Figures (4)  Tables (5)
    • Figure 1. 

      Fluctuation characteristics of TPI over different periods.

    • Figure 2. 

      Relative importance of different influencing factors.

    • Figure 3. 

      Comparison of TPI prediction results for one week.

    • Figure 4. 

      Comparison of TPI prediction results for rainy, snowy, and hazy weather.

    • NameSymbolCount
      Month0: January; 1: February; ...; 11: December18 months
      Week0: Sunday; 1: Monday; ...; 6: Saturday72 weeks
      Time period21:0500-0515; 22:0515-0530; ...; 92:2245-230039,312 periods
      Day type0: Weekday; 1: Weekend546 d
      Public holiday1: First day of holiday12 d
      2: Middle day(s) during holiday25 d
      3: Last day of holiday12 d
      Summer or
      winter vacation
      0: Normal days426 d
      1: Summer and winter vacation120 d
      Special holiday0: Normal day421 d
      1: Special holiday5 d
      Car usage
      restriction policy
      0: The last digit of license plate number is 0 or 5.73 d
      1: The last digit of license plate number is 1 or 6.74 d
      2: The last digit of license plate number is 2 or 7.73 d
      3: The last digit of license plate number is 3 or 8.71 d
      4: The last digit of license plate number is 4 or 9.70 d
      5: No limit185 d
      Weather0: Sunny, or cloudy
      1: Rain
      490 d
      63 d
      2: Snow6 d
      3: Haze31 d
      Special events1: Short-term events252 times
      2: Large events lasting the whole day314 times

      Table 1. 

      Descriptive statistics of influencing factors.

    • XGBoost Pseudo-code:
      Input: Training set D = {(xi, yi)}, where xi represents the i-th input vector and yi is the corresponding label.
      Output: Prediction model f(x).
      // Step 1: Initialize the ensemble
      Initialize the base prediction model as a constant value: f0(x) = initialization_constant
      // Step 2: Iterate over the boosting rounds
      for m = 1 to M: // M is the number of boosting rounds
      // Step 3: Compute the pseudo-residuals
      Compute the negative gradient of the loss function with respect to the current model's predicted values:
      rmi = - ∂L(yi, fm−1(xi)) / ∂fm−1(xi)
      // Step 4: Fit a base learner to the pseudo-residuals
      Fit a base learner (e.g., decision tree) to the pseudo-residuals: hm(x).
      // Step 5: Update the prediction model
      Update the prediction model by adding the new base learner:
      fm(x) = fm−1(x) + η * hm(x), where η is the learning rate.
      // Step 6: Output the final prediction model
      Output the final prediction model: f(x) = fm(x)

      Table 2. 

      The pseudo-code of XGBoost algorithm.

    • Learning rateThe number of treesR2MAEMSE
      Maxmium depth of the tree = 3
      0.051,4000.88000.49340.4911
      0.11,3000.87790.49780.4998
      0.51600.86660.52740.5461
      11400.81170.64420.7708
      Maxmium depth of the tree = 4
      0.057000.87970.49230.4927
      0.16000.89780.46400.4430
      0.51200.88720.47630.4620
      11100.88890.47910.4550
      Maxmium depth of the tree = 5*
      0.053500.88650.47340.4646
      0.1*160*0.89500.44740.4309
      0.5500.88860.47300.4560
      1300.87560.51030.5095
      Maxmium depth of the tree = 6
      0.051950.88960.46550.4520
      0.1700.87910.49020.4950
      0.5300.89450.45720.4321
      1200.88600.48380.4666

      Table 3. 

      Performance of extreme gradient boosting (XGBoost) models for daily TPI prediction.

    • Forecast dataPrediction accuracy
      Week 1 (April 22 to April 28, 2019)94.3%
      Week 2 (April 29 to May 5 2019)85.3%
      Week 3 (May 6 to May 12, 2019)91.1%
      Week 4 (May 13 to May 19, 2019)89.1%
      Average value90.0%

      Table 4. 

      Forecast accuracy of TPI for each week.

    • TPI predictionPerformance of different models
      (Measured by MAE, MSE and R2)
      SVRElatsicNetBayesian
      Ridge
      Linear
      Regression
      XGBoost
      MAE0.6111.6681.5812.1890.396*
      MSE1.6933.1114.1213.5530.989*
      R20.7840.0340.1130.3910.786*
      MAE, Mean Absolute Error; MSE, Mean Squared Error

      Table 5. 

      Accuracy verification result of different models.