A Forecasting Model Based on High-Order Fluctuation Trends and Information Entropy
Abstract
:1. Introduction
2. Preliminaries
2.1. Fuzzy Set (FS)
2.2. Fuzzy Time Series (FTS)
2.3. Fuzzy-Fluctuation Time Series (FFTS)
2.4. Information Entropy
2.5. Neutrosophic Set (NS)
2.6. Neutrosophic Logical Relationship (NLR)
2.7. Deneutrosophication of a Neutrosphic Set
3. Proposed Model Based on High-Order Fluctuation Trends and Information Entropy
4. Empirical Analysis
4.1. Forecasting Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX)
4.2. Forecasting Hong Kong Heng Seng Index (HIS)
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Date (DD/MM/YYYY) | Actual | Forecast | (Forecast − Actual)2 | Date (DD/MM/YYYY) | Actual | Forecast | (Forecast − Actual)2 |
---|---|---|---|---|---|---|---|
1/11/1999 | 7814.89 | 7867.09 | 2724.84 | 1/12/1999 | 7766.20 | 7723.08 | 1859.33 |
2/11/1999 | 7721.59 | 7826.66 | 11,039.54 | 2/12/1999 | 7806.26 | 7768.72 | 1408.89 |
3/11/1999 | 7580.09 | 7723.14 | 20,462.00 | 3/12/1999 | 7933.17 | 7807.11 | 15,891.12 |
4/11/1999 | 7469.23 | 7577.85 | 11,798.99 | 4/12/1999 | 7964.49 | 7932.85 | 1001.33 |
5/11/1999 | 7488.26 | 7466.21 | 486.03 | 6/12/1999 | 7894.46 | 7964.17 | 4859.38 |
6/11/1999 | 7376.56 | 7485.29 | 11,822.59 | 7/12/1999 | 7827.05 | 7893.82 | 4458.83 |
8/11/1999 | 7401.49 | 7370.82 | 940.50 | 8/12/1999 | 7811.02 | 7825.78 | 217.71 |
9/11/1999 | 7362.69 | 7395.82 | 1097.82 | 9/12/1999 | 7738.84 | 7810.16 | 5086.43 |
10/11/1999 | 7401.81 | 7357.09 | 1999.66 | 10/12/1999 | 7733.77 | 7736.72 | 8.67 |
11/11/1999 | 7532.22 | 7404.90 | 16,210.15 | 13/12/1999 | 7883.61 | 7734.83 | 22,134.74 |
15/11/1999 | 7545.03 | 7526.69 | 336.36 | 14/12/1999 | 7850.14 | 7882.73 | 1062.35 |
16/11/1999 | 7606.20 | 7541.78 | 4149.94 | 15/12/1999 | 7859.89 | 7849.27 | 112.73 |
17/11/1999 | 7645.78 | 7606.20 | 1566.58 | 16/12/1999 | 7739.76 | 7868.73 | 16,633.26 |
18/11/1999 | 7718.06 | 7653.40 | 4180.83 | 17/12/1999 | 7723.22 | 7747.76 | 602.21 |
19/11/1999 | 7770.81 | 7719.84 | 2598.34 | 18/12/1999 | 7797.87 | 7730.15 | 4586.55 |
20/11/1999 | 7900.34 | 7784.54 | 13,409.46 | 20/12/1999 | 7782.94 | 7799.05 | 259.55 |
22/11/1999 | 8052.31 | 7919.68 | 17,589.44 | 21/12/1999 | 7934.26 | 7784.10 | 22,546.71 |
23/11/1999 | 8046.19 | 8058.99 | 163.80 | 22/12/1999 | 8002.76 | 7938.25 | 4161.84 |
24/11/1999 | 7921.85 | 8052.64 | 17,105.57 | 23/12/1999 | 8083.49 | 8002.58 | 6546.57 |
25/11/1999 | 7904.53 | 7925.99 | 460.58 | 24/12/1999 | 8219.45 | 8084.73 | 18,148.43 |
26/11/1999 | 7595.44 | 7908.62 | 98,080.84 | 27/12/1999 | 8415.07 | 8224.42 | 36,348.84 |
29/11/1999 | 7823.90 | 7597.74 | 51,147.40 | 28/12/1999 | 8448.84 | 8418.62 | 913.11 |
30/11/1999 | 7720.87 | 7823.13 | 10,456.55 | Root Mean Square Error(RMSE) | 102.05 |
m | |||||||||
---|---|---|---|---|---|---|---|---|---|
6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | |
RMSE | 102.76 | 102.52 | 102.2 | 102.05 | 102.61 | 102.89 | 102.9 | 102.88 | 103.4 |
Method | RMSE | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | Average | |
Chen and Chang [36] | N | N | 123.64 | 131.1 | 115.08 | 73.06 | 66.36 | 60.48 | N | 94.95 |
Chen and Chen [37] | 140.86 | 144.13 | 119.32 | 129.87 | 123.12 | 71.01 | 65.14 | 61.94 | N | 106.92 |
Chen et al. [38] | 138.41 | 113.88 | 102.34 | 131.25 | 113.62 | 65.77 | 52.23 | 56.16 | N | 96.71 |
Cheng et al. [39] | N | N | 100.74 | 125.62 | 113.04 | 62.94 | 51.46 | 54.24 | N | 84.67 |
Guan et al. [40] | 141.89 | 119.85 | 99.03 | 128.62 | 125.64 | 66.29 | 53.2 | 56.11 | 55.83 | 94.05 |
Cheng et al. [41] | N | 120.8 | 110.7 | 150.6 | 113.2 | 66.0 | 53.1 | 58.6 | 53.5 | 102.4 |
Our model | 140.33 | 114.35 | 102.05 | 129.97 | 113.32 | 66.26 | 54.66 | 55.19 | 53.33 | 92.16 |
Method | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | Average |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Yu [42] | 291.4 | 469.6 | 297.05 | 316.85 | 123.7 | 186.16 | 264.34 | 112.4 | 252.44 | 912.67 | 684.9 | 442.64 | 382.06 | 419.67 | 239.11 | 359.66 |
Wan et al. [43] | 326.62 | 637.1 | 356.7 | 299.43 | 155.09 | 226.38 | 239.63 | 147.2 | 466.24 | 1847.8 | 2179 | 437.24 | 445.41 | 688.04 | 477.34 | 595.26 |
Ren et al. [44] | 296.67 | 761.9 | 356.81 | 254.07 | 155.4 | 199.58 | 540.19 | 1127 | 407.89 | 1028.7 | 593.8 | 435.18 | 718.33 | 578.7 | 442.44 | 526.46 |
Our model | 200.72 | 224.81 | 254.56 | 158.88 | 105.53 | 122.99 | 104.51 | 103.66 | 177.49 | 686.79 | 466.81 | 311.76 | 273.49 | 348.57 | 182.85 | 248.23 |
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Guan, H.; Dai, Z.; Guan, S.; Zhao, A. A Forecasting Model Based on High-Order Fluctuation Trends and Information Entropy. Entropy 2018, 20, 669. https://doi.org/10.3390/e20090669
Guan H, Dai Z, Guan S, Zhao A. A Forecasting Model Based on High-Order Fluctuation Trends and Information Entropy. Entropy. 2018; 20(9):669. https://doi.org/10.3390/e20090669
Chicago/Turabian StyleGuan, Hongjun, Zongli Dai, Shuang Guan, and Aiwu Zhao. 2018. "A Forecasting Model Based on High-Order Fluctuation Trends and Information Entropy" Entropy 20, no. 9: 669. https://doi.org/10.3390/e20090669
APA StyleGuan, H., Dai, Z., Guan, S., & Zhao, A. (2018). A Forecasting Model Based on High-Order Fluctuation Trends and Information Entropy. Entropy, 20(9), 669. https://doi.org/10.3390/e20090669