差異區(qū)域平衡法探索時間序列變化的因果關(guān)系
doi: 10.11999/JEIT200756
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福建師范大學(xué)數(shù)學(xué)與信息學(xué)院 福州 350117
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福建師范大學(xué)數(shù)字福建環(huán)境監(jiān)測物聯(lián)網(wǎng)實驗室 福州 350117
基金項目: 國家自然科學(xué)基金(61672157)，福建省自然科學(xué)基金 (2018J01778)
Different-region Balance Method for Exploring Varying Causal Relations Between Time Series
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College of Mathematics and Informatics, Fujian Normal University, Fuzhou 350117, China
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Digit Fujian Internet-of-Things Laboratory of Environmental Monitoring, Fuzhou 350117, China
Funds: The National Natural Science Foundation of China (61672157), The Natural Science Foundation of Fujian Province (2018J01778)
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摘要: 針對探索時間序列之間隨時間變化的因果關(guān)系問題，在每個窗口進(jìn)行Granger因果檢測的滑動時間窗口方法是求解該問題的常用方法，但其性能對窗寬敏感，不合適的窗寬很可能導(dǎo)致低性能。該文提出一種差異區(qū)域平衡方法，首先計算當(dāng)前滑動窗口W內(nèi)序列的波動程度Sw并作為波動界，計算窗口W的前向相鄰區(qū)域U內(nèi)序列的波動程度Su。然后，實施前向探索策略：若Su未超過Sw，則實施不同長度區(qū)域的平衡檢測方案，即對窗口W、對窗口W與U的合并區(qū)域、對窗口W與后向相鄰區(qū)域V的合并區(qū)域這3種不同長度的差異區(qū)域，分別進(jìn)行時間序列之間因果關(guān)系的檢測；若Su超過Sw，則實施上述平衡檢測方案時，其中區(qū)域U和V的長度取相同值。最后，將窗口W的多次檢測結(jié)果進(jìn)行綜合后輸出。新方法將不同長度區(qū)域的結(jié)果進(jìn)行綜合，能夠降低方法的性能對窗寬的敏感性，保障最終結(jié)果的準(zhǔn)確性和穩(wěn)定性。在1個模擬數(shù)據(jù)集和4個真實數(shù)據(jù)集上的實驗結(jié)果顯示，該文方法能有效地揭示出時間序列之間隨時間變化的因果關(guān)系，在正確率高且性能穩(wěn)定的綜合性能上優(yōu)于對比方法。
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關(guān)鍵詞:
- 時間序列 /
- 變化的因果關(guān)系 /
- Granger因果檢測 /
- 差異區(qū)域平衡
Abstract: For discovering time-varying causal relations between time series, a common method is the sliding-window method with Granger causal tests on every window. However, the method performance is sensitive to window sizes, and an unsuitable size probably leads to poor performance. The different-region balance method is proposed. The variation degree of time series in current sliding window W (called variation bound Sw) is first computed, and the degree Su in front neighbor region U of W is computed. Then a forward exploring strategy is adopted: when Su≤Sw, a different-length-region balance test measure is carried out, i.e., causal-relation tests respectively in window W, combined region W and U, and combined window W and back neighbor region V of W; when Su>Sw, it uses the above-mentioned measure where region V has the same length as region U; Finally, in each region, all the test results are synthesized to give a final result. The new method combines the results from different-length regions to reduce its sensitivity to window sizes, and guarantees the accuracy and stability of final results. The experiments on one simulated data set and four real data sets show that, the new method can discover time-varying causal relations between time series effectively, and outperforms the compared methods on the balance performance of high accuracy and stability. -
表 1 不同方法在模擬數(shù)據(jù)集上發(fā)掘因果關(guān)系的正確率(%)
窗口寬度 滑動步長 噪聲方差0.01 噪聲方差0.2 噪聲方差0.5 常規(guī) F界 轉(zhuǎn)折 平衡 常規(guī) F界 轉(zhuǎn)折 平衡 常規(guī) F界 轉(zhuǎn)折 平衡 20 5 91.32 88.18 90.99 95.40 80.82 94.56 58 84.13 80.57 91.00 50.29 82.52 10 88.98 88.18 91.91 95.06 80.25 94.56 53.39 83.33 80.15 91.00 46.33 82.54 15 86.78 88.18 90.00 94.43 78.1 94.56 44.86 83.26 78.52 91.00 46.22 82.03 20 83.65 88.18 89.17 92.77 77.05 94.56 45.4 82.15 77.98 91.00 45.48 81.87 30 5 95.85 88.18 90.61 95.87 85.69 94.56 60.4 92.31 83.63 91.00 47.37 87.78 10 94.43 88.18 90.15 95.49 84.95 94.56 53.01 91.95 83.69 91.00 46.4 87.41 15 94.07 88.18 90.85 94.91 83.22 94.56 51.62 91.65 81.93 91.00 45.98 86.84 20 92.96 88.18 90.95 95.57 81.62 94.56 53.21 91.37 81.18 91.00 46.38 86.96 40 5 95.56 88.18 91.83 94.85 92.46 94.56 63.52 94.65 87.62 91.00 46.43 92.17 10 95.31 88.18 90.07 94.87 91.05 94.56 58.89 94.27 87.08 91.00 45.38 92.22 15 94.95 88.18 90.65 94.77 90.62 94.56 58.77 94.55 86.87 91.00 46.39 91.76 20 94.59 88.18 89.9 94.31 89.5 94.56 52.31 93.93 85.86 91.00 45.80 91.03 
下載: 導(dǎo)出CSV
表 2 在數(shù)據(jù)集Dropoff-tweet上發(fā)掘因果關(guān)系的正確率(%)
窗口
寬度滑動
步長常規(guī)滑
動窗F界檢測法 轉(zhuǎn)折點法 差異平衡法 12 4 91.95 92.62 93.56 93.42 8 90.87 92.62 93.56 93.83 12 89.26 92.62 94.36 90.20 18 4 94.09 92.62 94.90 95.30 8 94.36 92.62 94.36 94.77 12 92.21 92.62 94.36 94.77 24 4 94.36 92.62 94.09 96.51 8 97.05 92.62 96.24 96.78 12 91.95 92.62 91.41 95.70
下載: 導(dǎo)出CSV
表 3 在數(shù)據(jù)集Tweet-pickup上發(fā)掘因果關(guān)系的正確率(%)
窗口
寬度滑動
步長常規(guī)滑
動窗F界檢測法 轉(zhuǎn)折點法 差異平衡法 12 4 90.87 94.90 90.87 93.29 8 91.95 94.90 94.09 94.09 12 92.48 94.90 94.09 91.01 18 4 92.48 94.90 88.19 94.90 8 92.48 94.90 93.83 94.90 12 93.02 94.90 94.09 93.02 24 4 92.75 94.90 91.41 95.44 8 93.29 94.90 82.82 95.97 12 92.21 94.90 95.44 95.44
下載: 導(dǎo)出CSV
表 4 在數(shù)據(jù)集Fish-school上發(fā)掘因果關(guān)系的正確率(%)
窗口
寬度滑動
步長常規(guī)滑動窗 F界檢測法 轉(zhuǎn)折點法 差異平衡法 140 10 89.60 54.19 69.80 90.1 20 86.24 54.19 69.80 93.29 30 91.28 54.19 69.80 95.64 150 10 89.60 54.19 69.80 84.90 20 83.22 54.19 69.80 91.28 30 89.93 54.19 69.80 99.66 160 10 83.22 54.19 69.80 86.91 20 69.80 54.19 69.80 93.62 30 81.54 54.19 69.80 92.95
下載: 導(dǎo)出CSV
表 5 在數(shù)據(jù)集Baboon-troop上發(fā)掘因果關(guān)系的正確率(%)
窗口
寬度滑動
步長常規(guī)滑動窗 F界檢測法 轉(zhuǎn)折點法 差異平衡法 110 10 80.63 35.39 59.10 80.63 20 70.62 35.39 59.10 82.30 30 70.62 35.39 59.10 80.47 120 10 80.63 35.39 59.10 81.64 20 62.27 35.39 59.10 83.31 30 63.94 35.39 59.10 83.97 130 10 80.80 35.39 59.10 82.30 20 75.79 35.39 59.10 83.97 30 82.30 35.39 59.10 82.97
下載: 導(dǎo)出CSV
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