A Multifactor Fuzzy Time-Series Fitting Model for Forecasting the Stock Index
Abstract
:1. Introduction
2. Related Work
2.1. Fuzzy Time Series
2.2. The Causality between Price and Volume
3. Proposed Model
3.1. Proposed Computational Step
- (1)
- α represents the degree of influence of the F(t + 1) forecast from the market signals of trading volume and the actual stock index. Taiwan stock has is a volatility limitation of ±7%, whereas HSI has no such restriction; thus, to obtain accurate factors and better train the forecasting equation, we extend the range of α to between −0.15 and 0.15.
- (2)
- β represents the degree of influence of the F(t + 1) forecast based on the difference between the forecast stock index and the actual stock index. Moreover, given the volatility limitation of TAIEX (±7%) and the lack of a limit for the HSI stock, we plot the daily fluctuation of HSI as shown in Figure 2. From Figure 2, we see that the daily fluctuation is no greater than ±15%. Then, we can set the range of β from −0.15 to 0.15 to search for the optimal β.
- (3)
- γ represents the degree of influence of the F(t + 1) forecast from the daily difference of two stock indexes; the range of γ is [−1, 1], where −1 is an entire negative correlation, and 1 represents completely positive correlation.
Algorithm 1: Multifactor FTS model |
Input: double array , , , , , , and begin sum = 0 min RMSE = 999999999 // refer Equation (8) for i←−150 to 150 do for j←−150 to 150 do for k←−1000 to 1000 do for x←0 to length of factor1 do forecast train // refer Equation (7), and set α = , β = , and γ = square error sum = sum + square error end if (min RMSE > RMSE) best(i) = i best(j) = j best(k) = k min RMSE = RMSE end RMSE = 0 square error = 0 end end end Output: best i, best j, best k |
3.2. The Pseudocode of the Proposed Model
: | stock index for training in the i-th year; |
: | trading volume for training in the i-th year; |
: | interaction between two stock markets for training in the i-th year; |
: | closing price for training in the i-th year; |
: | next half-year stock index for testing in the i-th year; |
: | next half-year trading volume for testing in the i-th year; |
: | next half-year interaction between two stock markets for testing in the i-th year; |
: | next half-year closing price for testing in the i-th year. |
4. Verification and Comparison
5. Findings and Discussion
- (1)
- From the literature review, the selected attributes (trading volume, stock index, and interaction between two stock markets) have been proved to have an impact on the forecast of the stock market, and the results have a minimal RMSE, which will lead to a higher profits for investors.
- (2)
- Table 4 and Table 5 indicate that the TAIEX is less volatile than the HSI. This is because Taiwan limits the volatility of shares to ±7%, whereas Hong Kong has no limit. From Figure 2, the daily fluctuation of HSI can help us to set the search range for quickly obtaining the optimal parameters for α and β.
- (3)
- (4)
- From Table 2 and Table 3, the maximal parameter is β = 0.057 for TAIEX (1999/07~2000/06) and β = 0.065 for HSI (2000/01~2000/12). During this period (1999/07~2000/12), we searched “2000 crisis”. The results pertaining to the Dot-com bubble (2000–2002) and the year 2000 issues carry tremendous risks of disruption in the operations of financial institutions and in financial markets. Hence, we think that the “2000 crisis” has influenced the fluctuations of the stock market.
- (5)
- The comparative results (Table 4 and Table 5) and statistical test (Table 6) show that the proposed model outperforms other models in forecast accuracy (less RMSE) because the proposed linear multifactor forecasting equation with three optimized parameters (α, β, and γ) produces an optimal prediction to match past stock index patterns and generates a more accurate forecast.
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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TAIEX’s Rule for Consecutive Trading Day | FLR |
---|---|
8763.27 (t = 2000/03/17)→8536.05 (t + 1 = 2000/03/20) | B6 (t)→B5 (t + 1) |
8536.05 (t = 2000/03/20)→9004.48 (t + 1 = 2000/03/21) | B5 (t)→B6 (t + 1) |
9004.48 (t = 2000/03/21)→9069.39 (t + 1 = 2000/03/22) | B6 (t)→B6 (t + 1) |
9069.39 (t = 2000/03/22)→9533.87 (t + 1 = 2000/03/23) | B6 (t)→B7 (t + 1) |
Training | Testing | α | β | γ | RMSE |
---|---|---|---|---|---|
1997/01~1997/12 | 1998/01~1998/06 | −0.004 | 0.002 | 0.002 | 112 |
1997/07~1998/06 | 1998/07~1998/12 | −0.006 | 0.005 | 0.002 | 104 |
1998/01~1998/12 | 1999/01~1999/06 | −0.008 | −0.001 | 0.002 | 97 |
1998/07~1999/06 | 1999/07~1999/12 | −0.008 | 0.001 | 0.003 | 122 |
1999/01~1999/12 | 2000/01~2000/06 | −0.009 | 0.049 | 0.003 | 168 |
1999/07~2000/06 | 2000/07~2000/12 | 0.0 | 0.057 | −0.001 | 147 |
2000/01~2000/12 | 2001/01~2001/06 | −0.006 | −0.003 | −0.002 | 94 |
2000/07~2001/06 | 2001/07~2001/12 | −0.01 | 0.016 | −0.003 | 91 |
2001/01~2001/12 | 2002/01~2002/06 | −0.013 | −0.003 | 0.001 | 98 |
2001/07~2002/06 | 2002/07~2002/12 | −0.009 | 0.007 | 0.001 | 82 |
2002/01~2002/12 | 2003/01~2003/06 | −0.005 | 0.024 | 0.0 | 71 |
2002/07~2003/06 | 2003/07~2003/12 | −0.008 | −0.002 | 0.002 | 61 |
2003/01~2003/12 | 2004/01~2004/06 | −0.005 | −0.01 | 0.003 | 112 |
2003/07~2004/06 | 2004/07~2004/12 | −0.006 | −0.004 | 0.002 | 59 |
Training | Testing | α | β | γ | RMSE |
---|---|---|---|---|---|
1997/01~1997/12 | 1998/01~1998/06 | −0.013 | −0.021 | −0.001 | 226 |
1997/07~1998/06 | 1998/07~1998/12 | 0.0 | −0.07 | −0.003 | 228 |
1998/01~1998/12 | 1999/01~1999/06 | −0.019 | 0.024 | −0.001 | 192 |
1998/07~1999/06 | 1999/07~1999/12 | 0.0 | −0.014 | 0.002 | 208 |
1999/01~1999/12 | 2000/01~2000/06 | −0.013 | 0.017 | 0.0 | 329 |
1999/07~2000/06 | 2000/07~2000/12 | −0.014 | 0.041 | −0.001 | 238 |
2000/01~2000/12 | 2001/01~2001/06 | −0.016 | 0.065 | −0.001 | 217 |
2000/07~2001/06 | 2001/07~2001/12 | 0.0 | −0.015 | −0.001 | 199 |
2001/01~2001/12 | 2002/01~2002/06 | −0.01 | 0.013 | 0.0 | 116 |
2001/07~2002/06 | 2002/07~2002/12 | −0.009 | 0.012 | 0.0 | 119 |
2002/01~2002/12 | 2003/01~2003/06 | −0.008 | −0.003 | 0.0 | 88 |
2002/07~2003/06 | 2003/07~2003/12 | −0.009 | 0.017 | 0.001 | 115 |
2003/01~2003/12 | 2004/01~2004/06 | 0.0 | 0.006 | 0.001 | 153 |
2003/07~2004/06 | 2004/07~2004/12 | −0.01 | −0.017 | 0.0 | 106 |
Testing | RMSE | |||||
---|---|---|---|---|---|---|
[4] | [9] | [7] | SVR | GRNN | Proposed | |
1998/01~1998/06 | 209 | 139 | 207 | 275 | 1208 | 112 a |
1998/07~1998/12 | 339 | 160 | 361 | 393 | 1964 | 104 a |
1999/01~1999/06 | 324 | 211 | 352 | 897 | 2381 | 97 a |
1999/07~1999/12 | 195 | 162 | 205 | 919 | 1624 | 122 a |
2000/01~2000/06 | 404 | 231 | 496 | 469 | 2508 | 168 a |
2000/07~2000/12 | 319 | 293 | 563 | 742 | 4159 | 147 a |
2001/01~2001/06 | 245 | 418 | 368 | 468 | 2813 | 94 a |
2001/07~2001/12 | 368 | 823 | 536 | 441 | 2032 | 91 a |
2002/01~2002/06 | 215 | 264 | 186 | 657 | 1797 | 98 a |
2002/07~2002/12 | 155 | 237 | 157 | 672 | 2077 | 82 a |
2003/01~2003/06 | 160 | 150 | 157 | 159 | 1582 | 71 a |
2003/07~2003/12 | 150 | 459 | 246 | 733 | 1473 | 61 a |
2004/01~2004/06 | 188 | 534 | 314 | 360 | 1924 | 112 a |
2004/07~2004/12 | 106 | 166 | 96 | 392 | 1357 | 59 a |
Average | 241 | 303 | 303 | 541 | 2064 | 101a |
Testing | RMSE | |||||
---|---|---|---|---|---|---|
[4] | [9] | [7] | SVR | GRNN | Proposed | |
1998/01~1998/06 | 620 | 491 | 1506 | 591 | 10192 | 226 a |
1998/07~1998/12 | 434 | 294 | 776 | 251 | 3844 | 228 a |
1999/01~1999/06 | 415 | 327 | 1197 | 758 | 6546 | 192 a |
1999/07~1999/12 | 728 | 357 | 856 | 729 | 8309 | 208 a |
2000/01~2000/06 | 678 | 460 | 924 | 353 | 5975 | 329 a |
2000/07~2000/12 | 372 | 304 | 503 | 726 | 3703 | 238 a |
2001/01~2001/06 | 589 | 466 | 662 | 504 | 4422 | 217 a |
2001/07~2001/12 | 626 | 415 | 1099 | 994 | 9973 | 199 a |
2002/01~2002/06 | 318 | 172 | 402 | 230 | 2761 | 116 a |
2002/07~2002/12 | 232 | 192 | 225 | 496 | 3380 | 119 a |
2003/01~2003/06 | 261 | 157 | 284 | 433 | 2091 | 88 a |
2003/07~2003/12 | 325 | 256 | 329 | 509 | 7329 | 115 a |
2004/01~2004/06 | 376 | 212 | 596 | 393 | 7913 | 153 a |
2004/07~2004/12 | 313 | 159 | 262 | 119 | 2572 | 106 a |
Average | 449 | 304 | 687 | 506 | 5644 | 181a |
TAIEX | [4] | [9] | [7] | SVR | GRNN |
Proposed | + * | + * | + * | + * | + * |
GRNN | − * | − * | − * | − * | |
SVR | − * | − * | − * | ||
[7] | − * | + | |||
[9] | − * | ||||
HSI | [4] | [9] | [7] | SVR | GRNN |
Proposed | + * | + * | + * | + * | + * |
GRNN | − * | − * | − * | − * | |
SVR | − | − * | + | ||
[7] | − * | − * | |||
[9] | + |
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Tsai, M.-C.; Cheng, C.-H.; Tsai, M.-I. A Multifactor Fuzzy Time-Series Fitting Model for Forecasting the Stock Index. Symmetry 2019, 11, 1474. https://doi.org/10.3390/sym11121474
Tsai M-C, Cheng C-H, Tsai M-I. A Multifactor Fuzzy Time-Series Fitting Model for Forecasting the Stock Index. Symmetry. 2019; 11(12):1474. https://doi.org/10.3390/sym11121474
Chicago/Turabian StyleTsai, Ming-Chi, Ching-Hsue Cheng, and Meei-Ing Tsai. 2019. "A Multifactor Fuzzy Time-Series Fitting Model for Forecasting the Stock Index" Symmetry 11, no. 12: 1474. https://doi.org/10.3390/sym11121474
APA StyleTsai, M.-C., Cheng, C.-H., & Tsai, M.-I. (2019). A Multifactor Fuzzy Time-Series Fitting Model for Forecasting the Stock Index. Symmetry, 11(12), 1474. https://doi.org/10.3390/sym11121474