1548 | 0.477 | −1.4238 | 0.1548 | 0.477 | −0.3233 | 0.7466 | 0.4948 |
JPY/USD | −0.2562 | 0.7978 | 0.4959 | 0.1922 | 0.8477 | 0.5031 | −0.3203 | 0.7488 | 0.4949 | −1.4106 | 0.1587 | 0.4774 |
SEK/USD | −0.2562 | 0.7978 | 0.4959 | 0.1922 | 0.8477 | 0.5031 | −0.3203 | 0.7488 | 0.4949 | −1.4106 | 0.1587 | 0.4774 |
ANN—Classification—With Time Dummies | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
All fundamentals | MM fundamentals | PPP fundamentals | UIP fundamentals | |||||||||
Currency pair | DM | p-value | CE | DM | p-value | CE | DM | p-value | CE | DM | p-value | CE |
PTE/USD | −1.8057 | 0.0715 * | 0.4631 | −0.819 | 0.4131 | 0.4832 | −1.3116 | 0.1902 | 0.4732 | −2.7179 | 0.0068 *** | 0.4446 |
AUD/USD | −3.0245 | 0.0026 *** | 0.4517 | −3.0895 | 0.0021 *** | 0.4507 | −2.8298 | 0.0048 *** | 0.4548 | −3.1545 | 0.0017 *** | 0.4497 |
CAN/USD | −4.5968 | 0.0000 *** | 0.4271 | −4.4646 | 0.0000 *** | 0.4292 | −3.3498 | 0.0008 *** | 0.4466 | −3.2847 | 0.0011 *** | 0.4476 |
CHF/USD | −4.0694 | 0.0001 *** | 0.4353 | −3.9381 | 0.0001 *** | 0.4374 | −2.0541 | 0.0402 ** | 0.4671 | −3.1545 | 0.0017 *** | 0.4497 |
DEM/USD | 0.1293 | 0.8971 | 0.5021 | −1.1645 | 0.2445 | 0.4812 | −1.1645 | 0.2445 | 0.4812 | −0.3879 | 0.6982 | 0.4937 |
DNK/USD | −3.6881 | 0.0002 *** | 0.439 | −3.8243 | 0.0001 *** | 0.4368 | −2.5381 | 0.0113 ** | 0.4579 | −3.2129 | 0.0014 *** | 0.4468 |
FRF/USD | −1.1069 | 0.2687 | 0.4809 | 0.6223 | 0.5339 | 0.5108 | 0.4148 | 0.6784 | 0.5072 | −0.2765 | 0.7822 | 0.4952 |
ITL/USD | 0.0647 | 0.9485 | 0.501 | 0.194 | 0.8463 | 0.5031 | 0.0647 | 0.9485 | 0.501 | −1.2293 | 0.2192 | 0.4801 |
JPY/USD | −4.5306 | 0.0000 *** | 0.4281 | −3.2196 | 0.0013 *** | 0.4487 | −3.9381 | 0.0001 *** | 0.4374 | −4.1351 | 0.0000 *** | 0.4343 |
SEK/USD | −1.7964 | 0.0727 * | 0.4713 | −3.0895 | 0.0021 *** | 0.4507 | −3.2196 | 0.0013 *** | 0.4487 | −2.7002 | 0.007 *** | 0.4569 |
ANN—Classification—No Time Dummies | ||||||||||||
All fundamentals | MM fundamentals | PPP fundamentals | UIP fundamentals | |||||||||
Currency pair | DM | p-value | CE | DM | p-value | CE | DM | p-value | CE | DM | p-value | CE |
PTE/USD | 0.6551 | 0.5127 | 0.5134 | 0.1637 | 0.87 | 0.5034 | 0.0819 | 0.9348 | 0.5017 | 0.5731 | 0.5668 | 0.5117 |
AUD/USD | 1.9896 | 0.0469 ** | 0.5318 | 1.9896 | 0.0469 ** | 0.5318 | 1.3463 | 0.1785 | 0.5216 | 2.1831 | 0.0293 ** | 0.5349 |
CAN/USD | 1.6677 | 0.0957 * | 0.5267 | 1.732 | 0.0836 * | 0.5277 | 1.732 | 0.0836 * | 0.5277 | 2.3122 | 0.021 ** | 0.537 |
CHF/USD | 1.732 | 0.0836 * | 0.5277 | 1.6034 | 0.1092 | 0.5257 | 2.3122 | 0.021 ** | 0.537 | 2.3122 | 0.021 ** | 0.537 |
DEM/USD | 0.0000 *** | 1.0 | 0.50 | −0.6466 | 0.518 | 0.4895 | −0.6466 | 0.518 | 0.4895 | −0.0647 | 0.9485 | 0.499 |
DNK/USD | 1.5996 | 0.11 | 0.5266 | 1.7333 | 0.0834 * | 0.5288 | 2.4037 | 0.0164 ** | 0.5399 | 2.875 | 0.0041 *** | 0.5477 |
FRF/USD | −0.3457 | 0.7297 | 0.494 | −1.5924 | 0.1117 | 0.4725 | −0.1383 | 0.8901 | 0.4976 | −0.2765 | 0.7822 | 0.4952 |
ITL/USD | −0.0647 | 0.9485 | 0.499 | −1.6834 | 0.0926 * | 0.4728 | −0.1293 | 0.8971 | 0.4979 | −0.0647 | 0.9485 | 0.499 |
JPY/USD | 1.732 | 0.0836 * | 0.5277 | 1.8608 | 0.0631 * | 0.5298 | 2.3122 | 0.021 ** | 0.537 | 1.9252 | 0.0545 * | 0.5308 |
SEK/USD | 1.9896 | 0.0469 ** | 0.5318 | 1.732 | 0.0836 * | 0.5277 | 2.1186 | 0.0344 ** | 0.5339 | 1.9896 | 0.0469 ** | 0.5318 |
XGBoost Regression | XGBoost Classification | |||||
---|---|---|---|---|---|---|
Currency pair | DM | p-value | Theil Ratio | DM | p-value | CE |
PTE/USD | −0.664 | 0.5069 | 0.9939 | −2.4682 | 0.0139 ** | 0.5503 |
AUD/USD | 0.5155 | 0.6063 | 1.0032 | −1.0254 | 0.3054 | 0.5164 |
CAN/USD | 0.5155 | 0.6063 | 1.0032 | −1.0254 | 0.3054 | 0.5164 |
CHF/USD | 0.5155 | 0.6063 | 1.0032 | −1.0254 | 0.3054 | 0.5164 |
DEM/USD | 1.1951 | 0.2323 | 1.0062 | −1.0998 | 0.2717 | 0.5178 |
DNK/USD | 0.9425 | 0.3462 | 1.006 | −1.7333 | 0.0834 * | 0.5288 |
FRF/USD | 1.4999 | 0.134 | 1.0099 | −1.1762 | 0.2399 | 0.5203 |
ITL/USD | 1.1951 | 0.2323 | 1.0062 | −1.0998 | 0.2717 | 0.5178 |
JPY/USD | 0.5155 | 0.6063 | 1.0032 | −1.0254 | 0.3054 | 0.5164 |
SEK/USD | 0.5155 | 0.6063 | 1.0032 | −1.0254 | 0.3054 | 0.5164 |
ANN Regression | ANN Classification | |||||
Currency pair | DM | p-value | Theil Ratio | DM | p-value | CE |
PTE/USD | 1.6533 | 0.0988 * | 1.0365 | 0.0000 | 1.0000 | 0.5000 |
AUD/USD | 0.7242 | 0.4691 | 1.0174 | −3.5455 | 0.0004 *** | 0.4435 |
CAN/USD | 0.2173 | 0.828 | 1.0104 | −2.1831 | 0.0293 ** | 0.4651 |
CHF/USD | 0.8895 | 0.3739 | 1.0139 | −3.2196 | 0.0013 ** | 0.4487 |
DEM/USD | 4.0828 | 0.0000 *** | 1.0302 | 0.0000 | 1.0000 | 0.5000 |
DNK/USD | 1.2517 | 0.211 | 1.0219 | −2.4037 | 0.0164 ** | 0.4601 |
FRF/USD | 5.234 | 0.0000 *** | 1.0734 | 0.0691 | 0.9449 | 0.5012 |
ITL/USD | 4.3449 | 0.0000 *** | 1.0398 | −0.1293 | 0.8971 | 0.4979 |
JPY/USD | −0.4738 | 0.6357 | 1.0067 | −3.415 | 0.0007 *** | 0.4456 |
SEK/USD | −0.3102 | 0.7565 | 1.0019 | −3.7416 | 0.0002 *** | 0.4405 |
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Pfahler, J.F. Exchange Rate Forecasting with Advanced Machine Learning Methods. J. Risk Financial Manag. 2022, 15, 2. https://doi.org/10.3390/jrfm15010002
Pfahler JF. Exchange Rate Forecasting with Advanced Machine Learning Methods. Journal of Risk and Financial Management. 2022; 15(1):2. https://doi.org/10.3390/jrfm15010002
Chicago/Turabian StylePfahler, Jonathan Felix. 2022. "Exchange Rate Forecasting with Advanced Machine Learning Methods" Journal of Risk and Financial Management 15, no. 1: 2. https://doi.org/10.3390/jrfm15010002